Relevant bibliographies by topics / Quantum Error Correction

Academic literature on the topic 'Quantum Error Correction'

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Published: 4 June 2021
Last updated: 14 September 2024

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Journal articles on the topic "Quantum Error Correction"

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khan, Md Khalik, and Dr Sapna jain. "ERROR CORRECTION USING QUANTUM COMPUTING." International Journal of Engineering Applied Sciences and Technology 8, no. 1 (May 1, 2023): 78–85. http://dx.doi.org/10.33564/ijeast.2023.v08i01.014.

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Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the quantum system. In this context, the goal of a simulation sweep like the one performed in the code is to study the performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error-correction problems.
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Khan, Khalik, and Sapna Jain. "Error Correction Using Quantum Computation." Journal of Digital Science 5, no. 1 (June 25, 2023): 12–22. http://dx.doi.org/10.33847/2686-8296.5.1_2.

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Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the quantum system. In this context, the goal of a simulation sweeps like the one performed in the code is to study the performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error-correction problems.
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Khalifa, Othman O., Nur Amirah bt Sharif, Rashid A. Saeed, S. Abdel-Khalek, Abdulaziz N. Alharbi, and Ali A. Alkathiri. "Digital System Design for Quantum Error Correction Codes." Contrast Media & Molecular Imaging 2021 (December 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/1101911.

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Quantum computing is a computer development technology that uses quantum mechanics to perform the operations of data and information. It is an advanced technology, yet the quantum channel is used to transmit the quantum information which is sensitive to the environment interaction. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental problem of communication, and/or information storage, in the presence of noise. The interruption made by the interaction makes transmission error during the quantum channel qubit. Hence, a quantum error correction code is needed to protect the qubit from errors that can be caused by decoherence and other quantum noise. In this paper, the digital system design of the quantum error correction code is discussed. Three designs used qubit codes, and nine-qubit codes were explained. The systems were designed and configured for encoding and decoding nine-qubit error correction codes. For comparison, a modified circuit is also designed by adding Hadamard gates.
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Locher, David F., Lorenzo Cardarelli, and Markus Müller. "Quantum Error Correction with Quantum Autoencoders." Quantum 7 (March 9, 2023): 942. http://dx.doi.org/10.22331/q-2023-03-09-942.

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Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we demonstrate how quantum neural networks, in the form of quantum autoencoders, can be trained to learn optimal strategies for active detection and correction of errors, including spatially correlated computational errors as well as qubit losses. We highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction and thereby extend the lifetime of a logical qubit.
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ARIMITSU, T., T. HAYASHI, S. KITAJIMA, and F. SHIBATA. "QUANTUM ERROR-CORRECTION FOR SPATIALLY CORRELATED ERRORS." International Journal of Quantum Information 06, supp01 (July 2008): 575–80. http://dx.doi.org/10.1142/s0219749908003803.

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It is shown that errors due to spatially correlated noises can be corrected by the quantum error-correction code and error-correction procedure prepared for those for independent noises. A model of noisy-channel which is under the influence of spatially correlated quantum Brownian motion is investigated within the framework of non-equilibrium thermo field dynamics that is a canonical operator formalism for dissipative quantum systems.
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Fowler, A. G., and K. Goyal. "Topological cluster state quantum computing." Quantum Information and Computation 9, no. 9&10 (September 2009): 721–38. http://dx.doi.org/10.26421/qic9.9-10-1.

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The quantum computing scheme described by Raussendorf et. al (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only, a threshold error rate approaching 1% and low overhead arbitrarily long-range logical gates. In this work, we review the scheme in detail framing the discussion solely in terms of the required 3-D cluster state and its stabilizers.
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Gushanskiy, Sergey, Maxim Polenov, and Viktor Potapov. "Development of a Scheme for Correcting Arbitrary Errors and Averaging Noise in Quantum Computing." Cybernetics and Information Technologies 22, no. 2 (June 1, 2022): 26–35. http://dx.doi.org/10.2478/cait-2022-0014.

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Abstract Intensive research is currently being carried out to develop and create quantum computers and their software. This work is devoted to study of the influence of the environment on the quantum system of qubits. Quantum error correction is a set of methods for protecting quantum information and quantum state from unwanted interactions of the environment (decoherence) and other forms and types of noise. The article discusses the solution to the problem of research and development of corrective codes for rectifying several types of quantum errors that occur during computational processes in quantum algorithms and models of quantum computing devices. The aim of the work is to study existing methods for correcting various types of quantum errors and to create a corrective code for quantum error rectification. The scientific novelty is expressed in the exclusion of one of the shortcomings of the quantum computing process.
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Dauphinais, Guillaume, David W. Kribs, and Michael Vasmer. "Stabilizer Formalism for Operator Algebra Quantum Error Correction." Quantum 8 (February 21, 2024): 1261. http://dx.doi.org/10.22331/q-2024-02-21-1261.

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We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction and subsystem codes (OQEC). The construction generates hybrid classical-quantum stabilizer codes and we formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code, generalizing the fundamental theorems for the QEC and OQEC stabilizer formalisms. We discover hybrid versions of the Bacon-Shor subsystem codes motivated by the formalism, and we apply the theorem to derive a result that gives the distance of such codes. We show how some recent hybrid subspace code constructions are captured by the formalism, and we also indicate how it extends to qudits.
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LIDAR, D. A., and K. KHODJASTEH. "ROBUST DYNAMICAL DECOUPLING: FEEDBACK-FREE ERROR CORRECTION." International Journal of Quantum Information 03, supp01 (November 2005): 41–52. http://dx.doi.org/10.1142/s0219749905001237.

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Dynamical decoupling is a feed-back free scheme for quantum error correction against noise and decoherence errors. An efficiency analysis of dynamical decoupling is performed. Furthermore we provide the basic concepts of dynamical decoupling and quantum error correcting codes, and give an example of a hybrid protection scheme. Some interesting extensions of dynamical decoupling are discussed at the end.
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Sharma, Sangat, Suresh Basnet, and Raju Khanal. "Implementation of Error Correction on IBM Quantum Computing Devices." Journal of Nepal Physical Society 8, no. 1 (December 13, 2022): 7–15. http://dx.doi.org/10.3126/jnphyssoc.v8i1.48278.

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Quantum noise cannot be avoided in the quantum computing devices due to unstable nature of qubits and signals. The error caused by quantum noise can be detected and corrected using different error correcting codes. In this work, we have tested the feasibility and accuracy of three qubit bit flip and phase flip error correcting code in quantum computer provided by International Business Machine Quantum Experience (IBM QX) cloud platform. Among five quantum processors, ibmq_ourense is found to have highest average accuracy 77.9% ± 3.09% on all qubits simultaneously. Three qubits bit flip error correction circuit gave correct output 89.9% ± 1.01% of the time on average. Similarly three qubits phase flip error correction circuit give 88.05% ±1.89%. The measurement error mitigation has improved the accuracy of bit flip and phase flip error correction code by 5.01% and 7.01% respectively on average. The error rate shows that the error in quantum computations are random in nature and can be corrected. IBM QX quantum computer are suitable for only small scale quantum computation and demonstrate purpose. Furthermore, the accuracy of error correction codes can be increased with the use of higher accuracy quantum qubits and quantum gates.
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Dissertations / Theses on the topic "Quantum Error Correction"

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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.

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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,  typically holds, and one must then assume that the environment has a "memory". In this thesis, I describe a short quantum error-correcting code (QECC), adapted for photons interacting with a cold environment, i.e., this code protects from an environment that continuously records which error occurred in the coded quantum state. Also, it is of interest to compare the performance of different QECCs - But which yardstick should one use? We compare two such figures of merit, namely the quantum mutual information and the quantum fidelity, and show that they can not, in general, be simultaneously maximised in an error correcting procedure. To show this, we have used a five-qubit perfect code, but assumed a channel that only cause bit-flip errors. It appears that quantum mutual information is the better suited yardstick of the two, however more tedious to calculate than quantum fidelity - which is more commonly used.
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 , och vi måste anta att reservoiren faktiskt har ett "minne". I avhandlingen beskrivs en kort, kvantfelrättande kod som är anpassad för fotoner i växelverkan med en "kall" omgivning, d.v.s. denna kod skyddar mot en omgivning som kontinuerligt registrerar vilket fel som uppstått i det kodade tillståndet.  Det är också av stort intresse att kunna jämföra prestanda hos kvantfelrättande koder, utifrån någon slags "måttstock" - men vilken? Jag jämför två sådana mått, nämligen ömsesidig kvantinformation, samt kvantfidelitet, och visar att dessa i allmänhet inte kan maximeras samtidigt i en felrättningsprocedur. För att visa detta har en 5-qubitarskod använts i en tänkt kanal där bara bitflip-fel uppstår, och utrymme därför finns att detektera fel. Ömsesidig kvantinformation framstår som det bättre måttet, dock är detta mått betydligt mer arbetskrävande att beräkna, än kvantfidelitet - som är det mest förekommande måttet.

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.

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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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Books on the topic "Quantum Error Correction"

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Lidar, Daniel A., Todd A. Brun, and Todd Brun, eds. Quantum Error Correction. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781139034807.

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La Guardia, Giuliano Gadioli. Quantum Error Correction. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1.

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Parthasarathy, K. R. Lectures on quantum computation, quantum error: Correcting codes and information theory. New Delhi: Published for the Tata Institute of Fundamental Research [by] Narosa Pub. House, 2006.

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Quantum Error Correction. Cambridge University Press, 2013.

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Lidar, Daniel A., and Todd A. Brun. Quantum Error Correction. Cambridge University Press, 2013.

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Quantum Information Processing and Quantum Error Correction. Elsevier, 2012. http://dx.doi.org/10.1016/c2010-0-66917-3.

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Quantum Information Processing, Quantum Computing, and Quantum Error Correction. Elsevier, 2021. http://dx.doi.org/10.1016/c2019-0-04873-x.

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Gaitan, Frank. Quantum Error Correction and Fault Tolerant Quantum Computing. Taylor & Francis Group, 2008.

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Gaitan, Frank. Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, 2018. http://dx.doi.org/10.1201/b15868.

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Gaitan, Frank. Quantum Error Correction and Fault Tolerant Quantum Computing. Taylor & Francis Group, 2018.

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Book chapters on the topic "Quantum Error Correction"

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La Guardia, Giuliano Gadioli. "Quantum Code Constructions." In Quantum Error Correction, 57–124. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_5.

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La Guardia, Giuliano Gadioli. "Asymmetric Quantum Codes." In Quantum Error Correction, 125–61. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_6.

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La Guardia, Giuliano Gadioli. "Quantum Error-Correcting Codes." In Quantum Error Correction, 25–41. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_3.

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La Guardia, Giuliano Gadioli. "Some Linear Algebra." In Quantum Error Correction, 1–16. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_1.

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La Guardia, Giuliano Gadioli. "A Little Bit of Quantum Mechanics." In Quantum Error Correction, 17–23. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_2.

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La Guardia, Giuliano Gadioli. "Linear Block Codes." In Quantum Error Correction, 43–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_4.

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La Guardia, Giuliano Gadioli. "Constructions of QCCs." In Quantum Error Correction, 163–211. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48551-1_7.

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Scherer, Wolfgang. "Error Correction." In Mathematics of Quantum Computing, 343–402. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12358-1_7.

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Baaquie, Belal Ehsan, and Leong-Chuan Kwek. "Quantum Error Correction." In Quantum Computers, 257–68. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-7517-2_17.

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Parthasarathy, K. R. "Quantum Error Correction." In Texts and Readings in Mathematics, 135–70. Gurgaon: Hindustan Book Agency, 2013. http://dx.doi.org/10.1007/978-93-86279-59-0_5.

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Conference papers on the topic "Quantum Error Correction"

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Iqbal, M., M. Svaluto Moreolo, Arturo Villegas, Laia Nadal, and Luis Velasco. "Analyzing Quantum Secure Direct Communication with Forward Error Correction." In Quantum 2.0, QTh3A.3. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/quantum.2024.qth3a.3.

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We implement a quantum equivalent to classical QPSK communication on IBMQ and NetSquid. Results show that forward error correction fails to provide error-free transmission using near-term devices. Error-free transmission is possible when qubit fidelity reaches 0.981.
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Zhu, Yanzhang, and Myung-Joong Hwang. "Harnessing strong symmetry breaking finite-component system phase transition for quantum error correction." In Quantum 2.0, QTu3A.8. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/quantum.2024.qtu3a.8.

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We investigate a dissipative finite-component system phase transition induced by two photon loss mechanism, which features a strong symmetry breaking of the Liouvillian. We characterize the mean-field phase diagram and demonstrate that the system could be harnessed to implement passive error correction for a hybrid qubit-oscillator qubit.
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Brunel, Léandre, Miller Eaton, Hussain Zaidi, and Olivier Pfister. "Generating foliated quantum error-correcting codes with quantum optics." In CLEO: Fundamental Science, FF1H.4. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.ff1h.4.

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We present a graph generation algorithm, using quantum optical circuits, for general continuous-variable cluster states of arbitrary dimension. We describe its application to the large-scale generation of the foliated toric code for quantum error correction.
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Hu, Tianjie, Jindi Wu, and Qun Li. "Quantum Network Routing Based on Surface Code Error Correction." In 2024 IEEE 44th International Conference on Distributed Computing Systems (ICDCS), 1236–47. IEEE, 2024. http://dx.doi.org/10.1109/icdcs60910.2024.00117.

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K, Veeresh, Deepak S, and Srinivas T. "RL-QEC: Harnessing Reinforcement Learning for Quantum Error Correction Advancements." In 2024 International Conference on Trends in Quantum Computing and Emerging Business Technologies (TQCEBT), 1–5. IEEE, 2024. http://dx.doi.org/10.1109/tqcebt59414.2024.10545200.

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Choi, Hyeongrak, Marc G. Davis, Álvaro G. Iñesta, and Dirk Englund. "Scalable Photonic Quantum Network." In CLEO: Fundamental Science, FTu3F.4. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.ftu3f.4.

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Preskill, J. "Quantum error correction." In International Conference on Quantum Information. Washington, D.C.: OSA, 2001. http://dx.doi.org/10.1364/icqi.2001.t3.

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Sarovar, Mohan. "Continuous Quantum Error Correction." In QUANTUM COMMUNICATION, MEASUREMENT AND COMPUTING. AIP, 2004. http://dx.doi.org/10.1063/1.1834397.

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Sarovar, Mohan, and G. J. Milburn. "Continuous quantum error correction." In SPIE Third International Symposium on Fluctuations and Noise, edited by Philip R. Hemmer, Julio R. Gea-Banacloche, Peter Heszler, Sr., and M. Suhail Zubairy. SPIE, 2005. http://dx.doi.org/10.1117/12.608548.

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Wan, Lingxiao, Hui Zhang, Huihui Zhu, Leong Chuan Kwek, and Ai-Qun Liu. "Quantum Computing Chip with Error-Correction Encoding." In CLEO: QELS_Fundamental Science. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.ff2i.5.

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We design and fabricate a quantum photonic circuit to implement a quantum error correction code. A single logical qubit is encoded with 4 physical qubits to demonstrate its capability of detecting and correcting a single-bit error with an average state fidelity of 86%. We further extend the scheme to demonstrate a fault-tolerant teleportation process.
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Reports on the topic "Quantum Error Correction"

1

Lidar, Daniel, and Aephraim Steinberg. Underlying Information Technology Tailored Quantum Error Correction. Fort Belvoir, VA: Defense Technical Information Center, July 2006. http://dx.doi.org/10.21236/ada455920.

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Saffman, Mark. Quantum Error Correction with a Globally-Coupled Array of Neutral Atom Qubits. Fort Belvoir, VA: Defense Technical Information Center, February 2013. http://dx.doi.org/10.21236/ada579666.

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