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Quantum Computing in the NISQ Era
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Quantum Computing in the NISQ Era

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 6465

Special Issue Editors

Dr. Xiao Yuan

E-Mail Website
Guest Editor
Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
Interests: quantum computing; quantum information; quantum resource theories
Dr. Xiaoming Zhang

E-Mail Website
Guest Editor
Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
Interests: quantum computing; quantum algorithms; quantum circuit; quantum control; quantum error mitigation; quantum machine learning
Dr. Bálint Koczor

E-Mail Website
Guest Editor
Department of Materials, University of Oxford, Oxford OX1 3PH, UK
Interests: quantum information theory; quantum physics; quantum computing; quantum algorithms; quantum error mitigation

Special Issue Information

Dear Colleagues,

Realizing a universal quantum computer is challenging with the current technology. Before having a fully fledged quantum computer, a more practical question is what we can do with current and near-term quantum hardware, i.e., the noisy-intermediate-scaled-quantum (NISQ) era. Leveraging the idea of hybrid quantum-classical computing, many works have shown the potential of NISQ devices in solving various tasks, such as in chemistry, materials, many-body physics, machine learning, etc. However, owing to the limitations of NISQ hardware, it remains an open problem to realize quantum advantages for practical problems over classical computation methods. On the other hand, new theoretical tools are being demanded for benchmarking the performance and power of NISQ devices, which typically have restricted number of qubits, gate fidelities and connectivity.

This Special Issue will focus on recent theoretical and experimental developments of quantum computing in the NISQ era. This Special Issue will accept unpublished original papers and comprehensive reviews focused on (but not restricted to) the following research areas:

  • Design of more efficient variational quantum algorithms;
  • Analysis of the performance of hybrid quantum-classical algorithms;
  • Theoretical tools for studying the expressivity of ansatz and trainability of variational quantum algorithms;
  • Applications of quantum algorithms for chemistry, materials, and other physics problems;
  • Applications of quantum algorithms in machine learning, combinatorial problems, and other problems beyond physics;
  • Quantum error mitigation;
  • Quantum error correction;
  • Benchmarking the performance and power of NISQ devices;
  • Experimental realization of variational quantum algorithms.

Dr. Xiao Yuan
Dr. Xiaoming Zhang
Dr. Bálint Koczor
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum computing
  • noisy intermediate-scale quantum
  • variational quantum simulation
  • quantum computational chemistry
  • quantum materials
  • quantum error mitigation
  • quantum error correction

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Published Papers (6 papers)

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Research

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30 pages, 5446 KiB  
Article
On the Exploration of Quantum Polar Stabilizer Codes and Quantum Stabilizer Codes with High Coding Rate
by Zhengzhong Yi, Zhipeng Liang, Yulin Wu and Xuan Wang
Entropy 2024, 26(10), 818; https://doi.org/10.3390/e26100818 - 25 Sep 2024
Viewed by 471
Abstract
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that [...] Read more.
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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19 pages, 991 KiB  
Article
Effect of Pure Dephasing Quantum Noise in the Quantum Search Algorithm Using Atos Quantum Assembly
by Maria Heloísa Fraga da Silva, Gleydson Fernandes de Jesus and Clebson Cruz
Entropy 2024, 26(8), 668; https://doi.org/10.3390/e26080668 - 6 Aug 2024
Viewed by 737
Abstract
Quantum computing is tipped to lead the future of global technological progress. However, the obstacles related to quantum software development are an actual challenge to overcome. In this scenario, this work presents an implementation of the quantum search algorithm in Atos Quantum Assembly [...] Read more.
Quantum computing is tipped to lead the future of global technological progress. However, the obstacles related to quantum software development are an actual challenge to overcome. In this scenario, this work presents an implementation of the quantum search algorithm in Atos Quantum Assembly Language (AQASM) using the quantum software stack my Quantum Learning Machine (myQLM) and the programming development platform Quantum Learning Machine (QLM). We present the creation of a virtual quantum processor whose configurable architecture allows the analysis of induced quantum noise effects on the quantum algorithms. The codes are available throughout the manuscript so that readers can replicate them and apply the methods discussed in this article to solve their own quantum computing projects. The presented results are consistent with theoretical predictions and demonstrate that AQASM and QLM are powerful tools for building, implementing, and simulating quantum hardware. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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20 pages, 931 KiB  
Article
Synergistic Dynamical Decoupling and Circuit Design for Enhanced Algorithm Performance on Near-Term Quantum Devices
by Yanjun Ji and Ilia Polian
Entropy 2024, 26(7), 586; https://doi.org/10.3390/e26070586 - 10 Jul 2024
Viewed by 736
Abstract
Dynamical decoupling (DD) is a promising technique for mitigating errors in near-term quantum devices. However, its effectiveness depends on both hardware characteristics and algorithm implementation details. This paper explores the synergistic effects of dynamical decoupling and optimized circuit design in maximizing the performance [...] Read more.
Dynamical decoupling (DD) is a promising technique for mitigating errors in near-term quantum devices. However, its effectiveness depends on both hardware characteristics and algorithm implementation details. This paper explores the synergistic effects of dynamical decoupling and optimized circuit design in maximizing the performance and robustness of algorithms on near-term quantum devices. By utilizing eight IBM quantum devices, we analyze how hardware features and algorithm design impact the effectiveness of DD for error mitigation. Our analysis takes into account factors such as circuit fidelity, scheduling duration, and hardware-native gate set. We also examine the influence of algorithmic implementation details, including specific gate decompositions, DD sequences, and optimization levels. The results reveal an inverse relationship between the effectiveness of DD and the inherent performance of the algorithm. Furthermore, we emphasize the importance of gate directionality and circuit symmetry in improving performance. This study offers valuable insights for optimizing DD protocols and circuit designs, highlighting the significance of a holistic approach that leverages both hardware features and algorithm design for the high-quality and reliable execution of near-term quantum algorithms. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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17 pages, 1472 KiB  
Article
Hybrid Classical–Quantum Branch-and-Bound Algorithm for Solving Integer Linear Problems
by Claudio Sanavio, Edoardo Tignone and Elisa Ercolessi
Entropy 2024, 26(4), 345; https://doi.org/10.3390/e26040345 - 19 Apr 2024
Viewed by 1107
Abstract
Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the [...] Read more.
Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. The results are obtained using the commercially available quantum hardware D-Wave Advantage, and they outline the strategy for a practical application of the quantum annealers. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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28 pages, 558 KiB  
Article
Leakage Benchmarking for Universal Gate Sets
by Bujiao Wu, Xiaoyang Wang, Xiao Yuan, Cupjin Huang and Jianxin Chen
Entropy 2024, 26(1), 71; https://doi.org/10.3390/e26010071 - 13 Jan 2024
Cited by 1 | Viewed by 1201
Abstract
Errors are common issues in quantum computing platforms, among which leakage is one of the most-challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult [...] Read more.
Errors are common issues in quantum computing platforms, among which leakage is one of the most-challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult to detect and correct than errors that preserve the computational subspace. As a result, leakage presents a significant obstacle to the development of fault-tolerant quantum computation. In this paper, we propose an efficient and accurate benchmarking framework called leakage randomized benchmarking (LRB), for measuring leakage rates on multi-qubit quantum systems. Our approach is more insensitive to state preparation and measurement (SPAM) noise than existing leakage benchmarking protocols, requires fewer assumptions about the gate set itself, and can be used to benchmark multi-qubit leakages, which has not been achieved previously. We also extended the LRB protocol to an interleaved variant called interleaved LRB (iLRB), which can benchmark the average leakage rate of generic n-site quantum gates with reasonable noise assumptions. We demonstrate the iLRB protocol on benchmarking generic two-qubit gates realized using flux tuning and analyzed the behavior of iLRB under corresponding leakage models. Our numerical experiments showed good agreement with the theoretical estimations, indicating the feasibility of both the LRB and iLRB protocols. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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Review

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26 pages, 5970 KiB  
Review
Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
by Yunyan Yao and Liang Xiang
Entropy 2024, 26(7), 592; https://doi.org/10.3390/e26070592 - 11 Jul 2024
Viewed by 1133
Abstract
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building [...] Read more.
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems. Full article
(This article belongs to the Special Issue Quantum Computing in the NISQ Era)
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