Journal articles: 'Qubit'

1

Moussa, Jonathan Edward. "Quantum circuits for qubit fusion." Quantum Information and Computation 16, no. 13&14 (October 2016): 1113–24. http://dx.doi.org/10.26421/qic16.13-14-3.

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We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, C^2_1 belong to C^4_2 belong to C^2_3 , where Cmn is the nth level of the m-dimensional qudit Clifford hierarchy. If we can convert between logical qubits and qudits, then qudit Clifford operators are qubit non-Clifford operators. Conversion is achieved by qubit fusion and qudit fission using stabilizer circuits that consume a resource state. This resource is a fused qubit stabilizer state with a faulttolerant state preparation using stabilizer circuits.

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Nikolaeva, Anstasiia S., Evgeniy O. Kiktenko, and Aleksey K. Fedorov. "Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits." Entropy 25, no. 2 (February 20, 2023): 387. http://dx.doi.org/10.3390/e25020387.

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Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

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LIU, YANG, GUI LU LONG, and YANG SUN. "ANALYTIC ONE-BIT AND CNOT GATE CONSTRUCTIONS OF GENERAL n-QUBIT CONTROLLED GATES." International Journal of Quantum Information 06, no. 03 (June 2008): 447–62. http://dx.doi.org/10.1142/s0219749908003621.

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General n-qubit controlled unitary gates are frequently used in quantum information processing tasks. Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor [Phys. Rev. A52 (1995) 3457] have given the general construction methods, and explicit results for up-to-four-qubits controlled unitary gates. We extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one-qubit and two-qubit CNOT gates. There are two expressions – one is exponential in the qubit number which is efficient for up to ten qubits, and the other is polynomial in the qubit number, which is efficient for more than ten qubits.

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DOLL, ROLAND, MARTIJN WUBS, SIGMUND KOHLER, and PETER HÄNGGI. "FIDELITY AND ENTANGLEMENT OF A SPATIALLY EXTENDED LINEAR THREE-QUBIT REGISTER." International Journal of Quantum Information 06, supp01 (July 2008): 681–87. http://dx.doi.org/10.1142/s0219749908003955.

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We study decoherence of a three-qubit array coupled to substrate phonons. Assuming an initial three-qubit entangled state that would be decoherence-free for identical qubit positions, allows us to focus on non-Markovian effects of the inevitable spatial qubit separation. It turns out that the coherence is most affected when the qubits are regularly spaced. Moreover, we find that up to a constant scaling factor, two-qubit entanglement is not influenced by the presence of the third qubit, even though all qubits interact via the phonon field.

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Espinel-López, Cristian, Alvaro Martínez-Gómez, Marisol Aguilar-Echeverría, and Hipatia Mañay-Mañay. "Evolución de componentes de computación cuántica y mediciones cuánticas no destructivas en la informática moderna. //Evolution of quantum computing components and non-destructive quantum measurements in modern computing." CIENCIA UNEMI 11, no. 28 (October 1, 2018): 57–69. http://dx.doi.org/10.29076/issn.2528-7737vol11iss28.2018pp57-69p.

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El presente trabajo, realiza una breve introducción a las medidas QND (Quantum nondemolition measurement) y sus características. Además, se describe teóricamente un qubit acoplado a un oscilador armónico cuántico forzado como ejemplo de una medición QND en un qubit. El formalismo desarrollado para este tipo de sistemas cuánticos acoplados se desenvuelve dentro de la teoría cuántica de la computación. Como parte del estudio de las mediciones QND, se introducen los qubits de flujo que hacen uso de los interferómetros superconductores cuánticos (SQUIDs). El análisis de este esquema informático intenta introducir al lector en los conceptos de computación cuántica como el quibit que es el componente base que permite procesar información de forma cuántica. El objetivo de este trabajo es caracterizar si las medidas elaboradas sobre el qubit acoplado son o no QND. En este sentido, la aplicación del formalismo expuesto permitirá vislumbrar los alcances y limitaciones de los qubits acoplados en el desarrollo y aplicación de los sistemas cuánticos de la computación hasta el día de hoy. Adicionalmente, la aplicación de esta teoría se puede emplear a mediciones QND sobre qubits superconductores articulados a un oscilador armónico cuántico. Todo este proceso es sujeto al análisis y metodología que nos proporciona la historia de la ciencia y la tecnología. AbstractThe present work makes a brief introduction to QND (Quantum non demolition measurement) measurements and its characteristics. In addition, a qubit coupled to a forced quantum harmonic oscillator which is described theoretically as an example of a QND measurement in a qubit. The formalism developed for this type of coupled quantum systems is developed within the quantum theory of computation. As part of the study of QND measurements, the flow qubits making use of quantum superconducting interferometers (SQUIDs) are introduced. The analysis of this computer schema attempts to introduce the reader to the concepts of quantum computing such as qubit, which is the basic component that allows information to be processed quantumly. The objective of this work is to characterize whether the elaborated measures on the coupled qubit are QND or not. In this sense, the application of the exposed formalism will allow us to glimpse the scope and limitations of coupled qubits in the development and application of quantum computing systems to this day. Additionally, the application of this theory can be applied to QND measurements on superconducting qubits coupled to a quantum harmonic oscillator. All this process is subject to the analysis and methodology provided by the history of science and technology.

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6

Childs, Andrew M., Debbie Leung, Laura Mancinska, and Maris Ozols. "Characterization of universal two-qubit Hamiltonians." Quantum Information and Computation 11, no. 1&2 (January 2011): 19–39. http://dx.doi.org/10.26421/qic11.1-2-3.

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Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal, an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian $H$ can fail to be universal: (1) H shares an eigenvector with the gate that swaps two qubits, (2) H acts on the two qubits independently (in any of a certain family of bases), or (3) H has zero trace (with the third condition relevant only when the global phase of the unitary matters). A 2-non-universal 2-qubit Hamiltonian can still be n-universal for some n \geq 3. We give some partial results on 3-universality.

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7

Assouline, A., L. Pugliese, H. Chakraborti, Seunghun Lee, L. Bernabeu, M. Jo, K. Watanabe, et al. "Emission and coherent control of Levitons in graphene." Science 382, no. 6676 (December 15, 2023): 1260–64. http://dx.doi.org/10.1126/science.adf9887.

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Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional qubits.

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8

Gidney, Craig, Michael Newman, and Matt McEwen. "Benchmarking the Planar Honeycomb Code." Quantum 6 (September 21, 2022): 813. http://dx.doi.org/10.22331/q-2022-09-21-813.

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We improve the planar honeycomb code by describing boundaries that need no additional physical connectivity, and by optimizing the shape of the qubit patch. We then benchmark the code using Monte Carlo sampling to estimate logical error rates and derive metrics including thresholds, lambdas, and teraquop qubit counts. We determine that the planar honeycomb code can create a logical qubit with one-in-a-trillion logical error rates using 7000 physical qubits at a 0.1% gate-level error rate (or 900 physical qubits given native two-qubit parity measurements). Our results cement the honeycomb code as a promising candidate for two-dimensional qubit architectures with sparse connectivity.

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9

Li, Xiangrong, and Dafa Li. "Rank-based SLOCC classification for odd $n$ qubits." Quantum Information and Computation 11, no. 7&8 (July 2011): 695–705. http://dx.doi.org/10.26421/qic11.7-8-10.

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We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect to qubits 1,2, ... n give rise to the classification of the space of odd $n$ qubits into 3^n families.

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10

PERDRIX, SIMON. "STATE TRANSFER INSTEAD OF TELEPORTATION IN MEASUREMENT-BASED QUANTUM COMPUTATION." International Journal of Quantum Information 03, no. 01 (March 2005): 219–23. http://dx.doi.org/10.1142/s0219749905000785.

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Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, four auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of one one-qubit measurement and four two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer: state transfer only retains the part of teleportation which is necessary for computation. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of three one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement).

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11

Said, Taoufik, Abdelhaq Chouikh, Karima Essammouni, and Mohamed Bennai. "Realizing an N-two-qubit quantum logic gate in a cavity QED with nearest qubit--qubit interaction." Quantum Information and Computation 16, no. 5&6 (April 2016): 465–82. http://dx.doi.org/10.26421/qic16.5-6-4.

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We propose an effective way for realizing a three quantum logic gates (NTCP gate, NTCP-NOT gate and NTQ-NOT gate) of one qubit simultaneously controlling N target qubits based on the qubit-qubit interaction. We use the superconducting qubits in a cavity QED driven by a strong microwave field. In our scheme, the operation time of these gates is independent of the number N of qubits involved in the gate operation. These gates are insensitive to the initial state of the cavity QED and can be used to produce an analogous CNOT gate simultaneously acting on N qubits. The quantum phase gate can be realized in a time (nanosecond-scale) much smaller than decoherence time and dephasing time (microsecond-scale) in cavity QED. Numerical simulation under the influence of the gate operations shows that the scheme could be achieved efficiently within current state-of-the-art technology.

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12

Ben-Aryeh, Y., and A. Mann. "Separability and entanglement of n-qubit and a qubit and a qudit using Hilbert–Schmidt decompositions." International Journal of Quantum Information 14, no. 05 (August 2016): 1650030. http://dx.doi.org/10.1142/s0219749916500301.

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Hilbert–Schmidt (HS) decompositions are employed for analyzing systems of [Formula: see text]-qubit, and a qubit with a qudit. Negative eigenvalues, obtained by partial-transpose (PT) plus local unitary (PTU) transformations for one qubit from the whole system, are used for indicating entanglement/separability. A sufficient criterion for full separability of the [Formula: see text]-qubit and qubit–qudit systems is given. We use the singular value decomposition (SVD) for improving the criterion for full separability. General properties of entanglement and separability are analyzed for a system of a qubit and a qudit and [Formula: see text]-qubit systems, with emphasis on maximally disordered subsystems (MDS) (i.e. density matrices for which tracing over any subsystem gives the unit density matrix). A sufficient condition that [Formula: see text] (MDS) is not separable is that it has an eigenvalue larger than [Formula: see text] for a qubit and a qudit, and larger than [Formula: see text] for [Formula: see text]-qubit system. The PTU transformation does not change the eigenvalues of the [Formula: see text]-qubit MDS density matrices for odd [Formula: see text]. Thus, the Peres–Horodecki (PH) criterion does not give any information about entanglement of these density matrices. The PH criterion may be useful for indicating inseparability for even [Formula: see text]. The changes of the entanglement and separability properties of the GHZ state, the Braid entangled state and the [Formula: see text] state by mixing them with white noise are analyzed by the use of the present methods. The entanglement and separability properties of the GHZ-diagonal density matrices, composed of mixture of 8[Formula: see text]GHZ density matrices with probabilities [Formula: see text], is analyzed as function of these probabilities. In some cases, we show that the PH criterion is both sufficient and necessary.

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13

Essammouni, K., A. Chouikh, T. Said, and M. Bennai. "niSWAP and NTCP gates realized in a circuit QED system." International Journal of Geometric Methods in Modern Physics 14, no. 07 (March 7, 2017): 1750100. http://dx.doi.org/10.1142/s0219887817501006.

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Based on superconducting qubit coupled to a resonator driven by a strong microwave field, we propose a method to implement two quantum logic gates ([Formula: see text]SWAP and NTCP gates) of one qubit simultaneously controlling [Formula: see text] qubits selected from [Formula: see text] qubits in a circuit QED [Formula: see text] by introducing qubit–qubit interaction. The interaction between the qubits and the circuit QED can be achieved by tuning the gate voltage and the external flux. The operation times of the logic gates are much smaller than the decoherence time and dephasing time. Moreover, the numerical simulation under the influence of the gates operations shows that the scheme could be achieved efficiently with presently available techniques.

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Said, T., A. Chouikh, K. Essammouni, and M. Bennai. "Implementing N-quantum phase gate via circuit QED with qubit–qubit interaction." Modern Physics Letters B 30, no. 05 (February 20, 2016): 1650050. http://dx.doi.org/10.1142/s0217984916500500.

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We propose a method for realizing a quantum phase gate of one qubit simultaneously controlling [Formula: see text] target qubits based on the qubit–qubit interaction. We show how to implement the proposed gate with one transmon qubit simultaneously controlling [Formula: see text] transmon qubits in a circuit QED driven by a strong microwave field. In our scheme, the operation time of this phase gate is independent of the number [Formula: see text] of qubits. On the other hand, this gate can be realized in a time of nanosecond-scale much smaller than the decoherence time and dephasing time both being the time of microsecond-scale. Numerical simulation of the occupation probabilities of the second excited lever shows that the scheme could be achieved efficiently within current technology.

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Herbert, Steven. "On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity." Quantum Information and Computation 20, no. 9&10 (August 2020): 787–806. http://dx.doi.org/10.26421/qic20.9-10-5.

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This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

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Choi, Jeong Ryeol. "Dynamics of Dispersive Measurements of Flux-Qubit States: Energy-Level Splitting Connected to Quantum Wave Mechanics." Nanomaterials 13, no. 17 (August 23, 2023): 2395. http://dx.doi.org/10.3390/nano13172395.

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Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit–oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit–oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength is not zero, the energy-level splitting of the resonator does not disappear even when the tunnel splitting in the qubit is zero. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.

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17

Solfanelli, Andrea, Alessandro Santini, and Michele Campisi. "Quantum thermodynamic methods to purify a qubit on a quantum processing unit." AVS Quantum Science 4, no. 2 (June 2022): 026802. http://dx.doi.org/10.1116/5.0091121.

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We report on a quantum thermodynamic method to purify a qubit on a quantum processing unit (QPU) equipped with (nearly) identical qubits. Our starting point is a three qubit design that emulates the well-known two qubit swap engine. Similar to standard fridges, the method would allow us to cool down a qubit at the expense of heating two other qubits. A minimal modification thereof leads to a more practical three qubit design that allows for enhanced refrigeration tasks, such as increasing the purity of one qubit at the expense of decreasing the purity of the other two. The method is based on the application of properly designed quantum circuits and can therefore be run on any gate model quantum computer. We implement it on a publicly available superconducting qubit based QPU and observe a purification capability down to 200 mK. We identify gate noise as the main obstacle toward practical application for quantum computing.

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MAKHLIN, YU, S. BACKEN, and A. SHNIRMAN. "TWO-QUBIT OPERATION ON MAJORANA QUBITS IN ORDINARY-QUBIT CHAINS." ПИСЬМА В ЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ 108, no. 11-12 (2018): 779–80. http://dx.doi.org/10.1134/s0370274x1823008x.

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Makhlin, Yu, S. Backens, and A. Shnirman. "Two-Qubit Operation on Majorana Qubits in Ordinary-Qubit Chains." JETP Letters 108, no. 11 (November 28, 2018): 763–67. http://dx.doi.org/10.1134/s0021364018230029.

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20

Чуйкин, О. А., Я. С. Гринберг, and А. А. Штыгашев. "Затухание вакуумных осцилляций Раби в двухкубитной структуре в высокодобротном резонаторе." Физика твердого тела 62, no. 9 (2020): 1407. http://dx.doi.org/10.21883/ftt.2020.09.49762.13h.

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In this work, we study the damping of vacuum Rabi oscillations for a system of two superconducting solid-state qubits placed in a high-quality microwave resonator. Two different cases are considered: the first qubit is excited at the initial moment, and the initial state is an entangled symmetric and antisymmetric pair. The dependence of the damping on various parameters, primarily on the photon-qubit coupling and on the distance between qubits, is studied in detail. It is shown that for some parameters, the relaxation time of the excited qubit is significantly longer than that for a single qubit in the cavity.

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Takeda, Kenta, Akito Noiri, Takashi Nakajima, Takashi Kobayashi, and Seigo Tarucha. "Quantum error correction with silicon spin qubits." Nature 608, no. 7924 (August 24, 2022): 682–86. http://dx.doi.org/10.1038/s41586-022-04986-6.

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AbstractFuture large-scale quantum computers will rely on quantum error correction (QEC) to protect the fragile quantum information during computation1,2. Among the possible candidate platforms for realizing quantum computing devices, the compatibility with mature nanofabrication technologies of silicon-based spin qubits offers promise to overcome the challenges in scaling up device sizes from the prototypes of today to large-scale computers3–5. Recent advances in silicon-based qubits have enabled the implementations of high-quality one-qubit and two-qubit systems6–8. However, the demonstration of QEC, which requires three or more coupled qubits1, and involves a three-qubit gate9–11 or measurement-based feedback, remains an open challenge. Here we demonstrate a three-qubit phase-correcting code in silicon, in which an encoded three-qubit state is protected against any phase-flip error on one of the three qubits. The correction to this encoded state is performed by a three-qubit conditional rotation, which we implement by an efficient single-step resonantly driven iToffoli gate. As expected, the error correction mitigates the errors owing to one-qubit phase-flip, as well as the intrinsic dephasing mainly owing to quasi-static phase noise. These results show successful implementation of QEC and the potential of a silicon-based platform for large-scale quantum computing.

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Yirka, Justin, and Yiğit Subaşı. "Qubit-efficient entanglement spectroscopy using qubit resets." Quantum 5 (September 2, 2021): 535. http://dx.doi.org/10.22331/q-2021-09-02-535.

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One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, Tr(ρn), (related to the Rényi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating Tr(ρn) for larger n than possible with previous algorithms.

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Yuan, Wei-Ping, Zhi-Cheng He, Sai Li, and Zheng-Yuan Xue. "Fast Reset Protocol for Superconducting Transmon Qubits." Applied Sciences 13, no. 2 (January 6, 2023): 817. http://dx.doi.org/10.3390/app13020817.

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For larger-scale quantum information processing, qubit reset plays an important role, as the coherent times for qubits are limited. However, previous schemes require either long reset times or a complex pulse calibration technique, leading to low efficiency in qubit reset. Here, we propose a fast and simple reset protocol for superconducting transmon qubits based on the coupler-coupled qubits architecture. In this setup, a mixing pulse is used to transfer the qubit excitation to the combined excitation of a low-qulity coupler and readout resonator, which will quickly decay to their respectively ground states, leading to efficient qubit reset to the ground state. Our numerical results show that the residual population of the qubit’s excited state can be suppressed to 0.04% within 28 ns; the reset time will be 283 ns if photon depletion of the readout resonator is required. Thus, our protocol provides a promising way for the high-efficiency superconducting qubit reset.

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Cai, J. M., Z. W. Zhou, and G. C. Guo. "Fully multi-qubit entangled states." Quantum Information and Computation 7, no. 8 (November 2007): 766–74. http://dx.doi.org/10.26421/qic7.8-6.

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We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in connected graph states of $N$ qubits there is no genuine $k$-qubit entanglement, $2\leq k\leq N-1$, among every $k$ qubits. These results about connected graph states naturally lead to the definition of fully multi-qubit entangled states. We also find that the connected graph states of four qubits is one but not the only one class of fully four-qubit entangled states.

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Royer, Baptiste, Arne L. Grimsmo, Nicolas Didier, and Alexandre Blais. "Fast and high-fidelity entangling gate through parametrically modulated longitudinal coupling." Quantum 1 (May 11, 2017): 11. http://dx.doi.org/10.22331/q-2017-05-11-11.

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We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubit-oscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.

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Aldeghi, Michele, Rolf Allenspach, and Gian Salis. "Modular nanomagnet design for spin qubits confined in a linear chain." Applied Physics Letters 122, no. 13 (March 27, 2023): 134003. http://dx.doi.org/10.1063/5.0139670.

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On-chip micromagnets enable electrically controlled quantum gates on electron spin qubits. Extending the concept to a large number of qubits is challenging in terms of providing large enough driving gradients and individual addressability. Here, we present a design aimed at driving spin qubits arranged in a linear chain and strongly confined in directions lateral to the chain. Nanomagnets are placed laterally to the one side of the qubit chain, one nanomagnet per two qubits. The individual magnets are “U”-shaped, such that the magnetic shape anisotropy orients the magnetization alternately toward and against the qubit chain even if an external magnetic field is applied along the qubit chain. The longitudinal and transversal stray field components serve as addressability and driving fields. Using micromagnetic simulations, we calculate driving and dephasing rates and the corresponding qubit quality factor. The concept is validated with spin-polarized scanning electron microscopy of Fe nanomagnets fabricated on silicon substrates, finding excellent agreement with micromagnetic simulations. Several features required for a scalable spin qubit design are met in our approach: strong driving and weak dephasing gradients, reduced crosstalk and operation at low external magnetic fields.

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Baßler, Pascal, Matthias Zipper, Christopher Cedzich, Markus Heinrich, Patrick H. Huber, Michael Johanning, and Martin Kliesch. "Synthesis of and compilation with time-optimal multi-qubit gates." Quantum 7 (April 20, 2023): 984. http://dx.doi.org/10.22331/q-2023-04-20-984.

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We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it can be switched on and off for individual qubits. Our method yields a time-optimal implementation of the multi-qubit gates. We numerically demonstrate that the total multi-qubit gate time scales approximately linear in the number of qubits. Using this gate synthesis as a subroutine, we provide compilation strategies for important use cases: (i) we show that any Clifford circuit on n qubits can be implemented using at most 2n multi-qubit gates without requiring ancilla qubits, (ii) we decompose the quantum Fourier transform in a similar fashion, (iii) we compile a simulation of molecular dynamics, and (iv) we propose a method for the compilation of diagonal unitaries with time-optimal multi-qubit gates, as a step towards general unitaries. As motivation, we provide a detailed discussion on a microwave controlled ion trap architecture with magnetic gradient induced coupling (MAGIC) for the generation of the Ising-type interactions.

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Javed, Shamiya, Ranjana Prakash, and Hari Prakash. "High success perfect transmission of 1-qubit information using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements." International Journal of Quantum Information 19, no. 02 (March 2021): 2150015. http://dx.doi.org/10.1142/s0219749921500155.

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We propose a new scheme in which perfect transmission of 1-qubit information is achieved with high success using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements (GBSM). Alice possesses initially all qubits and she makes repeated GBSM on the pair of qubits, consisting of (1) the qubit of information state and (2) one of the two entangled resource qubits (taken alternately) until transmission with perfect fidelity is indicated. Alice then sends to Bob, the qubit not used in the last GBSM and also the result of this GBSM and Bob applies a suitable unitary transformation to replicate exactly the information state. Continued probabilistic transmission with unit fidelity is achieved by changing continuously the generalized Bell basis and also the pair of measured qubits of the collapsed states. We calculate the success probability up to the third repeated attempt of GBSM and plot it with concurrence of the entangled resource state. We also discuss the maximal average fidelity.

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Kjaergaard, Morten, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I. J. Wang, Simon Gustavsson, and William D. Oliver. "Superconducting Qubits: Current State of Play." Annual Review of Condensed Matter Physics 11, no. 1 (March 10, 2020): 369–95. http://dx.doi.org/10.1146/annurev-conmatphys-031119-050605.

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Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The superconducting qubit modality has been used to demonstrate prototype algorithms in the noisy intermediate-scale quantum (NISQ) technology era, in which non-error-corrected qubits are used to implement quantum simulations and quantum algorithms. With the recent demonstrations of multiple high-fidelity, two-qubit gates as well as operations on logical qubits in extensible superconducting qubit systems, this modality also holds promise for the longer-term goal of building larger-scale error-corrected quantum computers. In this brief review, we discuss several of the recent experimental advances in qubit hardware, gate implementations, readout capabilities, early NISQ algorithm implementations, and quantum error correction using superconducting qubits. Although continued work on many aspects of this technology is certainly necessary, the pace of both conceptual and technical progress in recent years has been impressive, and here we hope to convey the excitement stemming from this progress.

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TAKAHASHI, YASUHIRO. "AN APPROXIMATELY UNIVERSAL SET CONSISTING OF TWO OBSERVABLES." International Journal of Quantum Information 09, no. 06 (September 2011): 1393–412. http://dx.doi.org/10.1142/s021974991100809x.

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We consider the problem of minimizing the resources required for approximate universality in measurement-only quantum computation. This problem is important not only for realizing a quantum computer, but also for understanding the computational power of quantum computation. The resources we focus on are observables, which describe projective measurements, and ancillary qubits. We show that, if we are allowed to use two ancillary qubits, the set of observables { cos (π/8)X - sin (π/8)Y ,Z ⊗ X} is approximately universal for quantum computation. This is the first construction of an approximately universal set consisting only of one one-qubit observable and one two-qubit observable. Using the proof of the approximate universality, we also show that, if we are allowed to use two initialized ancillary qubits, one two-qubit observable is sufficient for graph state preparation. The use of only one two-qubit observable is optimal in terms of the number of observables available and the number of qubits to be measured jointly.

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Sánchez-Burillo, Eduardo, Juanjo García-Ripoll, Luis Martín-Moreno, and David Zueco. "Nonlinear quantum optics in the (ultra)strong light–matter coupling." Faraday Discussions 178 (2015): 335–56. http://dx.doi.org/10.1039/c4fd00206g.

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The propagation of N photons in one dimensional waveguides coupled to M qubits is discussed, both in the strong and ultrastrong qubit–waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of N, M, qubit inter distance and light–matter coupling. The quantum evolution is numerically solved via the matrix product states technique. The time evolutions for both the field and qubits are computed. The nonlinear character (as a function of N/M) depends on the computed observable. While perfect reflection is obtained for N/M ≅ 1, photon–photon correlations are still resolved for ratios N/M = non-zero. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are robust against the number of qubits and that the qubit–qubit interaction mediated by the photons is qualitatively modified. The theory developed in this work models experiments in circuit QED, photonic crystals and dielectric waveguides.

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Xue, Xiao, Maximilian Russ, Nodar Samkharadze, Brennan Undseth, Amir Sammak, Giordano Scappucci, and Lieven M. K. Vandersypen. "Quantum logic with spin qubits crossing the surface code threshold." Nature 601, no. 7893 (January 19, 2022): 343–47. http://dx.doi.org/10.1038/s41586-021-04273-w.

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AbstractHigh-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to correct errors faster than they occur1. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code2,3. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology4. Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm5. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices.

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Gennaro, Giuseppe. "Relaxation Due to the Partial Swap Collisions with a Random Reservoir." Open Systems & Information Dynamics 18, no. 04 (December 2011): 353–62. http://dx.doi.org/10.1142/s1230161211000248.

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We analyze the dynamics of the system consisting of a qubit sequentially interacting with a chain of qubits that are initially individually in a pure random state. Each pairwise collision has been modeled as a partial swap transformation. The relaxation to equilibrium of the purity of the system qubit, averaged over all the initial states of the environment, is analytically computed. In particular, we show that the steady state depends on the parameter η of the partial swap transformation. Finally, we investigate aspects of the entanglement dynamics for qubits and show that such process can create typical multipartite entanglement between the system qubit and the qubits of the chain.

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FUJII, TOSHIYUKI, MUNEHIRO NISHIDA, SATOSHI TANDA, and NORIYUKI HATAKENAKA. "TALKING BREATHER QUBITS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4352–64. http://dx.doi.org/10.1142/s0217979209063511.

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Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

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Chao, Rui, Michael E. Beverland, Nicolas Delfosse, and Jeongwan Haah. "Optimization of the surface code design for Majorana-based qubits." Quantum 4 (October 28, 2020): 352. http://dx.doi.org/10.22331/q-2020-10-28-352.

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The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.Here, we present surface code error-correction schemes using only Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds.Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.

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Kumar, Preethika, and Steven R. Skinner. "Universal quantum computing in linear nearest neighbor architectures." Quantum Information and Computation 11, no. 3&4 (March 2011): 300–312. http://dx.doi.org/10.26421/qic11.3-4-8.

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We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.

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XU, PENG, LIE WU, and NIAN-QUAN JIANG. "REALIZATION OF 1 → n CONTROLLED PHASE GATE IN CAVITY QED." International Journal of Quantum Information 09, no. 02 (March 2011): 773–78. http://dx.doi.org/10.1142/s021974991100771x.

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A scheme for realizing a multi-qubit phase gate with one control qubit simultaneously controlling n target qubits in a cavity QED system is proposed. The operation time of the gate is independent of the number n of qubits. The realizability of the gate with current technology is also discussed.

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38

Zakharov, R. K., and E. K. Bashkirov. "Entanglement of two dipole-coupled qubits induced by a thermal field of one-mode lossless cavity with Kerr medium." Journal of Physics: Conference Series 2086, no. 1 (December 1, 2021): 012216. http://dx.doi.org/10.1088/1742-6596/2086/1/012216.

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Abstract We studied the dynamics of two qubits interacting with one-mode thermal quantum electromagnetic field of microwave cavity with Kerr medium. Using the exact solution for considered model we derived the qubit-qubit negativity for separa coherent initial qubits states. We showed that initial qubits coherencee interaction can greatly enhance the degree of qubits entanglement in the presence of the Kerr nonlinearity and dipole-dipole interactionyeven for high thermal field intensities.

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Mohamed, A. B. A., E. M. Khalil, M. F. Yassen, and H. Eleuch. "Two-Qubit Local Fisher Information Correlation beyond Entanglement in a Nonlinear Generalized Cavity with an Intrinsic Decoherence." Entropy 23, no. 3 (March 6, 2021): 311. http://dx.doi.org/10.3390/e23030311.

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In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit–qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit–qubit coupling and the initial coherent cavity states.

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Kamjam, Nattawut, Poramet Pathumsoot, and Areeya Chantasri. "Random-telegraph noise mitigation and qubit decoherence in solid-state experiments." Journal of Physics: Conference Series 2431, no. 1 (January 1, 2023): 012102. http://dx.doi.org/10.1088/1742-6596/2431/1/012102.

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Abstract We investigate the recently proposed theoretical models and algorithms in Song et al. [1] for mitigating decoherence in solid-state qubit systems, where qubits are affected by charge (random telegraph) noises. The model includes a setup of a logical qubit (data qubit) and a spectator qubit, where the latter is used as a probe of the noise. The probe results can be used in correcting the phase error in order to improve the decoherence of the data qubit. In this work, we apply the proposed model with parameters extracted from recent solid-state qubit experiments. We extract parameters such as the noise switching rates, the qubit sensitivities to noise, and the measurement dead time. Using these parameters, we then numerically simulate the data qubit’s phase and the qubit decoherence. We also show that the proposed phase-correction technique using Bayesian estimation can improve the data qubit decoherence significantly.

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41

Tholén, Mats O., Riccardo Borgani, Giuseppe Ruggero Di Carlo, Andreas Bengtsson, Christian Križan, Marina Kudra, Giovanna Tancredi, et al. "Measurement and control of a superconducting quantum processor with a fully integrated radio-frequency system on a chip." Review of Scientific Instruments 93, no. 10 (October 1, 2022): 104711. http://dx.doi.org/10.1063/5.0101398.

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We describe a digital microwave platform called Presto, designed for measurement and control of multiple quantum bits (qubits) and based on the third-generation radio-frequency system on a chip. Presto uses direct digital synthesis to create signals up to 9 GHz on 16 synchronous output ports, while synchronously analyzing responses on 16 input ports. Presto has 16 DC-bias outputs, four inputs and four outputs for digital triggers or markers, and two continuous-wave outputs for synthesizing frequencies up to 15 GHz. Scaling to a large number of qubits is enabled through deterministic synchronization of multiple Presto units. A Python application programming interface configures a firmware for synthesis and analysis of pulses, coordinated by an event sequencer. The analysis integrates template matching (matched filtering) and low-latency (184–254 ns) feedback to enable a wide range of multi-qubit experiments. We demonstrate Presto’s capabilities with experiments on a sample consisting of two superconducting qubits connected via a flux-tunable coupler. We show single-shot readout and active reset of a single qubit; randomized benchmarking of single-qubit gates showing 99.972% fidelity, limited by the coherence time of the qubit; and calibration of a two-qubit iSWAP gate.

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42

Zhang, Meiming, and Naihuan Jing. "Tighter monogamy relations of entanglement measures based on fidelity." Laser Physics Letters 19, no. 8 (July 11, 2022): 085205. http://dx.doi.org/10.1088/1612-202x/ac772e.

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Abstract We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates.

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Bultrini, Daniel, Samson Wang, Piotr Czarnik, Max Hunter Gordon, M. Cerezo, Patrick J. Coles, and Lukasz Cincio. "The battle of clean and dirty qubits in the era of partial error correction." Quantum 7 (July 13, 2023): 1060. http://dx.doi.org/10.22331/q-2023-07-13-1060.

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When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

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Benenti, G., G. Casati, and S. Montangero. "Stability of Quantum Computing in the Presence of Imperfections." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 3932–46. http://dx.doi.org/10.1142/s0217979203021927.

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We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. We show that above a critical inter-qubit coupling strength, quantum chaos sets in and this results in the interaction induced dynamical thermalization and occupation numbers well described by the Fermi–Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. We then construct a quantum algorithm which uses qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more significant than the errors of random noise in gate operations.

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Ferraro, Elena, and Marco De Michielis. "Bandwidth-Limited and Noisy Pulse Sequences for Single Qubit Operations in Semiconductor Spin Qubits." Entropy 21, no. 11 (October 26, 2019): 1042. http://dx.doi.org/10.3390/e21111042.

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Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few devices in the laboratories. In semiconductors, spin qubits can be built confining the spin of electrons in electrostatically defined quantum dots. Through this approach, it is possible to create different implementations: single electron spin qubit, singlet–triplet spin qubit, or a three-electron architecture, e.g., the hybrid qubit. For each qubit type, we study the single qubit rotations along the principal axis of Bloch sphere including the mandatory non-idealities of the control signals that realize the gate operations. The realistic transient of the control signal pulses are obtained by adopting an appropriate low-pass filter function. In addition. the effect of disturbances on the input signals is taken into account by using a Gaussian noise model.

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Militello, Benedetto, and Anna Napoli. "Synchronizing Two Superconducting Qubits through a Dissipating Resonator." Entropy 23, no. 8 (July 31, 2021): 998. http://dx.doi.org/10.3390/e23080998.

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A system consisting of two qubits and a resonator is considered in the presence of different sources of noise, bringing to light the possibility of making the two qubits evolve in a synchronized way. A direct qubit–qubit interaction turns out to be a crucial ingredient, as well as the dissipation processes involving the resonator. The detrimental role of the local dephasing of the qubits is also taken into account.

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47

Song, Gyeongju, Siwoo Eum, Hyeokdong Kwon, Minjoo Sim, Minwoo Lee, and Hwajeong Seo. "Optimized Quantum Circuit for Quantum Security Strength Analysis of Argon2." Electronics 12, no. 21 (October 31, 2023): 4485. http://dx.doi.org/10.3390/electronics12214485.

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This paper explores the optimization of quantum circuits for Argon2, a memory-hard function used in password hashing applications. With the rise of quantum computers, the security of classical cryptographic systems is at risk. This paper emphasizes the need to accurately measure the quantum security strength of cryptographic schemes through highly optimized quantum circuits for the target cryptography algorithm. The proposed method focuses on two perspectives: qubit reduction (qubit-optimized quantum circuit) and depth reduction (depth-optimized quantum circuit). The qubit-optimized quantum circuit was designed to find a point where an appropriate inverse is possible and reuses the qubit through the inverse to minimize the number of qubits. The start and end points of the inverse are determined by identifying a point where qubits can be reused with minimal computation. The depth-optimized quantum circuit reduces the depth of the quantum circuit by using the minimum number of qubits necessary without performing an inverse operation. The trade-off between qubit and depth is confirmed by modifying the internal structure of the circuits and the quantum adders. The qubit optimization achieved up to a 12,229 qubit reduction, while the depth optimization resulted in an approximately 196,741 (approximately 69.02%) depth reduction. In conclusion, this research demonstrates the importance of implementing and analyzing quantum circuits from multiple optimization perspectives. The results contribute to the post-quantum strength analysis of Argon2 and provide valuable insights for future research on optimized quantum circuit design, considering the appropriate trade-offs of quantum resources in response to advancements in quantum computing technology.

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Bagrov, A. R., and E. K. Bashkirov. "Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model." Vestnik of Samara University. Natural Science Series 30, no. 1 (April 24, 2024): 82–95. http://dx.doi.org/10.18287/2541-7525-2024-30-1-82-95.

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In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

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Chiew, Mitchell, and Sergii Strelchuk. "Discovering optimal fermion-qubit mappings through algorithmic enumeration." Quantum 7 (October 18, 2023): 1145. http://dx.doi.org/10.22331/q-2023-10-18-1145.

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Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians.All fermion-qubit mappings must use a numbering scheme for the fermionic modes in order for translation to qubit operations. We make a distinction between the unordered labelling of fermions and the ordered labelling of the qubits. This separation shines light on a new way to design fermion-qubit mappings by making use of the enumeration scheme for the fermionic modes. The purpose of this paper is to demonstrate that this concept permits notions of fermion-qubit mappings that are optimal with regard to any cost function one might choose. Our main example is the minimisation of the average number of Pauli matrices in the Jordan-Wigner transformations of Hamiltonians for fermions interacting in square lattice arrangements. In choosing the best ordering of fermionic modes for the Jordan-Wigner transformation, and unlike other popular modifications, our prescription does not cost additional resources such as ancilla qubits.We demonstrate how Mitchison and Durbin's enumeration pattern minimises the average Pauli weight of Jordan-Wigner transformations of systems interacting in square lattices. This leads to qubit Hamiltonians consisting of terms with average Pauli weights 13.9% shorter than previously known. By adding only two ancilla qubits we introduce a new class of fermion-qubit mappings, and reduce the average Pauli weight of Hamiltonian terms by 37.9% compared to previous methods. For n-mode fermionic systems in cellular arrangements, we find enumeration patterns which result in n1/4 improvement in average Pauli weight over naïve schemes.

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HUO, WEN YI, and GUI LU LONG. "GENERATING QUANTUM ENTANGLEMENT IN SCALABLE SUPERCONDUCTING CHARGE QUBITS." International Journal of Quantum Information 05, no. 06 (December 2007): 829–36. http://dx.doi.org/10.1142/s0219749907003286.

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We propose an efficient scheme to generate quantum entanglement in scalable superconducting charge qubits with a one-dimensional superconducting transmission line resonator (STLR) as data bus. The coupling between qubit and data bus may be turned on and off by controlling the DC gate voltage and externally applied flux of the superconducting charge qubit. In our proposal, the entanglement between two arbitrary qubits and W states of three qubits can be generated quickly and easily.

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Journal articles on the topic 'Qubit'

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