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Advances in Quantum Computing

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

Deadline for manuscript submissions: closed (15 September 2023) | Viewed by 48000

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Special Issue Editors

Applied Research Laboratories, The University of Texas at Austin, Austin, TX 78758, USA
Interests: quantum information science; quantum optics; quantum-inspired technologies; quantum foundations; signal and information processing; underwater acoustics
Dipartimento di Scienza e Alta Tecnologia, Università degli studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
Interests: thermoelectric transport; heat transport and thermal rectifiers; far from equilibrium quantum systems; quantum computation and quantum information; open quantum systems; many-body quantum systems; disordered systems; nonlinear and complex systems

Special Issue Information

Dear Colleagues,

The field of quantum information science has seen tremendous progress over the last several years, with advances in both hardware development and novel algorithms. Already, there have been several claims to the demonstration of quantum computational advantage, in both matter-based and photonic devices, and new large-scale systems promise to soon provide a practical advantage over classical digital processors in real-world applications.  Nevertheless, some of the early demonstrations of quantum advantage have more recently been challenged by new classical methods that can mimic the noisy and imprecise nature of realistic quantum devices. The future viability of quantum computers now appears to rely on demonstrating two key features: (1) that they are fundamentally distinct and more capable than classical devices, and (2) that they are practically scalable in the number of qubits.

This Special Issue focuses on the recent advances, and challenges, in developing large-scale, fault-tolerant quantum computers capable of solving tomorrow’s growing computational needs. Original unpublished papers and review articles are invited on the following topics: (1) advances in quantum computing hardware, (2) novel quantum and hybrid algorithms, (3) applications to real-world problems using noisy, intermediate-scale quantum devices, (4) quantum networks and distributed quantum computing, (5) classical challenges to demonstrations of quantum advantage, and (6) investigations into the scalability of different quantum hardware architectures.

Dr. Brian R. La Cour
Dr. Giuliano Benenti
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
  • quantum networks
  • dequantization
  • quantum advantage
  • nisq device
  • quantum mechanics
  • physics
  • algorithms
  • hardware
  • scalability

Published Papers (25 papers)

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Editorial

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4 pages, 194 KiB  
Editorial
Advances in Quantum Computing
by Brian La Cour
Entropy 2023, 25(12), 1633; https://doi.org/10.3390/e25121633 - 08 Dec 2023
Viewed by 1253
Abstract
Advances in quantum computing have continued to accelerate over the course of this Special Issue’s publication [...] Full article
(This article belongs to the Special Issue Advances in Quantum Computing)

Research

Jump to: Editorial

21 pages, 3087 KiB  
Article
Generalized Quantum Convolution for Multidimensional Data
by Mingyoung Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Muhammad Momin Rahman and Esam El-Araby
Entropy 2023, 25(11), 1503; https://doi.org/10.3390/e25111503 - 31 Oct 2023
Viewed by 1004
Abstract
The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by [...] Read more.
The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by the application of filters with data strides that are equal to the filter window sizes. One challenge with these implementations is preserving the spatial and temporal localities of the input features, specifically for data with higher dimensions. In addition, the deep circuits required to perform quantum convolution with a unity stride, especially for multidimensional data, increase the risk of violating decoherence constraints. In this work, we propose depth-optimized circuits for performing generalized multidimensional quantum convolution operations with unity stride targeting applications that process data with high dimensions, such as hyperspectral imagery and remote sensing. We experimentally evaluate and demonstrate the applicability of the proposed techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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44 pages, 8892 KiB  
Article
Principal Component Analysis and t-Distributed Stochastic Neighbor Embedding Analysis in the Study of Quantum Approximate Optimization Algorithm Entangled and Non-Entangled Mixing Operators
by Brian García Sarmina, Guo-Hua Sun and Shi-Hai Dong
Entropy 2023, 25(11), 1499; https://doi.org/10.3390/e25111499 - 30 Oct 2023
Cited by 1 | Viewed by 969
Abstract
In this paper, we employ PCA and t-SNE analyses to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at various depths. We utilize a dataset containing optimized parameters generated for max-cut problems [...] Read more.
In this paper, we employ PCA and t-SNE analyses to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at various depths. We utilize a dataset containing optimized parameters generated for max-cut problems with cyclic and complete configurations. This dataset encompasses the resulting RZ, RX, and RY parameters for QAOA models at different depths (1L, 2L, and 3L) with or without an entanglement stage within the mixing operator. Our findings reveal distinct behaviors when processing the different parameters with PCA and t-SNE. Specifically, most of the entangled QAOA models demonstrate an enhanced capacity to preserve information in the mapping, along with a greater level of correlated information detectable by PCA and t-SNE. Analyzing the overall mapping results, a clear differentiation emerges between entangled and non-entangled models. This distinction is quantified numerically through explained variance in PCA and Kullback–Leibler divergence (post-optimization) in t-SNE. These disparities are also visually evident in the mapping data produced by both methods, with certain entangled QAOA models displaying clustering effects in both visualization techniques. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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15 pages, 597 KiB  
Article
Quantum Honeypots
by Naya Nagy, Marius Nagy, Ghadeer Alazman, Zahra Hawaidi, Saja Mustafa Alsulaibikh, Layla Alabbad, Sadeem Alfaleh and Areej Aljuaid
Entropy 2023, 25(10), 1461; https://doi.org/10.3390/e25101461 - 18 Oct 2023
Viewed by 958
Abstract
Quantum computation offers unique properties that cannot be paralleled by conventional computers. In particular, reading qubits may change their state and thus signal the presence of an intruder. This paper develops a proof-of-concept for a quantum honeypot that allows the detection of intruders [...] Read more.
Quantum computation offers unique properties that cannot be paralleled by conventional computers. In particular, reading qubits may change their state and thus signal the presence of an intruder. This paper develops a proof-of-concept for a quantum honeypot that allows the detection of intruders on reading. The idea is to place quantum sentinels within all resources offered within the honeypot. Additional to classical honeypots, honeypots with quantum sentinels can trace the reading activity of the intruder within any resource. Sentinels can be set to be either visible and accessible to the intruder or hidden and unknown to intruders. Catching the intruder using quantum sentinels has a low theoretical probability per sentinel, but the probability can be increased arbitrarily higher by adding more sentinels. The main contributions of this paper are that the monitoring of the intruder can be carried out at the level of the information unit, such as the bit, and quantum monitoring activity is fully hidden from the intruder. Practical experiments, as performed in this research, show that the error rate of quantum computers has to be considerably reduced before implementations of this concept are feasible. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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13 pages, 397 KiB  
Article
Quantum-Walk-Inspired Dynamic Adiabatic Local Search
by Chen-Fu Chiang and Paul M. Alsing
Entropy 2023, 25(9), 1287; https://doi.org/10.3390/e25091287 - 31 Aug 2023
Viewed by 747
Abstract
We investigate the irreconcilability issue that arises when translating the search algorithm from the Continuous Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along the same path as the CTQW, it requires a [...] Read more.
We investigate the irreconcilability issue that arises when translating the search algorithm from the Continuous Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along the same path as the CTQW, it requires a constant energy gap in the Hamiltonian throughout the AQC schedule. To resolve the constant gap issue, we modify the CTQW-inspired AQC catalyst Hamiltonian from an XZ operator to a Z oracle operator. Through simulation, we demonstrate that the total running time for the proposed approach for AQC with the modified catalyst Hamiltonian remains optimal as CTQW. Inspired by this solution, we further investigate adaptive scheduling for the catalyst Hamiltonian and its coefficient function in the adiabatic path of Grover-inspired AQC to improve the adiabatic local search. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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24 pages, 2366 KiB  
Article
A Quantum Genetic Algorithm for Building a Semantic Textual Similarity Estimation Framework for Plagiarism Detection Applications
by Saad M. Darwish, Ibrahim Abdullah Mhaimeed and Adel A. Elzoghabi
Entropy 2023, 25(9), 1271; https://doi.org/10.3390/e25091271 - 29 Aug 2023
Viewed by 1235
Abstract
The majority of the recent research on text similarity has been focused on machine learning strategies to combat the problem in the educational environment. When the originality of an idea is copied, it increases the difficulty of using a plagiarism detection system in [...] Read more.
The majority of the recent research on text similarity has been focused on machine learning strategies to combat the problem in the educational environment. When the originality of an idea is copied, it increases the difficulty of using a plagiarism detection system in practice, and the system fails. In cases like active-to-passive conversion, phrase structure changes, synonym substitution, and sentence reordering, the present approaches may not be adequate for plagiarism detection. In this article, semantic extraction and the quantum genetic algorithm (QGA) are integrated in a unified framework to identify idea plagiarism with the aim of enhancing the performance of existing methods in terms of detection accuracy and computational time. Semantic similarity measures, which use the WordNet database to extract semantic information, are used to capture a document’s idea. In addition, the QGA is adapted to identify the interconnected, cohesive sentences that effectively convey the source document’s main idea. QGAs are formulated using the quantum computing paradigm based on qubits and the superposition of states. By using the qubit chromosome as a representation rather than the more traditional binary, numeric, or symbolic representations, the QGA is able to express a linear superposition of solutions with the aim of increasing gene diversity. Due to its fast convergence and strong global search capacity, the QGA is well suited for a parallel structure. The proposed model has been assessed using a PAN 13-14 dataset, and the result indicates the model’s ability to achieve significant detection improvement over some of the compared models. The recommended PD model achieves an approximately 20%, 15%, and 10% increase for TPR, PPV, and F-Score compared to GA and hierarchical GA (HGA)-based PD methods, respectively. Furthermore, the accuracy rate rises by approximately 10–15% for each increase in the number of samples in the dataset. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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21 pages, 1341 KiB  
Article
Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem
by Wenyang Qian, Robert A. M. Basili, Mary Mehrnoosh Eshaghian-Wilner, Ashfaq Khokhar, Glenn Luecke and James P. Vary
Entropy 2023, 25(8), 1238; https://doi.org/10.3390/e25081238 - 21 Aug 2023
Cited by 2 | Viewed by 1321
Abstract
The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the [...] Read more.
The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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9 pages, 419 KiB  
Article
Asymmetric Measurement-Device-Independent Quantum Key Distribution through Advantage Distillation
by Kailu Zhang, Jingyang Liu, Huajian Ding, Xingyu Zhou, Chunhui Zhang and Qin Wang
Entropy 2023, 25(8), 1174; https://doi.org/10.3390/e25081174 - 07 Aug 2023
Cited by 1 | Viewed by 1152
Abstract
Measurement-device-independent quantum key distribution (MDI-QKD) completely closes the security loopholes caused by the imperfection of devices at the detection terminal. Commonly, a symmetric MDI-QKD model is widely used in simulations and experiments. This scenario is far from a real quantum network, where the [...] Read more.
Measurement-device-independent quantum key distribution (MDI-QKD) completely closes the security loopholes caused by the imperfection of devices at the detection terminal. Commonly, a symmetric MDI-QKD model is widely used in simulations and experiments. This scenario is far from a real quantum network, where the losses of channels connecting each user are quite different. To adapt such a feature, an asymmetric MDI-QKD model is proposed. How to improve the performance of asymmetric MDI-QKD also becomes an important research direction. In this work, an advantage distillation (AD) method is applied to further improve the performance of asymmetric MDI-QKD without changing the original system structure. Simulation results show that the AD method can improve the secret key rate and transmission distance, especially in the highly asymmetric cases. Therefore, this scheme will greatly promote the development of future MDI-QKD networks. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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32 pages, 1786 KiB  
Article
On the Applicability of Quantum Machine Learning
by Sebastian Raubitzek and Kevin Mallinger
Entropy 2023, 25(7), 992; https://doi.org/10.3390/e25070992 - 28 Jun 2023
Viewed by 1683
Abstract
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these [...] Read more.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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16 pages, 25106 KiB  
Article
Quantum Image Encryption Based on Quantum DNA Codec and Pixel-Level Scrambling
by Jie Gao, Yinuo Wang, Zhaoyang Song and Shumei Wang
Entropy 2023, 25(6), 865; https://doi.org/10.3390/e25060865 - 29 May 2023
Cited by 5 | Viewed by 1694
Abstract
In order to increase the security and robustness of quantum images, this study combined the quantum DNA codec with quantum Hilbert scrambling to offer an enhanced quantum image encryption technique. Initially, to accomplish pixel-level diffusion and create enough key space for the picture, [...] Read more.
In order to increase the security and robustness of quantum images, this study combined the quantum DNA codec with quantum Hilbert scrambling to offer an enhanced quantum image encryption technique. Initially, to accomplish pixel-level diffusion and create enough key space for the picture, a quantum DNA codec was created to encode and decode the pixel color information of the quantum image using its special biological properties. Second, we used quantum Hilbert scrambling to muddle the image position data in order to double the encryption effect. In order to enhance the encryption effect, the altered picture was then employed as a key matrix in a quantum XOR operation with the original image. The inverse transformation of the encryption procedure may be used to decrypt the picture since all the quantum operations employed in this research are reversible. The two-dimensional optical image encryption technique presented in this study may significantly strengthen the anti-attack of quantum picture, according to experimental simulation and result analysis. The correlation chart demonstrates that the average information entropy of the RGB three channels is more than 7.999, the average NPCR and UACI are respectively 99.61% and 33.42%, and the peak value of the ciphertext picture histogram is uniform. It offers more security and robustness than earlier algorithms and can withstand statistical analysis and differential assaults. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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13 pages, 1282 KiB  
Article
Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets
by Manuel John, Julian Schuhmacher, Panagiotis Barkoutsos, Ivano Tavernelli and Francesco Tacchino
Entropy 2023, 25(6), 860; https://doi.org/10.3390/e25060860 - 27 May 2023
Cited by 1 | Viewed by 1568
Abstract
The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in [...] Read more.
The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects—hindering the trainability of quantum classifiers—have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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15 pages, 2756 KiB  
Article
Link Prediction with Continuous-Time Classical and Quantum Walks
by Mark Goldsmith, Harto Saarinen, Guillermo García-Pérez, Joonas Malmi, Matteo A. C. Rossi and Sabrina Maniscalco
Entropy 2023, 25(5), 730; https://doi.org/10.3390/e25050730 - 28 Apr 2023
Cited by 3 | Viewed by 1283
Abstract
Protein–protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism, and they form the basis for the field of network medicine. Since the biophysical and high-throughput methods used to form PPI networks are expensive, time-consuming, and [...] Read more.
Protein–protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism, and they form the basis for the field of network medicine. Since the biophysical and high-throughput methods used to form PPI networks are expensive, time-consuming, and often contain inaccuracies, the resulting networks are usually incomplete. In order to infer missing interactions in these networks, we propose a novel class of link prediction methods based on continuous-time classical and quantum walks. In the case of quantum walks, we examine the usage of both the network adjacency and Laplacian matrices for specifying the walk dynamics. We define a score function based on the corresponding transition probabilities and perform tests on six real-world PPI datasets. Our results show that continuous-time classical random walks and quantum walks using the network adjacency matrix can successfully predict missing protein–protein interactions, with performance rivalling the state-of-the-art. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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13 pages, 965 KiB  
Article
Generation of Pseudo-Random Quantum States on Actual Quantum Processors
by Gabriele Cenedese, Maria Bondani, Dario Rosa and Giuliano Benenti
Entropy 2023, 25(4), 607; https://doi.org/10.3390/e25040607 - 03 Apr 2023
Cited by 2 | Viewed by 1521
Abstract
The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of multipartite entanglement is nearly maximal. [...] Read more.
The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of multipartite entanglement is nearly maximal. We argue that the method is optimal, and use it to benchmark actual superconducting (IBM’s ibm_lagos) and ion trap (IonQ’s Harmony) quantum processors. Despite the fact that ibm_lagos has lower single-qubit and two-qubit error rates, the overall performance of Harmony is better thanks to its low error rate in state preparation and measurement and to the all-to-all connectivity of qubits. Our result highlights the relevance of the qubits network architecture to generate highly entangled states. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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14 pages, 655 KiB  
Article
A More General Quantum Credit Risk Analysis Framework
by Emanuele Dri, Antonello Aita, Edoardo Giusto, Davide Ricossa, Davide Corbelletto, Bartolomeo Montrucchio and Roberto Ugoccioni
Entropy 2023, 25(4), 593; https://doi.org/10.3390/e25040593 - 31 Mar 2023
Cited by 1 | Viewed by 3102
Abstract
Credit risk analysis (CRA) quantum algorithms aim at providing a quadratic speedup over classical analogous methods. Despite this, experts in the business domain have identified significant limitations in the existing approaches. Thus, we proposed a new variant of the CRA quantum algorithm to [...] Read more.
Credit risk analysis (CRA) quantum algorithms aim at providing a quadratic speedup over classical analogous methods. Despite this, experts in the business domain have identified significant limitations in the existing approaches. Thus, we proposed a new variant of the CRA quantum algorithm to address these limitations. In particular, we improved the risk model for each asset in a portfolio by enabling it to consider multiple systemic risk factors, resulting in a more realistic and complex model for each asset’s default probability. Additionally, we increased the flexibility of the loss-given-default input by removing the constraint of using only integer values, enabling the use of real data from the financial sector to establish fair benchmarking protocols. Furthermore, all proposed enhancements were tested both through classical simulation of quantum hardware and, for this new version of our work, also using QPUs from IBM Quantum Experience in order to provide a baseline for future research. Our proposed variant of the CRA quantum algorithm addresses the significant limitations of the current approach and highlights an increased cost in terms of circuit depth and width. In addition, it provides a path to a substantially more realistic software solution. Indeed, as quantum technology progresses, the proposed improvements will enable meaningful scales and useful results for the financial sector. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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22 pages, 4492 KiB  
Article
A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods
by Corey Jason Trahan, Mark Loveland, Noah Davis and Elizabeth Ellison
Entropy 2023, 25(4), 580; https://doi.org/10.3390/e25040580 - 28 Mar 2023
Cited by 3 | Viewed by 2103
Abstract
Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively [...] Read more.
Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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19 pages, 678 KiB  
Article
Dynamic Asset Allocation with Expected Shortfall via Quantum Annealing
by Hanjing Xu, Samudra Dasgupta, Alex Pothen and Arnab Banerjee
Entropy 2023, 25(3), 541; https://doi.org/10.3390/e25030541 - 21 Mar 2023
Cited by 1 | Viewed by 1706
Abstract
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem where a target return and a target [...] Read more.
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem where a target return and a target risk metric (expected shortfall) are specified. We propose an iterative algorithm that treats the target return as a constraint in a Markowitz portfolio optimization model, and dynamically adjusts the target return to satisfy the targeted expected shortfall. The Markowitz optimization is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The use of the expected shortfall risk metric enables the modeling of extreme market events. We compare the results from D-Wave’s 2000Q and Advantage quantum annealers using real-world financial data. Both quantum annealers are able to generate portfolios with more than 80% of the return of the classical optimal solutions, while satisfying the expected shortfall. We observe that experiments on assets with higher correlations tend to perform better, which may help to design practical quantum applications in the near term. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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32 pages, 2388 KiB  
Article
Quantum Annealing in the NISQ Era: Railway Conflict Management
by Krzysztof Domino, Mátyás Koniorczyk, Krzysztof Krawiec, Konrad Jałowiecki, Sebastian Deffner and Bartłomiej Gardas
Entropy 2023, 25(2), 191; https://doi.org/10.3390/e25020191 - 18 Jan 2023
Cited by 13 | Viewed by 3424
Abstract
We are in the noisy intermediate-scale quantum (NISQ) devices’ era, in which quantum hardware has become available for application in real-world problems. However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching [...] Read more.
We are in the noisy intermediate-scale quantum (NISQ) devices’ era, in which quantum hardware has become available for application in real-world problems. However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the train dispatching consequences of the arrival of an already delayed train to a given network segment. This problem is computationally hard and needs to be solved almost in real time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, which is compatible with the emerging quantum annealing technology. The model’s instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including the conventional solution of a linear integer version of the model as well as the solution of the QUBO model using a tensor network-based algorithm. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) does not perform well on those instances, either. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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12 pages, 1458 KiB  
Article
An Enhanced Quantum K-Nearest Neighbor Classification Algorithm Based on Polar Distance
by Congcong Feng, Bo Zhao, Xin Zhou, Xiaodong Ding and Zheng Shan
Entropy 2023, 25(1), 127; https://doi.org/10.3390/e25010127 - 08 Jan 2023
Cited by 8 | Viewed by 3189
Abstract
The K-nearest neighbor (KNN) algorithm is one of the most extensively used classification algorithms, while its high time complexity limits its performance in the era of big data. The quantum K-nearest neighbor (QKNN) algorithm can handle the above problem with satisfactory efficiency; however, [...] Read more.
The K-nearest neighbor (KNN) algorithm is one of the most extensively used classification algorithms, while its high time complexity limits its performance in the era of big data. The quantum K-nearest neighbor (QKNN) algorithm can handle the above problem with satisfactory efficiency; however, its accuracy is sacrificed when directly applying the traditional similarity measure based on Euclidean distance. Inspired by the Polar coordinate system and the quantum property, this work proposes a new similarity measure to replace the Euclidean distance, which is defined as Polar distance. Polar distance considers both angular and module length information, introducing a weight parameter adjusted to the specific application data. To validate the efficiency of Polar distance, we conducted various experiments using several typical datasets. For the conventional KNN algorithm, the accuracy performance is comparable when using Polar distance for similarity measurement, while for the QKNN algorithm, it significantly outperforms the Euclidean distance in terms of classification accuracy. Furthermore, the Polar distance shows scalability and robustness superior to the Euclidean distance, providing an opportunity for the large-scale application of QKNN in practice. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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12 pages, 296 KiB  
Article
Entanglement-Assisted Quantum Codes from Cyclic Codes
by Francisco Revson F. Pereira and Stefano Mancini
Entropy 2023, 25(1), 37; https://doi.org/10.3390/e25010037 - 24 Dec 2022
Cited by 9 | Viewed by 1356
Abstract
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes [...] Read more.
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes from cyclic codes. Afterwards, the method is applied to Reed–Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of EAQEC codes. Three families have been created: two families of EAQEC codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
18 pages, 1854 KiB  
Article
Binary Classification Quantum Neural Network Model Based on Optimized Grover Algorithm
by Wenlin Zhao, Yinuo Wang, Yingjie Qu, Hongyang Ma and Shumei Wang
Entropy 2022, 24(12), 1783; https://doi.org/10.3390/e24121783 - 06 Dec 2022
Cited by 3 | Viewed by 2050
Abstract
We focus on the problem that the Grover algorithm is not suitable for the completely unknown proportion of target solutions. Considering whether the existing quantum classifier used by the current quantum neural network (QNN) to complete the classification task can solve the problem [...] Read more.
We focus on the problem that the Grover algorithm is not suitable for the completely unknown proportion of target solutions. Considering whether the existing quantum classifier used by the current quantum neural network (QNN) to complete the classification task can solve the problem of the classical classifier, this paper proposes a binary quantum neural network classifical model based on an optimized Grover algorithm based on partial diffusion. Trial and error is adopted to extend the partial diffusion quantum search algorithm with the known proportion of target solutions to the unknown state, and to apply the characteristics of the supervised learning of the quantum neural network to binary classify the classified data. Experiments show that the proposed method can effectively retrieve quantum states with similar features. The test accuracy of BQM retrieval under the depolarization noise at the 20th period can reach 97% when the depolarization rate is 0.1. It improves the retrieval accuracy by about 4% and 10% compared with MSE and BCE in the same environment. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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13 pages, 841 KiB  
Article
Quantum Spatial Search with Electric Potential: Long-Time Dynamics and Robustness to Noise
by Thibault Fredon, Julien Zylberman, Pablo Arnault and Fabrice Debbasch
Entropy 2022, 24(12), 1778; https://doi.org/10.3390/e24121778 - 05 Dec 2022
Cited by 2 | Viewed by 1408
Abstract
We present various results on the scheme introduced in a previous work, which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field centered on the [...] Read more.
We present various results on the scheme introduced in a previous work, which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field centered on the the node to be found. In such a walk, the electric term acts as the oracle of the algorithm, and the free walk (i.e., without electric term) acts as the “diffusion” part, as it is called in Grover’s algorithm. The results are the following. First, we run long time simulations of this electric Dirac DQW, and observe that there is a second localization peak around the node marked by the oracle, reached in a time O(N), where N is the number of nodes of the 2D grid, with a localization probability scaling as O(1/lnN). This matches the state-of-the-art 2D-DQW search algorithms before amplitude amplification We then study the effect of adding noise on the Coulomb potential, and observe that the walk, especially the second localization peak, is highly robust to spatial noise, more modestly robust to spatiotemporal noise, and that the first localization peak is even highly robust to spatiotemporal noise. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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34 pages, 5152 KiB  
Article
Multi-Qubit Bose–Einstein Condensate Trap for Atomic Boson Sampling
by Sergey Tarasov, William Shannon, Vladimir Kocharovsky and Vitaly Kocharovsky
Entropy 2022, 24(12), 1771; https://doi.org/10.3390/e24121771 - 03 Dec 2022
Cited by 3 | Viewed by 1879
Abstract
We propose a multi-qubit Bose–Einstein-condensate (BEC) trap as a platform for studies of quantum statistical phenomena in many-body interacting systems. In particular, it could facilitate testing atomic boson sampling of the excited-state occupations and its quantum advantage over classical computing in a full, [...] Read more.
We propose a multi-qubit Bose–Einstein-condensate (BEC) trap as a platform for studies of quantum statistical phenomena in many-body interacting systems. In particular, it could facilitate testing atomic boson sampling of the excited-state occupations and its quantum advantage over classical computing in a full, controllable and clear way. Contrary to a linear interferometer enabling Gaussian boson sampling of non-interacting non-equilibrium photons, the BEC trap platform pertains to an interacting equilibrium many-body system of atoms. We discuss a basic model and the main features of such a multi-qubit BEC trap. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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20 pages, 658 KiB  
Article
Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics
by Andreas Burger, Leong Chuan Kwek and Dario Poletti
Entropy 2022, 24(12), 1766; https://doi.org/10.3390/e24121766 - 02 Dec 2022
Cited by 4 | Viewed by 2354
Abstract
Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an [...] Read more.
Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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24 pages, 9222 KiB  
Article
Quantum Algorithm for Variant Maximum Satisfiability
by Abdirahman Alasow, Peter Jin and Marek Perkowski
Entropy 2022, 24(11), 1615; https://doi.org/10.3390/e24111615 - 05 Nov 2022
Cited by 1 | Viewed by 1977
Abstract
In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying [...] Read more.
In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to log2T+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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16 pages, 616 KiB  
Article
Using Variational Quantum Algorithm to Solve the LWE Problem
by Lihui Lv, Bao Yan, Hong Wang, Zhi Ma, Yangyang Fei, Xiangdong Meng and Qianheng Duan
Entropy 2022, 24(10), 1428; https://doi.org/10.3390/e24101428 - 08 Oct 2022
Cited by 1 | Viewed by 2102
Abstract
The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms [...] Read more.
The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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