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1
Almlöf, Jonas. "Quantum error correction." Licentiate thesis, KTH, Kvantelektronik och -optik, QEO, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-106795.
Full textAbstract:
This thesis intends to familiarise the reader with quantum error correction, and also show some relations to the well known concept of information - and the lesser known quantum information. Quantum information describes how information can be carried by quantum states, and how interaction with other systems give rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. These phenomena include decoherence, as a consequence of entanglement. Decoherence can also be understood as "information leakage", i.e., knowledge of an event is transferred to the reservoir - an effect that in general destroys superpositions of pure states. It is possible to protect quantum states (e.g., qubits) from interaction with the environment - but not by amplification or duplication, due to the "no-cloning" theorem. Instead, this is done using coding, non-demolition measurements, and recovery operations. In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment "picks up" information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code. Often, it is assumed that the environment's ability to distinguish between error events is small, and I will denote such environments "memory-less". This assumption is not always valid, since the ability to distinguish error events is related to the \emph{temperature} of the environment, and in the particular case of information coded onto photons, Denna avhandling är en introduktion till kvantfelrättning, där jag undersöker släktskapet med teorin om klassisk information - men också det mindre välkända området kvantinformation. Kvantinformation beskriver hur information kan bäras av kvanttillstånd, och hur växelverkan med andra system ger upphov till åtskilliga typer av fel och effekter, varav många saknar motsvarighet i den klassiska informationsteorin. Bland dessa effekter återfinns dekoherens - en konsekvens av s.k. sammanflätning. Dekoherens kan också förstås som "informationsläckage", det vill säga att kunskap om en händelse överförs till omgivningen - en effekt som i allmänhet förstör superpositioner i rena kvanttillstånd. Det är möjligt att med hjälp av kvantfelrättning skydda kvanttillstånd (t.ex. qubitar) från omgivningens påverkan, dock kan sådana tillstånd aldrig förstärkas eller dupliceras, p.g.a icke-kloningsteoremet. Tillstånden skyddas genom att införa redundans, varpå tillstånden interagerar med omgivningen. Felen identifieras m.h.a. icke-förstörande mätningar och återställs med unitära grindar och ancilla-tillstånd.Men i realiteten kommer inte alla tänkbara fel att inträffa, utan dessa begränsas av vilken informationsbärare som används, vilken interaktion som uppstår med omgivningen, samt hur omgivningen "fångar upp" information om felhändelserna. Med kunskap om sådan karakteristik kan man bygga koder, s.k. kanalanpassade kvantfelrättande koder. Vanligtvis antas att omgivningens förmåga att särskilja felhändelser är liten, och man kan då tala om en minneslös omgivning. Antagandet gäller inte alltid, då denna förmåga bestäms av reservoirens temperatur, och i det speciella fall då fotoner används som informationsbärare gäller typiskt
QC 20121206
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Almlöf, Jonas. "Quantum error correction." Doctoral thesis, KTH, Kvantelektronik och -optik, QEO, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-180533.
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Quantum error correction is the art of protecting quantum states from the detrimental influence from the environment. To master this art, one must understand how the system interacts with the environment and gives rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. Such phenomena include decoherence, an effect that in general destroys superpositions of pure states as a consequence of entanglement with the environment. But decoherence can also be understood as “information leakage”, i.e., when knowledge of an encoded code block is transferred to the environment. In this event, the block’s information or entanglement content is typically lost. In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment “picks up” information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code. Often, it is assumed that the environment’s ability to distinguish between error events is small, and I will denote such environments “memory-less”. But this assumption is not always valid, since the ability to distinguish error events is related to the temperature of the environment, and in the particular case of information coded onto photons, kBTR «ℏω typically holds, and one must then assume that the environment has a “memory”. In the thesis I describe a short quantum error-correction code adapted for photons interacting with a “cold” reservoir, i.e., a reservoir which continuously probes what error occurred in the coded state. I also study other types of environments, and show how to distill meaningful figures of merit from codes adapted for these channels, as it turns out that resource-based figures reflecting both information and entanglement can be calculated exactly for a well-studied class of channels: the Pauli channels. Starting from these resource-based figures, I establish the notion of efficiency and quality and show that there will be a trade-off between efficiency and quality for short codes. Finally I show how to incorporate, into these calculations, the choices one has to make when handling quantum states that have been detected as incorrect, but where no prospect of correcting them exists, i.e., so-called detection errors.QC 20160115
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Babar, Zunaira. "Quantum error correction codes." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/380165/.
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Quantum parallel processing techniques are capable of solving certain complex problems at a substantially lower complexity than their classical counterparts. From the perspective of telecommunications, this quantum-domain parallel processing provides a plausible solution for achieving full-search based multi-stream detection, which is vital for future gigabit-wireless systems. The peculiar laws of quantum mechanics have also spurred interest in the absolutely secure quantum-based communication systems. Unfortunately, quantum decoherence imposes a hitherto insurmountable impairment on the practical implementation of quantum computation as well as on quantum communication systems, which may be overcome with the aid of efficient error correction codes. In this thesis, we design error correction codes for the quantum domain, which is an intricate journey from the realm of classical channel coding theory to that of the Quantum Error Correction Codes (QECCs). Since quantum-based communication systems are capable of supporting the transmission of both classical and quantum information, we initially focus our attention on the code design for entanglementassisted classical communication over the quantum depolarizing channel. We conceive an Extrinsic Information Transfer (EXIT) chart aided near-capacity classical-quantum code design, which invokes a classical Irregular Convolutional Code (IRCC) and a Unity Rate Code (URC) in conjunction with our proposed soft-decision aided SuperDense Code (SD). Hence, it is referred to as an ‘IRCC-URCSD’ arrangement. The proposed scheme is intrinsically amalgamated both with 2-qubit as well as 3-qubit SD coding protocols and it is benchmarked against the corresponding entanglement-assisted classical capacity. Since the IRCC-URC-SD scheme is a bit-based design, it incurs a capacity loss. As a further advance, we design a symbol based concatenated code design, referred to as a symbol-based ‘CC-URC-SD’, which relies on a single-component classical Convolutional Code (CC). Additionally, for the sake of reducing the associated decoding complexity, we also investigate the impact of the constraint length of the convolutional code on the achievable performance. Our initial designs, namely IRCC-URC-SD and CC-URC-SD, exploit redundancy in the classical domain. By contrast, QECCs relying on the quantum-domain redundancy are indispensable for conceiving a quantum communication system supporting the transmission of quantum information and also for quantum computing. Therefore, we next provide insights into the transformation from the family of classical codes to the class of quantum codes known as ‘Quantum Stabilizer Codes’ (QSC), which invoke the classical syndrome decoding. Particularly, we detail the underlying quantum-to classical isomorphism, which facilitates the design of meritorious families of QECCs from the known classical codes. We further study the syndrome decoding techniques operating over classical channels, which may be exploited for decoding QSCs. In this context, we conceive a syndrome-based block decoding approach for the classical Turbo Trellis Coded Modulation (TTCM), whose performance is investigated for transmission over an Additive White Gaussian Noise (AWGN) channel as well as over an uncorrelated Rayleigh fading channel. Pursuing our objective of designing efficient QECCs, we next consider the construction of Hashingbound-approaching concatenated quantum codes. In this quest, we appropriately adapt the conventional non-binary EXIT charts for Quantum Turbo Codes (QTCs) by exploiting the intrinsic quantumto- classical isomorphism. We further demonstrate the explicit benefit of our EXIT-chart technique for achieving a Hashing-bound-approaching code design. We also propose a generically applicable structure for Quantum Irregular Convolutional Codes (QIRCCs), which can be dynamically adapted to a specific application scenario with the aid of the EXIT charts. More explicitly, we provide a detailed design example by constructing a 10-subcode QIRCC and use it as an outer code in a concatenated quantum code structure for evaluating its performance. Working further in the direction of iterative code structures, we survey Quantum Low Density Parity Check (QLPDC) codes from the perspective of code design as well as in terms of their decoding algorithms. Furthermore, we propose a radically new class of high-rate row-circulant Quasi-Cyclic QLDPC (QC-QLDPC) codes, which can be constructed from arbitrary row-circulant classical QC LDPC matrices. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane (CSS)-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-4 cycles. Our modified decoder outperforms the state-of-the-art decoders in terms of their Word Error Rate (WER) performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic Uniformly-ReWeighted Belief Propagation (URW-BP) for the sake of achieving further performance improvement.
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Valentini, Lorenzo. "Quantum Error Correction for Quantum Networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019.
Find full textAbstract:
Le quantum networks e molte altre tecnologie, quali i quantum computer, necessitano di qubit affidabili per il loro funzionamento. Per ottenere ciò, in questo elaborato, si presenta il tema della quantum error correction ponendo particolare attenzione ai codici quantum low-density parity-check (QLDPC). In aggiunta, vengono testati alcuni algoritmi su IBMQ, la serie di computer quantistici resi disponibili online da IBM, per comprenderne le problematiche. Si conclude l'elaborato con alcune riflessioni su come i codici presentati possono arginare alcune delle problematiche riscontrate durante l'implementazione su quantum computer.
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Fletcher, Andrew Stephen. "Channel-adapted quantum error correction." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40497.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 159-163).
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and performance. We examine QEC methods that are adapted to the physical noise model. In physical systems, errors are not likely to be arbitrary; rather we will have reasonable models for the structure of quantum decoherence. We may choose quantum error correcting codes and recovery operations that specifically target the most likely errors. This can increase QEC performance and also reduce the required overhead. We present a convex optimization method to determine the optimal (in terms of average entanglement fidelity) recovery operation for a given channel, encoding, and information source. This is solvable via a semidefinite program (SDP). We derive an analytic solution to the optimal recovery for the case of stabilizer codes, the completely mixed input source, and channels characterized by Pauli group errors. We present computational algorithms to generate near-optimal recovery operations structured to begin with a projective syndrome measurement.
(cont.) These structured operations are more computationally scalable than the SDP required for computing the optimal; we can thus numerically analyze longer codes. Using Lagrange duality, we bound the performance of the structured recovery operations and show that they are nearly optimal in many relevant cases. We present two classes of channel-adapted quantum error correcting codes specifically designed for the amplitude damping channel. These have significantly higher rates with shorter block lengths than corresponding generic quantum error correcting codes. Both classes are stabilizer codes, and have good fidelity performance with stabilizer recovery operations. The encoding, syndrome measurement, and syndrome recovery operations can all be implemented with Clifford group operations.
by Andrew Stephen Fletcher.
Ph.D.
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Pondini, Andrea. "Quantum error correction e toric code." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21053/.
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L'elaborato studia la Quantum Error Correction, ovvero quella branca del Quantum Computing che studia gli errori nella computazione e come correggerli. Questo campo è di fondamentale importanza nella costruzione di computer quantistici, in cui l'interazione con l'ambiente porta rumore alla computazione e perdita di coerenza degli stati del sistema. Particolare attenzione è posta nello studio degli Stabilizer Codes, una particolare categoria di Quantum Error Correcting Codes. Tra questi si studia il Toric Code, esempio peculiare di stabilizer code ordinato topologicamente. Le peculiarità del codice sono conseguenza della sua definizione su un reticolo immerso in una superficie toroidale, come suggerisce il nome.
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Gul, Yusuf. "Entanglement Transformations And Quantum Error Correction." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12610773/index.pdf.
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The main subject of this thesis is the investigation of the transformations of pure
multipartite entangled states having Schmidt rank 2 by using only local operations
assisted with classical communications (LOCC). A new parameterization is used for
describing the entangled state of p particles distributed to p distant, spatially separated
persons. Product, bipartite and truly multipartite states are identified in this new
parametrization. Moreover, alternative parameterizations of local operations carried
out by each party are provided. For the case of a deterministic transformation to
a truly multipartite final state, one can find an analytic expression that determines
whether such a transformation is possible. In this case, a chain of measurements by
each party for carrying out the transformation is found. It can also be seen that,
under deterministic LOCC transformations, there are some quantities that remain
invariant. For the purpose of applying the results of this thesis in the context of the
quantum information and computation, brief reviews of the entanglement purification,
measurement based quantum computation and quantum codes are given.
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Gonzales, Alvin Rafer. "QUANTUM ERROR CORRECTION FOR GENERAL NOISE." OpenSIUC, 2021. https://opensiuc.lib.siu.edu/dissertations/1894.
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Large quantum computers have the potential to vastly outperform any classical computer. The biggest obstacle to building quantum computers of such size is noise. For example, state of the art superconducting quantum computers have average decoherence (loss of information) times of just microseconds. Thus, the field of quantum error correction is especially crucial to progress in the development of quantum technologies. In this research, we study quantum error correction for general noise, which is given by a linear Hermitian map. In standard quantum error correction, the usual assumption is to constrain the errors to completely positive maps, which is a special case of linear Hermitian maps. We establish constraints and sufficient conditions for the possible error correcting codes that can be used for linear Hermitian maps. Afterwards, we expand these sufficient conditions to cover a large class of general errors. These conditions lead to currently known conditions in the limit that the error map becomes completely positive. The later chapters give general results for quantum evolution maps: a set of weak repeated projective measurements that never break entanglement and the asymmetric depolarizing map composed with a not completely positive map that gives a completely positive composition. Finally, we give examples.
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Raissi, Zahra. "Quantum multipartite entangled states, classical and quantum error correction." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669995.
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Studying entanglement is essential for our understanding of such diverse areas as high-energy physics, condensed matter physics, and quantum optics. Moreover, entanglement allows us to surpass classical physics and technologies enabling better information processing, computation, and improved metrology. Recently, entanglement also played a prominent role in characterizing and simulating quantum many-body states and in this way deepened our understanding of quantum matter. While bipartite entanglement is well understood, multipartite entanglement is much richer and leads to stronger contradictions with classical physics. Among all possible entangled states, a special class of states has attracted attention for a wide range of tasks. These states are called k-uniform states and are pure multipartite quantum states of n parties and local dimension q with the property that all of their reductions to k parties are maximally mixed. Operationally, in a k-uniform state any subset of at most k parties is maximally entangled with the rest. The k = bn/2c-uniform states are called absolutely maximally entangled because they are maximally entangled along any splitting of the n parties into two groups. These states find applications in several protocols and, in particular, are the building blocks of quantum error correcting codes with a holographic geometry, which has provided valuable insight into the connections between quantum information theory and conformal field theory. Their properties and the applications are however intriguing, as we know little about them: when they exist, how to construct them, how they relate to other multipartite entangled states, such as graph states, or how they connect under local operations and classical communication. With this motivation in mind, in this thesis we first study the properties of k-uniform states and then present systematic methods to construct closed-form expressions of them. The structure of our methods proves to be particularly fruitful in understanding the structure of these quantum states, their graph-state representation and classification under local operations and classical communication. We also construct several examples of absolutely maximally entangled states whose existence was open so far. Finally, we explore a new family of quantum error correcting codes that generalize and improve the link between classical error correcting codes, multipartite entangled states, and the stabilizer formalism. The results of this thesis can have a role in characterizing and studying the following three topics: multipartite entanglement, classical error correcting codes and quantum error correcting codes. The multipartite entangled states can provide a link to find different resources for quantum information processing tasks and quantify entanglement. Constructing two sets of highly entangled multipartite states, it is important to know if they are equivalent under local operations and classical communication. By understanding which states belong to the same class of quantum resource, one may discuss the role they play in some certain quantum information tasks like quantum key distribution, teleportation and constructing optimum quantum error correcting codes. They can also be used to explore the connection between the Antide Sitter/Conformal Field Theory holographic correspondence and quantum error correction, which will then allow us to construct better quantum error correcting codes. At the same time, their roles in the characterization of quantum networks will be essential to design functional networks, robust against losses and local noise.El estudio del entrelazamiento cuántico es esencial para la comprensión de diversas áreas como la óptica cuántica, la materia condensada e incluso la física de altas energías. Además, el entrelazamiento nos permite superar la física y tecnologías clásicas llevando a una mejora en el procesado de la información, la computación y la metrología. Recientemente se ha descubierto que el entrelazamiento desarrolla un papel central en la caracterización y simulación de sistemas cuánticos de muchos cuerpos, de esta manera facilitando nuestra comprensión de la materia cuántica. Mientras que se tiene un buen conocimiento del entrelazamiento en estados puros bipartitos, nuestra comprensión del caso de muchas partes es mucho más limitada, a pesar de que sea un escenario más rico y que presenta un contraste más fuerte con la física clásica. De entre todos los posibles estados entrelazados, una clase especial ha llamado la atención por su amplia gama de aplicaciones. Estos estados se llaman k-uniformes y son los estados multipartitos de n cuerpos con dimensión local q con la propiedad de que todas las reducciones a k cuerpos son máximamente desordenadas. Operacionalmente, en un estado k-uniforme cualquier subconjunto de hasta k cuerpos está máximamente entrelazado con el resto. Los estados k = n/2 -uniformes se llaman estados absolutamente máximamente entrelazados porque son máximamente entrelazados respecto a cualquier partición de los n cuerpos en dos grupos. Estos estados encuentran aplicaciones en varios protocolos y, en particular, forman los elementos de base para la construcción de los códigos de corrección de errores cuánticos con geometría holográfica, los cuales han aportado intuición importante sobre la conexión entre la teoría de la información cuántica y la teoría conforme de campos. Las propiedades y aplicaciones de estos estados son intrigantes porque conocemos poco sobre las mismas: cuándo existen, cómo construirlos, cómo se relacionan con otros estados con entrelazamiento multipartito, cómo los estados grafo, o como se relacionan mediante operaciones locales y comunicación clásica. Con esta motivación en mente, en esta tesis primero estudiamos las propiedades de los estados k-uniformes y luego presentamos métodos sistemáticos para construir expresiones cerradas de los mismos. La naturaleza de nuestros métodos resulta ser muy útil para entender la estructura de estos estados cuánticos, su representación como estados grafo y su clasificación bajo operaciones locales y comunicación clásica. También construimos varios ejemplos de estados absolutamente máximamente entrelazados, cuya existencia era desconocida. Finalmente, exploramos una nueva familia de códigos de corrección de errores cuánticos que generalizan y mejoran la conexión entre los códigos de corrección de errores clásicos, los estados entrelazados multipartitos y el formalismo de estabilizadores. Los resultados de esta tesis pueden desarrollar un papel importante en la caracterización y el estudio de las tres siguientes áreas: entrelazamiento multipartito, códigos de corrección de errores clásicos y códigos de corrección de errores cuánticos. Los estados de entrelazamiento multipartito pueden aportar una conexión para encontrar diferentes recursos para tareas de procesamiento de la información cuántica y cuantificación del entrelazamiento. Al construir dos conjuntos de estados multipartitos altamente entrelazados, es importante saber si son equivalentes entre operaciones locales y comunicación clásica. Entendiendo qué estados pertenecen a la misma clase de recurso cuántico, se puede discutir qué papel desempeñan en ciertas tareas de información cuántica, como la distribución de claves criptográficas cuánticas, la teleportación y la construcción de códigos de corrección de errores cuánticos óptimos. También se pueden usar para explorar la conexión entre la correspondencia holográfica Anti-de Sitter/Conformal Field Theory y códigos de corrección de errores cuánticos, que nos permitiría construir mejores códigos de corrección de errores. A la vez, su papel en la caracterización de redes cuánticas será esencial en el diseño de redes funcionales, robustas ante pérdidas y ruidos locales.
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Pegahan, Saeed. "QUANTUM ERROR CORRECTION AND LEAKAGE ELIMINATION FOR QUANTUM DOTS." OpenSIUC, 2015. https://opensiuc.lib.siu.edu/theses/1753.
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The development of a quantum computer presents one of the greatest challenges in science and engineering to date. The promise of more ecient computing based on entangled quantum states and the superposition principle has led to a worldwide explosion of interest in the elds of quantum information and computation. Decoherence is one of the main problems that gives rise to dierent errors in the quantum system. However, the discovery of quantum error correction and the establishment of the accuracy threshold theorem provide us comprehensive tools to build a quantum computer. This thesis contributes to this eort by investigating a particular class of quantum error correcting codes, called Decoherence free subsystems. The passive approach to error correction taken by these encodings provides an ecient means of protection for symmetrically coupled system-bath interactions. Here I will present methods for determining the subsystem-preserving evolutions for noiseless subsystem encodings and more importantly implementing a Universal quantum computing over three-quantum dots.
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Gaspari, Andrea. "Quantum error correction and the toric code." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21591/.
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Quantum error correction is the main subject of this thesis. After a general introduction of the fundamentals of quantum mechanics and quantum computing, the problem is presented and further analysed using two different approaches, one, more practical, based on quantum circuits and one, purely theoretical, based on the stabilizer formalism. Examples of the principal quantum codes are progressively supplied to help the comprehension. To conclude the attention is drawn to the Toric code which represents one of the most promising platforms to store quantum information.
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Sheldon, Sarah (Sarah Elizabeth). "Second order error correction in quantum computing." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44834.
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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2008.Includes bibliographical references (leaf 23).
Error correction codes are necessary for the development of reliable quantum computers. Such codes can prevent the lost of information from decoherence caused by external perturbations. This thesis evaluates a five qubit code for correcting second order bit-flip errors. The code consists of encoding, decoherence, decoding, and error correction steps. This work analyzes the proposed code using geometric algebra methods and examines the state of the system after each step in the process.
by Sarah Sheldon.
S.B.
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Layden, David. "Device- and application-adapted quantum error correction." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/127314.
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Thesis: Ph. D. in Quantum Science and Engineering, Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, May, 2020Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 185-194).
Precise control of coherent quantum systems could enable new generations of sensing, communication and computing technologies. Such systems, however, are typically noisy and difficult to stabilize. One promising technique to this end is called quantum error correction, which encodes quantum states in such a way that errors can be detected and corrected, much like in classical error-correcting codes. Quantum error-correcting codes usually cast a wide net, in that they are designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. It comes at a cost, however: conventional quantum codes are typically resource-intensive in terms of both the system size and the control operations they require. Yet, in smaller-scale devices the main error sources are often well-understood. In the near term, it may therefore be advantageous to cast a more targeted net through specialized codes. This thesis presents new families of such quantum error-correcting codes, which are adapted either for leading candidate devices, or for near-term applications. The device-adapted codes require exponentially less overhead than conventional codes to achieve the same level of protection, whereas the application-adapted codes can enhance quantum sensors, in which conventional codes cannot readily be used. The new techniques presented in this thesis adapt cornerstones of conventional theory in light of key experimental challenges and opportunities. The ultimate goal of this research is to help bridge the gap between the exacting requirements of proposed quantum technologies and the realities of emerging quantum devices. Bridging this gap is critical, if quantum technologies are to realize their full potential.
by David Layden.
Ph. D. in Quantum Science and Engineering
Ph.D.inQuantumScienceandEngineering Massachusetts Institute of Technology, Department of Nuclear Science and Engineering
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Cohen, Joachim. "Autonomous quantum error correction with superconducting qubits." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE008/document.
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Dans cette thèse, nous développons plusieurs outils pour la Correction d’Erreur Quantique (CEQ) autonome avec les qubits supraconducteurs.Nous proposons un schéma de CEQ autonome qui repose sur la technique du « reservoir engineering », dans lequel trois qubits de type transmon sont couplés à un ou plusieurs modes dissipatifs. Grâce à la mise au point d’une interaction effective entre les systèmes, l’entropie créée par les éventuelles erreurs est évacuée à travers les modes dissipatifs.La deuxième partie de ce travail porte sur un type de code récemment développé, le code des chats, à travers lequel l’information logique est encodée dans le vaste espace de Hilbert d’un oscillateur harmonique. Nous proposons un protocole pour réaliser des mesures continues et non-perturbatrices de la parité du nombre de photons dans une cavité micro-onde, ce qui correspond au syndrome d’erreur pour le code des chats. Enfin, en utilisant les résultats précédents, nous présentons plusieurs protocoles de CEQ continus et/ou autonomes basés sur le code des chats. Ces protocoles offrent une protection robuste contre les canaux d’erreur dominants en présence de dissipation stimulée à plusieurs photonsIn this thesis, we develop several tools in the direction of autonomous Quantum Error Correction (QEC) with superconducting qubits. We design an autonomous QEC scheme based on quantum reservoir engineering, in which transmon qubits are coupled to lossy modes. Through an engineered interaction between these systems, the entropy created by eventual errors is evacuated via the dissipative modes.The second part of this work focus on the recently developed cat codes, through which the logical information is encoded in the large Hilbert space of a harmonic oscillator. We propose a scheme to perform continuous and quantum non-demolition measurements of photon-number parity in a microwave cavity, which corresponds to the error syndrome in the cat code. In our design, we exploit the strongly nonlinear Hamiltonian of a highimpedance Josephson circuit, coupling ahigh-Q cavity storage cavity mode to a low-Q readout one. Last, as a follow up of the above results, we present several continuous and/or autonomous QEC schemes using the cat code. These schemes provide a robust protection against dominant error channels in the presence of multi-photon driven dissipation
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Denys, Aurélie. "Quantum key distribution and quantum error correction with bosonic systems." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS152.
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Cette thèse porte sur l'étude théorique de la distribution quantique de clef et de la correction d'erreurs quantiques, mises en œuvre avec des systèmes bosoniques. Dans le premier chapitre, une borne analytique sur le taux secret asymptotique de clé des protocoles de distribution de clef quantique à variables continues est dérivée. Ce nombre permet de quantifier la sécurité d'un protocole et donc de comparer la sécurité de différentes instances d'un protocole pour faire un choix éclairé. Le chapitre 2 de la thèse présente et étudie un nouveau code bosonique, le qutrit 2T. Ce codage a la particularité d'utiliser deux modes bosoniques, ce qui signifie que l'espace dans lequel l'information est encodée est encore plus grand que lorsqu'un seul mode est utilisé. Ces travaux ont ensuite inspiré la construction d'importantes familles de codes multimodes, dont certains des codes introduits au chapitre 3. Ce dernier présente une construction générale de codes correcteurs d'erreurs qui sont tels que l'information encodée peut ensuite être facilement manipulée pour effectuer les calculs logiques souhaitésThis thesis concerns the theoretical study of quantum key distribution and quantum error correction implemented with bosonic systems. The former is referred to as continuous-variable quantum key distribution while the latter is called bosonic error correction. In the first chapter, an analytical bound on the asymptotic secret key rate of continuous-variable quantum key distribution protocols is derived. This quantity broadly quantifies the security of a protocol. This is a significant contribution as it helps to compare the security of different instances of a protocol and to make an informed choice. In Chapter 2, a new bosonic code, the 2T-qutrit, is introduced and studied. This encoding has the particularity of using two bosonic modes, which means the space in which the information is encoded is even bigger than when only a single mode is used. This work then inspired the construction of important families of multi-mode codes, including some of the codes introduced in Chapter 3. The latter presents a general construction of error correcting codes such that the encoded information can easily be manipulated to carry out the desired logical computations
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Tomita, Yu. "Numerical and analytical studies of quantum error correction." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53468.
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A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computation.
In this dissertation, we present our investigation into new methods to reduce errors in quantum computers from three different directions: quantum memory, quantum control, and quantum error correcting codes. For quantum memory, we pursue the potential of the quantum equivalent of a magnetic hard drive using two-body-interaction structures in fractal dimensions. With regard to quantum control, we show that it is possible to arbitrarily reduce error when manipulating multiple quantum bits using a technique popular in nuclear magnetic resonance. Finally, we introduce an efficient tool to study quantum error correcting codes and present analysis of the codes' performance on model quantum architectures.
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Urbani, Camilla. "Stabilizer Codes for Quantum Error Correction and Synchronization." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.
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This thesis project aims to deepen the basic concepts of quantum mechanics with particular reference to quantum information theory and quantum error correction codes, fundamental for a correct reception of information.
The relations between these codes and classical ones have been investigated, based upon their representation in terms of stabilizers and then developing a possible error detection code.
It has also been examined a classical problem in communication systems, namely frame synchronization, discussing it in quantum communication systems.
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Watson, Fern. "Performance of topological codes for quantum error correction." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/28907.
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In this thesis we present three main contributions to the field of topological quantum error correcting codes. We focus on some of the properties of such codes required for fault-tolerant quantum computation. Prior work has concentrated on determining error rate thresholds of particular models, but increasingly other parameters are gaining prominence. One of these is the overhead -- the quantity of a named resource required to achieve a desired level of performance from the code. We characterise the qubit overhead of the toric code in a fault-tolerant setting. These results provide a general framework for determining the overhead for other code constructions with more complicated noise models. Next we introduce a decoding algorithm, applicable to topological codes in a qudit architecture, specifically those where fault-tolerance is achieved through repeated syndrome measurements. It is computationally light and capable of decoding qudits of arbitrarily high dimension with negligible increase in its run time. The threshold of the decoder is limited by the percolation of the syndromes. Using local matching techniques we are able to overcome this limitation, increasing the threshold by almost a factor of two for high qudit dimensions. Finally, we turn our attention to a second family of topological quantum codes: the colour codes. In three and higher spatial dimensions such codes can support transversal non-Clifford gates. We show, using a technique that we call a star-bipartition of the vertices of the lattice, that any existing qubit colour code lattice can be used to define a qudit colour code. By generalising the notion of triorthogonal matrices we derive analogous transversality properties in the qudit codes.
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Gourlay, Iain. "Quantum computation." Thesis, Heriot-Watt University, 2000. http://hdl.handle.net/10399/568.
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Lu, Feng. "Studies of a quantum scheduling algorithm and on quantum error correction." Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3540.
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Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an R||C_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, time-correlated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code, perfect or non-perfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes.Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Science PhD
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Pari, Andrea. "Quantum error correction e decoder per il toric code." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24282/.
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L’argomento principale della tesi è la quantum error correction, in particolare
viene esaminato il codice di correzione del toric code e del planar code. Viene inoltre implementato un decoder impiegando l’algoritmo di Edmond che trova il minimum weight perfect matching in un grafo.
Dopo un’introduzione sulla meccanica quantistica dei sistemi a due stati e
sulla computazione quantistica, viene esaminato l’argomento della quantum
error correction nel formalismo degli stabilizer. In seguito viene descritto
il codice di correzione del toric code e del planar code e viene illustrata
un’implementazione in python di un decoder per il planar code.
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Nawaf, Sameer Obaid. "EFFECT OF ANCILLA LOSSES ON FAULT-TOLERANT QUANTUM ERROR CORRECTION IN THE [[7,1,3]] STEANE CODE." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/theses/1333.
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Fault tolerant quantum error correction is a procedure which satisfies the feature that if one of the gates in the procedure has failed then the failure causes at most one error in the output qubits of the encoded block. Quantum computer is based on the idea of two quantum state systems (Qubits). However, the majority of systems are constructed from higher than two- level subspace. Bad control and environmental interactions in these systems lead to leakage fault. Leakage errors are errors that couple the states inside a code subspace to the states outside a code subspace. One example for leakage fault is loss errors. Since the fault tolerant procedure may be unable to recognize the leakage fault because it was designed to deal with Pauli errors. In that case a single leakage fault might disrupt the fault tolerant technique. In this thesis we investigate the effect of ancilla losses on fault-tolerant quantum error correction in the [[7,1,3]] Steane code. We proved that both Shor and Steane methods are still fault tolerant if loss errors occur.
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Robertson, Alan Martin. "Error Aware Clifford Circuit Compilation." Thesis, The University of Sydney, 2019. https://hdl.handle.net/2123/21642.
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We demonstrate that small quantum memories, realised via quantum error correction in multi-qubit devices and implemented using noisy Clifford circuits, can benefit significantly from tailoring the choice of code to the error model of the Cliffords gates and environment. We present a simulation of these errors and the results of searching across random quantum error correcting codes and implementing the associated Clifford encoding circuits. This modeling incorporates a better representation of the experimental complexity involved in implementing these codes and demonstrates that tailored codes can outperform the Steane code with more realistic experimental noise. Depending on the error model, they are required to surpass the fault tolerant threshold. These Pauli error models correspond to individual Clifford generators and environmental noise on the wires. We present error models which incorporate independent identically distributed (IID) errors and biased Pauli errors in the construction and optimisation of Clifford circuits associated with maintaining a quantum memory.
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Hill, Charles. "Algorithms, gates and error correction for the Kane quantum computer /." [St. Lucia, Qld.], 2006. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19975.pdf.
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Sjöborg, Martin, and Hanna Linn. "Simulating a Quantum Computer : Grover's Search Algorithm with Error Correction." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-231739.
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Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.Klassiska simuleringar av kvantdatorer ger oss en inblick i vad kvantalgoritmer kan åstadkomma, hur vi kan verifiera att algoritmerna fungerar, vilka problem vi måste lösa innan kvantdator- erna blir en verklighet, samt hur vi kanske kan hantera problemen. Vi bygger ett bibliotek i Python för att simulera en kvantdator som kan utföra alla kvantalgoritmer genom att definiera en grinduniversalmängd, ur vilken alla kvantgrindar – och därmed alla kretsar – kan konstrueras. Vi implementar två algoritmer som båda belyser två viktiga aspekter hos kvantberäkning: Grover’s kvantsökning, som demonstrerar effektiviteten hos kvantalgoritmer över deras klassiska analoger, samt en felhanteringsalgoritm, Shorkoden, som kan jämka Paulifel och är betydelsefull för att förstå vikten hos felkorrigering.Vi prövar motståndskraften hos Grovers algoritm genom att utsätta den för slumpmässiga ro- tationer hos en qubit, och finner att algoritmen är resistent mot mindre Paulifel, men snabbt slutar producera meningsfulla resultat vid större Paulifel.
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Rodriguez, Fernandez Carlos Gustavo. "Machine learning quantum error correction codes : learning the toric code /." São Paulo, 2018. http://hdl.handle.net/11449/180319.
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Orientador: Mario Leandro AolitaBanca:Alexandre Reily Rocha
Banca: Juan Felipe Carrasquilla
Resumo: Usamos métodos de aprendizagem supervisionada para estudar a decodificação de erros em códigos tóricos de diferentes tamanhos. Estudamos múltiplos modelos de erro, e obtemos figuras da eficácia de decodificação como uma função da taxa de erro de um único qubit. Também comentamos como o tamanho das redes neurais decodificadoras e seu tempo de treinamento aumentam com o tamanho do código tórico.
Abstract: We use supervised learning methods to study the error decoding in toric codes ofdifferent sizes. We study multiple error models, and obtain figures of the decoding efficacyas a function of the single qubit error rate. We also comment on how the size of thedecoding neural networks and their training time scales with the size of the toric code
Mestre
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Schwarz, Lucia. "Error Models for Quantum State and Parameter Estimation." Thesis, University of Oregon, 2014. http://hdl.handle.net/1794/18526.
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Within the field of Quantum Information Processing, we study two subjects: For quantum state tomography, one common assumption is that the experimentalist possesses a stationary source of identical states. We challenge this assumption and propose a method to detect and characterize the drift of nonstationary quantum sources. We distinguish diffusive and systematic drifts and examine how quickly one can determine that a source is drifting. Finally, we give an implementation of this proposed measurement for single photons.
For quantum computing, fault-tolerant protocols assume that errors are of certain types. But how do we detect errors of the wrong type? The problem is that for large quantum states, a full state description is impossible to analyze, and so one cannot detect all types of errors. We show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike Information Criterion. Our example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size.
This dissertation includes previously published co-authored material.
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Webster, Paul Thomas. "Fault-Tolerant Logical Operators in Quantum Error-Correcting Codes." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25112.
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Performing quantum computing that is robust against noise will require that all operations are fault-tolerant, meaning that they succeed with high probability even if a limited number of errors occur. We address the problem of fault-tolerantly implementing logical operators on quantum error-correcting codes – operators that apply logic gates to information protected by such codes. Specifically, we investigate what classes of logical operators are possible by particular approaches in important types of codes, especially topological stabiliser codes. We also analyse what fundamental limitations constrain the goal of realising fault-tolerant quantum computing by such implementations and how these limitations can be overcome.
We begin by presenting necessary background theory on quantum computing, quantum error-correcting codes and fault tolerance. We then specifically consider the approach to fault tolerance of locality-preserving logical operators in topological stabiliser codes. We present a method for determining the set of such operators admitted by a wide range of such codes and apply this method to important examples such as surface codes and colour codes. Next, we consider the alternative approach of implementing logical operators in topological stabiliser codes with defects, especially by the technique of braiding. We show that such approaches are fundamentally limited, but that effective schemes can nonetheless be constructed, both within these limitations and by circumventing them. We then consider fault tolerance in a more general context. We prove a highly general no-go theorem in this context, applicable to a wide range of stabiliser codes. We also show that this proof illuminates how it can be circumvented and provides perspective on a range of fault-tolerant schemes. Finally, we conclude by reviewing how these results collectively address our research questions and suggesting future work.
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Shaw, Mackenzie Hooper. "Quantum Computation with Gottesman-Kitaev-Preskill Codes: Logical Gates, Measurements, and Analysis Techniques." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/29663.
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The Gottesman-Kitaev-Preskill (GKP) error-correcting code uses one or more bosonic modes to encode a finite-dimensional logical space, allowing a low-error logical qubit to be encoded in a small number of resonators. In this thesis, I propose new methods to implement logical gates and measurements with GKP codes and analyse their performance. The logical gate scheme uses the single-qubit Clifford frame to greatly reduce the number of gates needed to implement an algorithm without increasing the hardware requirements. The logical measurement scheme uses one ancilla mode to achieve a 0.1% logical error rate over a measurement time of 630 ns when the measurement efficiency is as low as 75%. Finally, I provide a subsystem decomposition which can be used to analyse GKP codes efficiently even as the Fock space distribution of the codestates goes to infinity.
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Chinthamani, Neelima. "Quantum convolutional stabilizer codes." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/466.
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Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.
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Niset, Julien. "Quantum information with optical continuous variables: nonlocality, entanglement, and error correction." Doctoral thesis, Universite Libre de Bruxelles, 2008. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210459.
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L'objectif de ce travail de recherche est l'étude des posibilités offertes par une nouvelle approche de l'information quantique basée sur des variables quantiques continues. Lorsque ces variables continues sont portées par le champs éléctromagnétique, un grand nombre de protocoles d'information quantique peuvent être implémentés à l'aide de lasers et d'éléments d'optique linéaire standards. Cette simplicité expérimentale rend cette approche très intéressantes d'un point de vue pratique, en particulier pour le développement des futurs réseaux de communications quantiques.Le travail peut se diviser en deux parties complémentaires. Dans la première partie, plus fondamentale, la relation complexe qui existe entre l'intrication et la nonlocalité de la mécanique quantique est étudiée sur base des variables optiques continues. Ces deux ressources étant essentielles pour l'information quantique, il est nécessaire de bien les comprendre et de bien les caractériser. Dans la seconde partie, orientée vers des applications concrètes, le problème de la correction d'erreur à variables continues est étudié. Pouvoir transmettre et manipuler l'information sans erreurs est nécessaire au bon développemnent de l'information quantique, mais, en pratique, les erreurs sont inévitables. Les codes correcteurs d'erreurs permettent de détecter et corriger ces erreures de manière efficace.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Lescanne, Raphaël. "Engineering multi-photon dissipation in superconducting circuits for quantum error correction." Thesis, Université Paris sciences et lettres, 2020. http://www.theses.fr/2020UPSLE005.
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Les états quantiques peuvent occuper des états particuliers tels que les états de superposition ou intriqués. Ces états sont fragiles et finissent toujours par être détruits par d’inévitables interactions avec l’environnement. La protection d’états quantiques contre la décohérence est un problème fondamental en physique, mais aussi un point crucial pour l’avenir de l’informatique quantique. Dans cette thèse, nous discutons d’expériences conduites sur des circuits supraconducteurs qui cherchent à mettre en évidence un nouveau qubit : le qubit de chat de Schrödinger. Ce qubit appartient à la classe des codes bosoniques qui encodent l’information quantique dans l’espace de Hilbert de dimension infinie d’un résonateur microonde. En modelant avec soin la dissipation de ce résonateur, nous parvenons à stabiliser les états de base du qubit de chat sans affecter leurs superpositions. En terme d’erreurs, cela se traduit en un taux de bit-flip réduit sans augmenter le taux de phase-flip initial. Cette approche vient défier l’intuition selon laquelle un qubit doit être isolé de son environnement. Au lieu de cela, cette dissipation bien choisie agit comme une boucle de rétroaction qui corrige les erreurs de manière continue et autonome. Cette dissipation décisive est connue sous le nom de dissipation à deux photons et est générée grâce à la méthode du pompage paramétrique. Dans notre cas, il est utilisé pour intensifier sélectivement une interaction d’échange de photons deux-pour-un entre le résonateur du qubit de chat et un autre résonateur dissipatif. Pour démontrer la correction d’erreur avec les qubits de chats, des efforts expérimentaux ont été fournis pendant cette thèse pour franchir le seuil au delà duquel la correction est plus rapide que l’apparition de nouvelles erreurs, notamment celles induites par le mécanisme de correction lui-même. Ceci nous a conduit à questionner les limites actuelles du pompage paramétrique afin de mieux concevoir nos circuits supraconducteurs. Maitriser ces dissipations exotiques nous a aussi amené à d’autres applications telles que la détection de photon microondes itinérants pour laquelle une preuve de principe expérimentale a été réalisée au cours de cette thèseQuantum systems can occupy peculiar states, such as superposition or entangled states. These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the environment. Protecting quantum states against decoherence is a fundamental problem in physics and is pivotal for the future of quantum computing. In this thesis, we discuss experiments on superconducting circuits that investigate a new kind of qubit: the Schrödinger cat qubit. It belongs to the class of bosonic codes that store quantum information in the infinite dimensional Hilbert space of a microwave resonator. By carefully tailoring the dissipation of the resonator, we are able to stabilize the two basis states of the cat-qubit without affecting their superposition. In terms of errors, this translates into a reduced bit-flip rate while keeping a native phase-flip rate. This approach challenges the intuition that a qubit must be isolated from its environment. Instead, the dissipation acts as a feedback loop which continuously and autonomously corrects against errors. This enabling dissipation is known as two-photon dissipation and was engineered by the general method of parametric pumping. In our case, it is used to selectively intensify a two-to-one photon exchange interaction between the cat-qubit resonator and a dissipative resonator. To demonstrate error correction with cat-qubits, experimental efforts have been made during this thesis to cross the demanding threshold where the correction is faster than the occurrence of all errors, including those induced by the correcting mechanism itself. This has led us to question the current limitations of parametric pumping to better design our superconducting circuits. Mastering the dissipation engineering toolbox also brought us to other applications such as itinerant microwave photon detection for which an experimental proof of principle was realised during this thesis
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Tuckett, David Kingsley. "Tailoring surface codes: Improvements in quantum error correction with biased noise." Thesis, The University of Sydney, 2020. https://hdl.handle.net/2123/22132.
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For quantum computers to reach their full potential will require error correction. We study the surface code, one of the most promising quantum error correcting codes, in the context of predominantly dephasing (Z-biased) noise, as found in many quantum architectures. We find that the surface code is highly resilient to Y-biased noise, and tailor it to Z-biased noise, whilst retaining its practical features. We demonstrate ultrahigh thresholds for the tailored surface code: ~39% with a realistic bias of = 100, and ~50% with pure Z noise, far exceeding known thresholds for the standard surface code: ~11% with pure Z noise, and ~19% with depolarizing noise. Furthermore, we provide strong evidence that the threshold of the tailored surface code tracks the hashing bound for all biases. We reveal the hidden structure of the tailored surface code with pure Z noise that is responsible for these ultrahigh thresholds. As a consequence, we prove that its threshold with pure Z noise is 50%, and we show that its distance to Z errors, and the number of failure modes, can be tuned by modifying its boundary. For codes with appropriately modified boundaries, the distance to Z errors is O(n) compared to O(n1/2) for square codes, where n is the number of physical qubits. We demonstrate that these characteristics yield a significant improvement in logical error rate with pure Z and Z-biased noise. Finally, we introduce an efficient approach to decoding that exploits code symmetries with respect to a given noise model, and extends readily to the fault-tolerant context, where measurements are unreliable. We use this approach to define a decoder for the tailored surface code with Z-biased noise. Although the decoder is suboptimal, we observe exceptionally high fault-tolerant thresholds of ~5% with bias = 100 and exceeding 6% with pure Z noise. Our results open up many avenues of research and, recent developments in bias-preserving gates, highlight their direct relevance to experiment.
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Abu-Nada, Ali. "THE EFFECT OF THE ANCILLA VERIFICATION ON THE QUANTUM ERROR CORRECTION." OpenSIUC, 2015. https://opensiuc.lib.siu.edu/dissertations/1037.
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Communication is the prototypical application of error-correction methods. To communicate, a sender needs to convey information to a receiver over a noisy "communication channel." Such a channel can be thought of as a means of transmitting an information-carrying physical system from one place to another. During transmission, the physical system is subject to disturbances (noise) that can adversely affect the information carried. To use a communication channel, the sender needs to encode the information to be transmitted in the physical system. After transmission, the receiver decodes the information. Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal with both noise on stored quantum information, and also with faulty quantum gates, faulty quantum preparation,and faulty measurements. In this dissertation, we look at how additional information about the structure of the quantum circuit and noise can improve or alter the performance of techniques in quantum error correction. Chapter 1 and 2, are an introduction to the quantum computation, quantum error correction codes and fault-tolerant quantum computing. These chapters are written to be a useful for students at the graduate and advanced undergraduate level. Also. The first two chapters of this dissertation will be useful to researchers in other fields who would like to understand how quantum error correction and fault-tolerant quantum computing are possible. In chapter 3, we present numerical simulation results comparing the logical error rates for the fault-tolerant [[7, 1, 3]] 's 7 code using the technique of ancilla verification vs. the newer method of ancilla decoding as described in [1]. In chapter 4, we determine how often one should apply error correction. Therefore, we provide a relationship between the logical error rate and the physical error rate for a sequence of logical gates, sometimes followed by noisy quantum error correction
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Gutierrez, Arguedas Mauricio. "Accurate modeling of noise in quantum error correcting circuits." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54443.
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A universal, scalable quantum computer will require the use of quantum error correction in order to achieve fault tolerance. The assessment and comparison of error-correcting strategies is performed by classical simulation. However, due to the prohibitive exponential scaling of general quantum circuits, simulations are restrained to specific subsets of quantum operations. This creates a gap between accuracy and efficiency which is particularly problematic when modeling noise, because most realistic noise models are not efficiently simulable on a classical computer. We have introduced extensions to the Pauli channel, the traditional error channel employed to model noise in simulations of quantum circuits. These expanded error channels are still computationally tractable to simulate, but result in more accurate approximations to realistic error channels at the single qubit level. Using the Steane [[7,1,3]] code, we have also investigated the behavior of these expanded channels at the logical error-corrected level. We have found that it depends strongly on whether the error is incoherent or coherent. In general, the Pauli channel will be an excellent approximation to incoherent channels, but an unsatisfactory one for coherent channels, especially because it severely underestimates the magnitude of the error. Finally, we also studied the honesty and accuracy of the expanded channels at the logical level. Our results suggest that these measures can be employed to generate lower and upper bounds to a quantum code's threshold under the influence of a specific error channel.
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Corazza, Federico Augusto. "Analysis of graph-based quantum error-correcting codes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23801/.
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With the advent of quantum computers, there has been a growing interest in the practicality of this device. Due to the delicate conditions that surround physical qubits, one could wonder whether any useful computation could be implemented on such devices. As we describe in this work, it is possible to exploit concepts from classical information theory and employ quantum error-correcting techniques. Thanks to the Threshold Theorem, if the error probability of physical qubits is below a given threshold, then the logical error probability corresponding to the encoded data qubit can be arbitrarily low. To this end, we describe decoherence which is the phenomenon that quantum bits are subject to and is the main source of errors in quantum memories. From the cause of error of a single qubit, we then introduce the error models that can be used to analyze quantum error-correcting codes as a whole. The main type of code that we studied comes from the family of topological codes and is called surface code. Of these codes, we consider both the toric and planar structures. We then introduce a variation of the standard planar surface code which better captures the symmetries of the code architecture. Once the main properties of surface codes have been discussed, we give an overview of the working principles of the algorithm used to decode this type of topological code: the minimum weight perfect matching. Finally, we show the performance of the surface codes that we introduced, comparing them based on their architecture and properties. These simulations have been performed with different error channel models to give a more thorough description of their performance in several situations showing relevant results.
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Aung, Joe 1978. "Quantum error modelling and correction in long distance teleportation using singlet states." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/87202.
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Roberts, Sam. "Symmetry-Protected Topological Phases for Robust Quantum Computation." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/21192.
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In recent years, topological phases of matter have presented exciting new avenues to achieve scalable quantum computation. In this thesis, we investigate a class of quantum many-body spin models known as symmetry-protected topological (SPT) phases for use in quantum information processing and storage. We explore the fault-tolerant properties of SPT phases, and how they can be utilized in the design of a quantum computer. Of central importance in this thesis is the concept of quantum error-correction, which in addition to its importance in fault-tolerant quantum computation, is used to characterise the stability of topological phases at finite temperature. We begin with an introduction to quantum computation, quantum error correction, and topological phases of matter. We then focus on the fundamental question of whether symmetry-protected topological phases of matter can exist in thermal equilibrium; we prove that systems protected by global onsite symmetries cannot be ordered at nonzero temperature. Subsequently, we show that certain three-dimensional models with generalised higher-form symmetries can be thermally SPT ordered, and we relate this order to the ability to perform fault-tolerant measurement-based quantum computation. Following this, we assess feasibility of these phases as quantum memories, motivated by the fact that SPT phases in three dimensions can possess protected topological degrees of freedom on their boundary. We find that certain SPT ordered systems can be self-correcting, allowing quantum information to be stored for arbitrarily long times without requiring active error correction. Finally, we develop a framework to construct new schemes of fault-tolerant measurement-based quantum computation. As a notable example, we develop a cluster-state scheme that simulates the braiding and fusion of surface-code defects, offering novel alternative methods to achieve fault-tolerant universal quantum computation.
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Ahn, Charlene Sonja Preskill John P. "Extending quantum error correction : new continuous measurement protocols and improved fault-tolerant overhead /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-05192004-164713.
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O'Gorman, Joe. "Architectures for fault-tolerant quantum computation." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:4219548d-798b-45f8-b376-91025bbe3ec4.
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Quantum computing has enormous potential, but this can only be realised if quantum errors can be controlled sufficiently to allow quantum algorithms to be completed reliably. However, quantum-error-corrected logical quantum bits (qubits) which can be said to have achieved meaningful error suppression have not yet been demonstrated. This thesis reports research on several topics related to the challenge of designing fault-tolerant quantum computers. The first topic is a proposal for achieving large-scale error correction with the surface code in a silicon donor based quantum computing architecture. This proposal relaxes some of the stringent requirements in donor placement precision set by previous ideas from the single atom level to the order of 10 nm in some regimes. This is shown by means of numerical simulation of the surface code threshold. The second topic then follows, it is the development of a method for benchmarking and assessing the performance of small error correcting codes in few-qubit systems, introducing a metric called 'integrity' - closely linked to the trace distance -- and a proposal for experiments to demonstrate various stepping stones on the way to 'strictly superior' quantum error correction. Most quantum error correcting codes, including the surface code, do not allow for fault-tolerant universal computation without the addition of extra gadgets. One method of achieving universality is through a process of distilling and then consuming high quality 'magic states'. This process adds additional overhead to quantum computation over and above that incurred by the use of the base level quantum error correction. The latter parts of this thesis report an investigation into how many physical qubits are needed in a `magic state factory' within a surface code quantum computer and introduce a number of techniques to reduce the overhead of leading magic state techniques. It is found that universal quantum computing is achievable with ∼ 16 million qubits if error rates across a device are kept below 10-4. In addition, the thesis introduces improved methods of achieving magic state distillation for unconventional magic states that allow for logical small angle rotations, and show that this can be more efficient than synthesising these operations from the gates provided by traditional magic states.
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Mariense, Wickert Ricardo [Verfasser], and Peter van [Akademischer Betreuer] Loock. "Optical Implementations of Quantum Error Correction Codes / Ricardo Mariense Wickert. Gutachter: Peter van Loock." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2015. http://d-nb.info/1080610987/34.
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Bishop, Clifford Allen. "UNIVERSAL CONTROL OF NOISELESS SUBSYSTEMS FROM SYSTEMS WITH ARBITRARY DIMENSION." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/451.
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The development of a quantum computer presents one of the greatest challenges in science and engineering to date. The promise of more efficient computing based on entangled quantum states and the superposition principle has led to a worldwide explosion of interest in the fields of quantum information and computation. Among the number of hurdles which must first be cleared before we witness a physical realization are problems associated with environment-induced decoherence and noise more generally. However, the discovery of quantum error correction and the establishment of the accuracy threshold theorem provide us with the hope of someday harnessing the potential power a functioning fault-tolerant quantum information processor has to offer. This dissertation contributes to this effort by investigating a particular class of quantum error correcting codes, namely noiseless subsystem encodings. The passive approach to error correction taken by these encodings provides an efficient means of protection from symmetrically coupled system-environment interactions. Here I will present methods for determining the subsystem-preserving evolutions for noiseless subsystem encodings supported by arbitrary-dimensional physical quantum systems. Implications for universal, collective decoherence-free quantum computation using the derived operations are discussed. Moreover, I will present a proposal for an optical device which is capable of preparing a variety of these noiseless subsystem encodings through a postselection strategy.
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Djordjevic, Ivan B. "Integrated Optics Modules Based Proposal for Quantum Information Processing, Teleportation, QKD, and Quantum Error Correction Employing Photon Angular Momentum." IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2016. http://hdl.handle.net/10150/615122.
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To address key challenges for both quantum communication and quantum computing applications in a simultaneous manner, we propose to employ the photon angular momentum approach by invoking the well-known fact that photons carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM). SAM is associated with polarization, while OAM is associated with azimuthal phase dependence of the complex electric field. Given that OAM eigenstates are mutually orthogonal, in principle, an arbitrary number of bits per single photon can be transmitted. The ability to generate/analyze states with different photon angular momentum, by using either holographic or interferometric methods, allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide an infinite basis state, while SAM states are 2-D only, the OAM can also be used to increase the security for quantum key distribution (QKD) applications and improve computational power for quantum computing applications. The goal of this paper is to describe photon angular momentum based deterministic universal quantum qudit gates, namely, {generalized-X, generalized-Z, generalized-CNOT} qudit gates, and different quantum modules of importance for various applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. For instance, the basic quantum modules for quantum teleportation applications include the generalized-Bell-state generation module and the QFT-module. The basic quantum module for quantum error correction and fault-tolerant computing is the nonbinary syndrome calculator module. The basic module for entanglement assisted QKD is either the generalized-Bell-state generation module or the Weyl-operator-module. The possibility of implementing all these modules in integrated optics is discussed as well. Finally, we provide security analysis of entanglement assisted multidimensional QKD protocols, employing the proposed qudit modules, by taking into account the imperfect generation of OAM modes.
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Chubb, Christopher. "Noise in Quantum Information Processing." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/20682.
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Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
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Bergmann, Marcel [Verfasser]. "Optical quantum error correction and detection against photon loss for qubits and beyond / Marcel Bergmann." Mainz : Universitätsbibliothek Mainz, 2019. http://d-nb.info/1193141168/34.
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Cardona, Sanchez Gerardo. "Stabilisation exponentielle des systèmes quantiques soumis à des mesures non destructives en temps continu." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM032/document.
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Dans cette thèse, nous développons des méthodes de contrôle pour stabiliser des systèmes quantiques en temps continu sous mesures quantiques non-destructives. En boucle ouverte, ces systèmes convergent vers un état propre de l'opérateur de mesure, mais l'état résultant est aléatoire. Le rôle du contrôle est de préparer un état prescrit avec une probabilité de un. Le nouvel élément pour atteindre cet objectif est l'utilisation d'un mouvement Brownien pour piloter les actions de contrôle. En utilisant la théorie stochastique de Lyapunov, nous montrons stabilité exponentielle globale du système en boucle fermés. Nous explorons aussi la syntèse du contrôle pour stabiliser un code correcteur d'erreurs quantiques en temps continu. Un autre sujet d'intérêt est l'implementation de contrôles efficacement calculables dans un contexte expérimental. Dans cette direction, nous proposons l'utilisation de contrôles et filtres qui calculent seulement les characteristiques classiques du système, correspondant a la base propre de l'opérateur de mesure. La formulation de dites filtres est importante pour adresser les problèmes de scalabilité du filtre posées par l'avancement des technologies quantiquesIn this thesis, we develop control methods to stabilize quantum systems in continuous-time subject to quantum nondemolition measurements. In open-loop such quantum systems converge towards a random eigenstate of the measurement operator. The role of feedback is to prepare a prescribed eigenstate with unit probability. The novel element to achieve this is the introduction of an exogenous Brownian motion to drive the control actions. By using standard stochastic Lyapunov techniques, we show global exponential stability of the closed-loop dynamics. We explore as well the design of the control layer for a quantum error correction scheme in continuous-time. Another theme of interest is towards the implementation of efficiently computable control laws in experimental settings. In this direction, we propose the use control laws and of reduced-order filters which only track classical characteristics of the system, corresponding to the populations on the measurement eigenbasis. The formulation of these reduced filters is important to address the scalability issues of the filter posed by the advancement of quantum technologies
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Shettell, Nathan. "Quantum Information Techniques for Quantum Metrology." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS504.
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La métrologie quantique est une discipline prometteuse de l'information quantique qui connaît actuellement une vague de percées expérimentales et de développements théoriques. L'objectif principal de la métrologie quantique est d'estimer des paramètres inconnus aussi précisément que possible. En utilisant des ressources quantiques comme sondes, il est possible d'atteindre une précision de mesure qui serait autrement impossible en utilisant les meilleures stratégies classiques. Par exemple, en ce qui concerne la tâche d'estimation de la phase, la précision maximale (la limite d'Heisenberg) est un gain de précision quadratique par rapport aux meilleures stratégies classiques. Bien entendu, la métrologie quantique n'est pas la seule technologie quantique qui connaît actuellement des avancées. Le thème de cette thèse est l'exploration de la manière dont la métrologie quantique peut être améliorée par d'autres techniques quantiques lorsque cela est approprié, à savoir : les états graphiques, la correction d'erreurs et la cryptographie. Les états de graphes sont une ressource incroyablement utile et polyvalente dans l'information quantique. Nous aidons à déterminer l'étendue de l'applicabilité des états de graphes en quantifiant leur utilité pour la tâche de métrologie quantique de l'estimation de phase. En particulier, l'utilité d'un état de graphe peut être caractérisée en fonction de la forme du graphe correspondant. À partir de là, nous concevons une méthode pour transformer tout état de graphe en un état de graphe plus grand (appelé "bundled graph states") qui sature approximativement la limite de Heisenberg. En outre, nous montrons que les états de graphe constituent une ressource robuste contre les effets du bruit (le déphasage et un petit nombre d'effacements) et que la limite quantique de Cramér-Rao peut être saturée par une simple stratégie de mesure. Le bruit issu de l’environnement est l'un des principaux obstacles à la métrologie quantique, qui limite la précision et la sensibilité qu'elle peut atteindre. Il a été démontré que si le bruit environnemental peut être distingué de la dynamique de la tâche de métrologie quantique, des applications fréquentes de correction d'erreurs peuvent être utilisées pour combattre les effets du bruit. En pratique, cependant, la fréquence de correction d'erreurs requise pour maintenir une précision de type Heisenberg est impossible à atteindre pour les technologies quantiques actuelles. Nous explorons les limites de la métrologie quantique améliorée par la correction d'erreurs en prenant en compte les contraintes et les obstacles technologiques, à partir desquels nous établissons le régime dans lequel la limite d'Heisenberg peut être maintenue en présence de bruit. La mise en œuvre complète d'un problème de métrologie quantique est technologiquement exigeante : des états quantiques intriqués doivent être générés et mesurés avec une grande fidélité. Une solution, dans le cas où l'on ne dispose pas de tout le matériel quantique nécessaire, consiste à déléguer une tâche à un tiers. Ce faisant, plusieurs problèmes de sécurité se posent naturellement en raison de la possibilité d'interférence d'un adversaire malveillant. Nous abordons ces questions en développant la notion de cadre cryptographique pour la métrologie quantique. Nous montrons que la précision du problème de la métrologie quantique peut être directement liée à la solidité d'un protocole cryptographique employé. En outre, nous développons des protocoles cryptographiques pour une variété de paramètres motivés par la cryptographie, à savoir : la métrologie quantique sur un canal quantique non sécurisé et la métrologie quantique avec une tâche déléguée à une partie non fiable. Les réseaux de détection quantique ont suscité un intérêt croissant dans la communauté de la métrologie quantique au cours des dernières années. Ils constituent un choix naturel pour les problèmes distribués dans l'espace et les problèmes multiparamètres.[...]Quantum metrology is an auspicious discipline of quantum information which is currently witnessing a surge of experimental breakthroughs and theoretical developments. The main goal of quantum metrology is to estimate unknown parameters as accurately as possible. By using quantum resources as probes, it is possible to attain a measurement precision that would be otherwise impossible using the best classical strategies. For example, with respect to the task of phase estimation, the maximum precision (the Heisenberg limit) is a quadratic gain in precision with respect to the best classical strategies. Of course, quantum metrology is not the sole quantum technology currently undergoing advances. The theme of this thesis is exploring how quantum metrology can be enhanced with other quantum techniques when appropriate, namely: graph states, error correction and cryptography. Graph states are an incredibly useful and versatile resource in quantum information. We aid in determining the full extent of the applicability of graph states by quantifying their practicality for the quantum metrology task of phase estimation. In particular, the utility of a graph state can be characterised in terms of the shape of the corresponding graph. From this, we devise a method to transform any graph state into a larger graph state (named a bundled graph state) which approximately saturates the Heisenberg limit. Additionally, we show that graph states are a robust resource against the effects of noise, namely dephasing and a small number of erasures, and that the quantum Cramér-Rao bound can be saturated with a simple measurement strategy. Noise is one of the biggest obstacles for quantum metrology that limits its achievable precision and sensitivity. It has been showed that if the environmental noise is distinguishable from the dynamics of the quantum metrology task, then frequent applications of error correction can be used to combat the effects of noise. In practise however, the required frequency of error correction to maintain Heisenberg-like precision is unobtainable for current quantum technologies. We explore the limitations of error correction enhanced quantum metrology by taking into consideration technological constraints and impediments, from which, we establish the regime in which the Heisenberg limit can be maintained in the presence of noise. Fully implementing a quantum metrology problem is technologically demanding: entangled quantum states must be generated and measured with high fidelity. One solution, in the instance where one lacks all of the necessary quantum hardware, is to delegate a task to a third party. In doing so, several security issues naturally arise because of the possibility of interference of a malicious adversary. We address these issues by developing the notion of a cryptographic framework for quantum metrology. We show that the precision of the quantum metrology problem can be directly related to the soundness of an employed cryptographic protocol. Additionally, we develop cryptographic protocols for a variety of cryptographically motivated settings, namely: quantum metrology over an unsecured quantum channel and quantum metrology with a task delegated to an untrusted party. Quantum sensing networks have been gaining interest in the quantum metrology community over the past few years. They are a natural choice for spatially distributed problems and multiparameter problems. The three proposed techniques, graph states, error correction and cryptography, are a natural fit to be immersed in quantum sensing network. Graph states are an well-known candidate for the description of a quantum network, error correction can be used to mitigate the effects of a noisy quantum channel, and the cryptographic framework of quantum metrology can be used to add a sense of security. Combining these works formally is a future perspective
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Thakre, Purva. "USING A NUMERICAL ALGORITHM TO SEARCH FOR DECOHERENCE-FREE SUB-SYSTEMS." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/theses/2465.
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In this paper, we discuss the need for quantum error correction. We also describe some basic techniques used in quantum error correction which includes decoherence-free subspaces and subsystems. These subspaces and subsystems are described in detail. We also introduce a numerical algorithm that was used previously to search for these decoherence-free subspaces and subsystems under collective error. It is useful to search for them as they can be used to store quantum information. We use this algorithm in some specific examples involving qubits and qutrits. The results of these algorithm are then compared with the error algebra obtained using Young tableaux. We use these results to describe how the specific numerical algorithm can be used for the search of approximate decoherence-free subspaces and subsystems and minimal noise subsystems.
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López, Delgado Daniel Antonio 1987. "Threshold theorem for a quantum memory in a correlated environment : Teorema do limiar para uma memória quântica em um ambiente correlacionado." [s.n.], 2016. http://repositorio.unicamp.br/jspui/handle/REPOSIP/321757.
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Orientadores: Amir Ordacgi Caldeira, Eduardo Peres Novais de SáTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
Made available in DSpace on 2018-09-01T01:58:28Z (GMT). No. of bitstreams: 1 LopezDelgado_DanielAntonio_D.pdf: 831710 bytes, checksum: 17fbe60b2052b9d8534b963d0e85fe0e (MD5) Previous issue date: 2016
Resumo: A criação de um computador quântico é um projeto que guia, ao mesmo tempo, avanços tecnológicos e um melhor entendimento das propriedades de sistemas quânticos e da Mecânica Quântica em geral. O teorema do limiar é derivado da teoria quântica de correção de erros e garante que, se o ruido estocástico que afeta os componentes de um computador quântico encontra-se abaixo de um valor limite, podemos operar esse computador quântico confiavelmente. Investigamos como esse teorema é modificado quando consideramos uma memória quântica (a qual usa o código de superfície para corrigir erros) acoplada a um ambiente correlacionado. O limiar de erros nesse caso é relacionado à transição de fase ordem-desordem de um sistema de spin equivalente
Abstract: The design of a quantum computer is a project which drives, at the same time, technological advancement and a better understanding of the properties of quantum systems and of Quantum Mechanics in general. The threshold theorem comes from quantum error correction theory and it guarantees that, if stochastic noise affecting the components of a quantum computer is below some threshold value, we can operate this quantum computer reliably. We investigate how this theorem is modified when we consider a quantum memory (which uses the surface code to correct errors) coupled to a correlated environment. The error threshold in this case is related the order-disorder phase transition of an equivalent spin system
Doutorado
Física
Doutor em Ciências
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Verney, Lucas. "Strongly driven quantum Josephson circuits." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE008/document.
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Dans cette thèse, nous étudions le comportement de circuits Josephson sous l'action de champs microondes forts. Les circuits Josephson dans le régime quantique sont une brique pour émuler une variété d'hamiltoniens, utiles pour traiter l'information quantique. Nous étudions ici le transmon, constitué d'une jonction Josephson et d'un condensateur en parallèle. À travers des simulations numériques et en comparant aux résultats expérimentaux, nous montrons que ces champs conduisent à une instabilité qui envoie le circuit sur des états qui ne sont plus confinés par le potentiel Josephson en cosinus. Quand le transmon occupe de tels états, le circuit se comporte comme si la jonction avait été remplacée par un interrupteur ouvert et toute non-linéarité est perdue, ce qui se traduit par des limitations sur les amplitudes maximales des hamiltoniens émulés. Dans une deuxième partie, nous proposons et étudions un circuit alternatif basé sur un transmon avec une inductance en parallèle, qui fournit un confinement harmonique. La dynamique de ce circuit est stable et bien capturée par un modèle moyennisé qui fournit alors un outil pratique pour l'analyse analytique ou les simulations rapides. Nous avons développé un nouvel outil de simulations modulaire et basé sur la théorie de FloquetMarkov pour permettre de simuler facilement d'autres circuits Josephson en évitant les limitations des analyses perturbatives. Enfin, nous étudions les propriétés d'une version asymétrique du Josephson Ring Modulator, un circuit actuellement utilisé pour l'amplification et la conversion, comme source de non-linéarité pour émuler les hamiltoniens d'interaction à deux et quatre photons requis pour l'encodage de l'information quantique sur des états de chats de SchrödingerIn this thesis, we investigate the behavior of Josephson circuits under the action of strong microwave drives. Josephson circuits in the quantum regime are a building block to emulate a variety of Hamiltonians, useful to process quantum information. We are here considering a transmon device, made of a Josephson junction and a capacitor in parallel. Through numerical simulations and comparison with experimental results, we show that these drives lead to an instability which results in the escape of the circuit state into states which are no longer confined by the Josephson cosine potential. When the transmon occupies such states, the circuit behaves as if the junction had been removed and all non-linearities are lost, which translates into limitations on the emulated Hamiltonian strengths. In a second part, we propose and study an alternative circuit consisting of a transmon device with an extra inductive shunt, providing a harmonic confinement. This circuit is found to be stable for all pump powers. The dynamics of this circuit is also well captured by a time-averaged model, providing a useful tool for analytical investigation and fast numerical simulations. We developed a novel numerical approach that avoids the built-in limitations of perturbative analysis to investigate the dynamical behavior of both of these circuits. This approach, based on the Floquet-Markov theory, resulted in a modular simulation framework which can be used to study other Josephson-based circuits. Last, we study the properties of an asymmetric version of the Josephson Ring Modulator, a circuit currently used for amplification and conversion, as a more robust source of non-linearity to engineer two-photon and four-photon interaction Hamiltonians required for the catstate encoding of quantum information