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Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counter-diabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model's relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era. [ABSTRACT FROM AUTHOR]

Quantum phenomena, including entanglement, superposition, tunneling, and spin-orbit interactions, among others, are foundational to the development of recent innovations in quantum computing, teleportation, encryption, sensing, and new modalities of electronics, such as spintronics, spinorbitronics, caloritronics, magnonics, twistronics, and valleytronics. These emerging technologies provide disruptive influences to global commercial markets. These remarkable advances in quantum technologies are nearly always enabled by the discovery of materials and their quantum behaviors. Such advances are governed by quantum principles that are strongly influenced by environmental, physical, topological, and morphological conditions such as very small length scales, short time durations, ultrahigh pressures, ultralow temperatures, etc., which lead to quantum behaviors that manifest as quantum tunneling, entanglement, superpositioning, superfluidity, low-dimensional, high-temperature and high-pressure superconductivity, quantum fluctuations, Bose-Einstein condensates, topological effects, and other phenomena that are not yet fully understood nor adequately explored. Here, we provide a review of quantum materials developed up to 2023. Remarkable advances in quantum materials occur daily, and therefore, by the time of publication, new and exciting breakthroughs will have occurred that are regrettably not covered herein. [ABSTRACT FROM AUTHOR]

Quantum Computing has emerged as a promising alternative, utilising quantum mechanics for faster computations. This paper explores the nearest neighbour compliance (NNC) Problem in Gate-based Quantum Computers, where quantum gates are constrained to operate on physically adjacent qubits. The NNC problem aims to optimise the insertion of SWAP-gates to ensure compliance with these constraints while minimising their count. This work introduces Quantum Annealing to tackle the NNC problem, proposing two Quadratic Unconstrained Optimisation Problem formulations. The formulations are tested on a contemporary Quantum Annealer, and their performance is compared with previous methods. It shows that the prospect of using Quantum Annealing is promising, however, the current state of the hardware makes that finding the embedding is the limiting factor. [ABSTRACT FROM AUTHOR]

Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave's Advantage™ quantum annealer, Fujitsu's digital annealer V3, D-Wave's quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms. [ABSTRACT FROM AUTHOR]

High-value payment systems (HVPSs) are typically liquidity intensive because payments are settled on a gross basis. State-of-the-art solutions to this problem include algorithms that seek netting sets and allow for ad hoc reordering of submitted payments. This paper introduces a new algorithm that explores the entire space of payments reordering to improve the liquidity efficiency of these systems without significantly increasing payment delays. Finding the optimal payment order among the entire space of reorderings is, however, an NP-hard combinatorial optimization problem. We solve this problem using a hybrid quantum annealing algorithm. Despite the limitations in size and speed of today's quantum computers, our algorithm provides quantifiable liquidity savings when applied to the Canadian HVPS using a 30-day sample of transaction data. By reordering batches of 70 payments, we achieve an average of Canadian (C) $240 million in daily liquidity savings, with a settlement delay of approximately 90 seconds. For a few days in the sample, the liquidity savings exceed C$1 billion. Compared with classical computing and with current algorithms in HVPS, our quantum algorithm offers larger liquidity savings, and it offers more reliable and consistent solutions, particularly under time constraints. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.00314. [ABSTRACT FROM AUTHOR]

Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric optimization problem of scheduling Automatic Guided Vehicles (AGVs). Some solvers can already leverage noisy intermediate-scale quantum (NISQ) devices. In our study, we utilize D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit. This hybrid methodology performs comparably to existing classical solvers. However, due to the proprietary nature of the software, the precise contribution of quantum computation remains unclear. Our analysis focuses on a practical, business-oriented scenario: scheduling AGVs within a factory constrained by limited space, simulating a realistic production setting. Our approach maps a realistic AGVs problem onto one reminiscent of railway scheduling and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable. The main idea here is to highlight the potential usefulness of a hybrid approach for handling AGVs scheduling problems of practical sizes. We show that a scenario involving up to 21 AGVs, significant due to possible deadlocks, can be efficiently addressed by a hybrid solver in seconds. [ABSTRACT FROM AUTHOR]

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for 57 % of 459 random Erdos–Rényi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing. [ABSTRACT FROM AUTHOR]

Abstract Quantum Computing has emerged as a promising alternative, utilising quantum mechanics for faster computations. This paper explores the nearest neighbour compliance (NNC) Problem in Gate-based Quantum Computers, where quantum gates are constrained to operate on physically adjacent qubits. The NNC problem aims to optimise the insertion of SWAP-gates to ensure compliance with these constraints while minimising their count. This work introduces Quantum Annealing to tackle the NNC problem, proposing two Quadratic Unconstrained Optimisation Problem formulations. The formulations are tested on a contemporary Quantum Annealer, and their performance is compared with previous methods. It shows that the prospect of using Quantum Annealing is promising, however, the current state of the hardware makes that finding the embedding is the limiting factor.

Abstract Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave’s Advantage™ quantum annealer, Fujitsu’s digital annealer V3, D-Wave’s quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.

Abstract Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric optimization problem of scheduling Automatic Guided Vehicles (AGVs). Some solvers can already leverage noisy intermediate-scale quantum (NISQ) devices. In our study, we utilize D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit. This hybrid methodology performs comparably to existing classical solvers. However, due to the proprietary nature of the software, the precise contribution of quantum computation remains unclear. Our analysis focuses on a practical, business-oriented scenario: scheduling AGVs within a factory constrained by limited space, simulating a realistic production setting. Our approach maps a realistic AGVs problem onto one reminiscent of railway scheduling and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable. The main idea here is to highlight the potential usefulness of a hybrid approach for handling AGVs scheduling problems of practical sizes. We show that a scenario involving up to 21 AGVs, significant due to possible deadlocks, can be efficiently addressed by a hybrid solver in seconds.

Feature selection is a technique in statistical prediction modeling that identifies features in a record with a strong statistical connection to the target variable. Excluding features with a weak statistical connection to the target variable in training not only drops the dimension of the data, which decreases the time complexity of the algorithm, it also decreases noise within the data which assists in avoiding overfitting. In all, feature selection assists in training a robust statistical model that performs well and is stable. Recent advancements in feature selection that leverages quantum annealing (QA) give a scalable technique that aims to maximize the predictive power of the features while minimizing redundancy. As a consequence, it is expected that this algorithm would assist in the bias/variance trade-off yielding better features for training a statistical model. This paper tests this intuition against classical methods by utilizing open-source data sets and evaluates the efficacy of each trained statistical model well-known prediction algorithms. The numerical results display an advantage utilizing the features selected from the algorithm that leveraged QA. [ABSTRACT FROM AUTHOR]

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems' Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future. [ABSTRACT FROM AUTHOR]

Abstract Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research.

We propose a number-theory-based quantized mathematical optimization scheme for various NP-hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization-based optimization proposal also depends on stochastic features (i.e., the white-noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization-based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

Academic achievement is a critical measure of intellectual ability, prompting extensive research into cognitive tasks as potential predictors. Neuroimaging technologies, such as functional near-infrared spectroscopy (fNIRS), offer insights into brain hemodynamics, allowing understanding of the link between cognitive performance and academic achievement. Herein, we explored the association between cognitive tasks and academic achievement by analyzing prefrontal fNIRS signals. A novel quantum annealer (QA) feature selection algorithm was applied to fNIRS data to identify cognitive tasks correlated with CSAT scores. Twelve features (signal mean, median, variance, peak, number of peaks, sum of peaks, range, minimum, kurtosis, skewness, standard deviation, and root mean square) were extracted from fNIRS signals at two time windows (10- and 60-s) to compare results from various feature variable conditions. The feature selection results from the QA-based and XGBoost regressor algorithms were compared to validate the former's performance. In a two-step validation process using multiple linear regression models, model fitness (adjusted R2) and model prediction error (RMSE) values were calculated. The quantum annealer demonstrated comparable performance to classical machine learning models, and specific cognitive tasks, including verbal fluency, recognition, and the Corsi block tapping task, were correlated with academic achievement. Group analyses revealed stronger associations between Tower of London and N-back tasks with higher CSAT scores. Quantum annealing algorithms have significant potential in feature selection using fNIRS data, and represents a novel research approach. Future studies should explore predictors of academic achievement and cognitive ability. [ABSTRACT FROM AUTHOR]

Objectives To introduce quantum computing technologies as a tool for biomedical research and highlight future applications within healthcare, focusing on its capabilities, benefits, and limitations. Target Audience Investigators seeking to explore quantum computing and create quantum-based applications for healthcare and biomedical research. Scope Quantum computing requires specialized hardware, known as quantum processing units, that use quantum bits (qubits) instead of classical bits to perform computations. This article will cover (1) proposed applications where quantum computing offers advantages to classical computing in biomedicine; (2) an introduction to how quantum computers operate, tailored for biomedical researchers; (3) recent progress that has expanded access to quantum computing; and (4) challenges, opportunities, and proposed solutions to integrate quantum computing in biomedical applications. [ABSTRACT FROM AUTHOR]

Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research. [ABSTRACT FROM AUTHOR]

Two classes of quantum-annealing-inspired-algorithms (QAIA), namely different variants of simulated coherent Ising machine and simulated bifurcation, have been proposed for efficiently solving combinatorial optimization problems recently. In order to certify the superiority of these algorithms, standardized comparisons among them and against other physics-based algorithms are necessary. In this work, for Max-Cut problems up to 20,000 nodes, we benchmark QAIA against quantum annealing and other physics-based algorithms. We found that ballistic simulated bifurcation excelled for chimera and small-scale graphs, achieving nearly a 50-fold reduction in time-to-solution compared to quantum annealing. For large-scale graphs, discrete simulated bifurcation achieves the lowest time-to-target and outperforms D-Wave Advantage system when tasked with finding the maximum cut value in pegasus graphs. Our results suggest that QAIA represents a promising means for solving combinatorial optimization problems in practice, and can act as a natural baseline for competing quantum algorithms. One of the most considered applications for quantum-inspired algorithms is solving combinatorial optimization problems. In this manuscript, the authors benchmark several quantum-annealing-inspired algorithms against other state-of-the-art optimizers and quantum annealer, comparing their success probabilities and time-to-solution. [ABSTRACT FROM AUTHOR]

Superconducting quantum computers are rapidly reaching scales where bottlenecks to scaling arise from the practical aspects of the fabrication process. To improve quantum computer performance, implementation technology that guarantees the scalability of the number of qubits is essential. Increasing the degrees of freedom in routing by 2.5-dimensional implementation is important for realizing circuit scalability. We report an implementation technology to overcome the scaling bottlenecks using a reliable connection qubit with a demonstration of quantum annealing. The method comprises interconnection based on quantum annealing using a superconducting flux qubit, precise coupling status control, and flip-chip bonding. We perform experiments and simulations with a proof-of-concept demonstration of qubit coupling via interconnection using a flux qubit. The coupling status is strictly controllable by quantum annealing. A low-temperature flip-chip bonding technology is introduced for the 2.5-dimensional interconnection. The superconducting flux qubit, formed across two different chips via bumps, is demonstrated for the first time to show a state transition like that in a conventional qubit. The quantum annealing flux qubit and flip-chip bonding enable new interconnections between qubits. A perspective on the possibility of applying this technology to the connection between gate-type qubits is described. [ABSTRACT FROM AUTHOR]

The main limitation of wireless sensor networks (WSNs) lies in their reliance on battery power. Therefore, the primary focus of the current research is to determine how to transmit data in a rational and efficient way while simultaneously extending the network's lifespan. In this paper, a hybrid of a fuzzy logic system and a quantum annealing algorithm-based clustering and routing protocol (FQA) is proposed to improve the stability of the network and minimize energy consumption. The protocol uses a fuzzy inference system (FIS) to select appropriate cluster heads (CHs). In the routing phase, we used the quantum annealing algorithm to select the optimal route from the CHs and the base station (BS). Furthermore, we defined an energy threshold to filter candidate CHs in order to save computation time. Unlike with periodic clustering, we adopted an on-demand re-clustering mechanism to perform global maintenance of the network, thereby effectively reducing the computation and overhead. The FQA was compared with FRNSEER, BOA-ACO, OAFS-IMFO, and FC-RBAT in different scenarios from the perspective of energy consumption, alive nodes, network lifetime, and throughput. According to the simulation results, the FQA outperformed all the other methods in all scenarios. [ABSTRACT FROM AUTHOR]

Context: Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving certain combinatorial optimization problems over traditional classical methods such as simulated annealing (SA). However, a recent study showed that a 2000-qubit QA hardware was still unable to outperform SA for the MU problem. Here, we propose the use of quantum-inspired algorithm to solve the MU problem, in order to go beyond traditional SA. We introduce a highly compact phase encoding method which can exponentially reduce the representation space, compared with the previous one-hot encoding method. For benchmarking, we tested this new approach on the public QM9 dataset generated by density functional theory (DFT). The root-mean-square deviation between the conformation determined by our approach and DFT is negligible (less than about 0.5Å), which underpins the validity of our approach. Furthermore, the median time-to-target metric can be reduced by a factor of five compared to SA. Additionally, we demonstrate a simulation experiment by MindQuantum using quantum approximate optimization algorithm (QAOA) to reach optimal results. These results indicate that quantum-inspired algorithms can be applied to solve practical problems even before quantum hardware becomes mature. Methods: The objective function of MU is defined as the sum of all internal distances between atoms in the molecule, which is a high-order unconstrained binary optimization (HUBO) problem. The degree of freedom of variables is discretized and encoded with binary variables by the phase encoding method. We employ the quantum-inspired simulated bifurcation algorithm for optimization. The public QM9 dataset is generated by DFT. The simulation experiment of quantum computation is implemented by MindQuantum using QAOA. [ABSTRACT FROM AUTHOR]

In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions. [ABSTRACT FROM AUTHOR]

Quantum annealing machines are next-generation computers for solving combinatorial optimization problems. Although physical simulations are one of the most promising applications of quantum annealing machines, a method how to embed the target problem into the machines has not been developed except for certain simple examples. In this study, we focus on a method of representing real numbers using binary variables, or quantum bits. One of the most important problems for conducting physical simulation by quantum annealing machines is how to represent the real number with quantum bits. The variables in physical simulations are often represented by real numbers but real numbers must be represented by a combination of binary variables in quantum annealing, such as quadratic unconstrained binary optimization (QUBO). Conventionally, real numbers have been represented by assigning each digit of their binary number representation to a binary variable. Considering the classical annealing point of view, we noticed that when real numbers are represented in binary numbers, there are numbers that can only be reached by inverting several bits simultaneously under the restriction of not increasing a given Hamiltonian, which makes the optimization very difficult. In this work, we propose three new types of real number representation and compared these representations under the problem of solving linear equations. As a result, we found experimentally that the accuracy of the solution varies significantly depending on how the real numbers are represented. We also found that the most appropriate representation depends on the size and difficulty of the problem to be solved and that these differences show a consistent trend for two annealing solvers. Finally, we explain the reasons for these differences using simple models, the minimum required number of simultaneous bit flips, one-way probabilistic bit-flip energy minimization, and simulation of ideal quantum annealing machine. [ABSTRACT FROM AUTHOR]

Model‐based acoustic localisation estimates the locations of underwater objects by comparing sensor measurements with model predictions. To obtain high quality predictions, propagation models need to be run for a large set of environmental parameters. However, real‐time Model‐based acoustic localisation estimations using onboard computational resources are often limited. To address this, the authors propose a Quantum annealing (QA) algorithm for enhancing underwater acoustic localisation. A restricted Boltzmann machine (RBM) is trained to predict the probability distribution of underwater targets. Advantage of this approach is that part of the computation is moved to offline‐training. Moreover, the probability distribution can potentially be sampled efficiently using a quantum annealer possibly enabling real‐time accurate target estimations being made onboard.The RBM is applied to a simplified multi‐sensor horizontal localisation problem where a constant and linear acoustic propagation is assumed. Using simulated annealing the authors show that the RBM is able to learn probability distributions that resemble target locations. Preliminary results show that training and sampling the RBM can be done using QA hardware by D‐Wave Systems.However, there remains room for improvement especially in ranging predictions. Further research into possible benefits of QA RBMs is needed to provide theoretical and practical results of a speed‐up. [ABSTRACT FROM AUTHOR]

We propose a number‐theory‐based quantized mathematical optimization scheme for various NP‐hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization‐based optimization proposal also depends on stochastic features (i.e., the white‐noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization‐based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes. [ABSTRACT FROM AUTHOR]

The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio's Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem. [ABSTRACT FROM AUTHOR]

Variational Bayes (VB) inference algorithm is used widely to estimate both the parameters and the unobserved hidden variables in generative statistical models. The algorithm-inspired by variational methods used in computational physics-is iterative and can get easily stuck in local minima, even when classical techniques, such as deterministic annealing (DA), are used. We study a VB inference algorithm based on a nontraditional quantum annealing approach-referred to as quantum annealing variational Bayes (QAVB) inference-and show that there is indeed a quantum advantage to QAVB over its classical counterparts. In particular, we show that such better performance is rooted in key quantum mechanics concepts: i) The ground state of the Hamiltonian of a quantum system-defined from the given data-corresponds to an optimal solution for the minimization problem of the variational free energy at very low temperatures; ii) such a ground state can be achieved by a technique paralleling the quantum annealing process; and iii) starting from this ground state, the optimal solution to the VB problem can be achieved by increasing the heat bath temperature to unity, and thereby avoiding local minima introduced by spontaneous symmetry breaking observed in classical physics based VB algorithms. We also show that the update equations of QAVB can be potentially implemented using ⌈logK⌉ qubits and ?(K) operations per step, where K is the number of values hidden categorical variables can take. Thus, QAVB can match the time complexity of existing VB algorithms, while delivering higher performance.

Quantum Machine Learning (QML) is a field that combines the principles of Quantum Computing (QC) and Machine Learning (ML). QC works by taking advantage of the properties of quantum physics, such as superposition and entanglement. To fully realize the potential of this technology, more research is necessary, as the field of QML is still in its early stages. Since QC technologies and devices continue to develop quickly, it is important to identify the use cases and applications that benefit the most. This paper investigates the potentials of QC, and more specifically, Quantum Annealing (QA), for clustering real-world data in transportation systems. The Bike Sharing System (BSS) is used as a case study applying a clustering model on QA computers. The main contribution of this research is to introduce a hybrid model to cluster stations in a BSS by solving it as a Constraint Satisfaction Problem (CSP) problem with different methods on a QA computer using a real-time dataset. In addition to the practical contribution, this research also offers theoretical advancements in the field of computational optimization by defining a new topology for the input data that is compatible with QC topology (e.g., Chimera topology). The goal of real-time clustering BSS stations based on dynamic and static datasets is, in fact, to assist decision-makers in better managing and minimizing the risk of bike unavailability at each station and rebalancing bikes shared. Three different methods have been used to determine the number of clusters, and Euclidean, Manhattan, Pearson, and Spearman dissimilarity functions have been applied to cluster the stations. The evaluation is done using the magnitude vs. cardinality approach. The distribution of the stations, magnitude, and cardinality of the results indicate the potential to use QC for clustering for a real-world application, e.g., BSS.

The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio’s Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

Abstract Thin-film optical diodes are important elements for miniaturizing photonic systems. However, the design of optical diodes relies on empirical and heuristic approaches. This poses a significant challenge for identifying optimal structural models of optical diodes at given wavelengths. Here, we leverage a quantum annealing-enhanced active learning scheme to automatically identify optimal designs of 130 nm-thick optical diodes. An optical diode is a stratified volume diffractive film discretized into rectangular pixels, where each pixel is assigned to either a metal or dielectric. The proposed scheme identifies the optimal material states of each pixel, maximizing the quality of optical isolation at given wavelengths. Consequently, we successfully identify optimal structures at three specific wavelengths (600, 800, and 1000 nm). In the best-case scenario, when the forward transmissivity is 85%, the backward transmissivity is 0.1%. Electromagnetic field profiles reveal that the designed diode strongly supports surface plasmons coupled across counterintuitive metal–dielectric pixel arrays. Thereby, it yields the transmission of first-order diffracted light with a high amplitude. In contrast, backward transmission has decoupled surface plasmons that redirect Poynting vectors back to the incident medium, resulting in near attenuation of its transmission. In addition, we experimentally verify the optical isolation function of the optical diode.

Abstract SARS‐CoV‐2 epidemic (severe acute respiratory corona virus 2 syndromes) has caused major impacts on a global scale. Several countries, including India, Europe, U.S.A., introduced a full state/nation lockdown to minimise the disease transmission through human interaction after the virus entered the population and to minimise the loss of human life. Millions of people have gone unemployed due to lockdown implementation, resulting in business and industry closure and leading to a national economic slowdown. Therefore, preventing the spread of the COVID‐19 virus in the world while also preserving the global economy is an essential problem requiring an effective and immediate solution. Using the compartmental epidemiology S, E, I, R or D (Susceptible, Exposed, Infectious, Recovery or Death) model extended to multiple population regions, the authors predict the evolution of the SARS‐CoV‐2 disease and construct an optimally scheduled lockdown calendar to execute lockdown over phases, using the well‐known Knapsack problem. A comparative analysis of both classical and quantum models shows that our model decreases SARS‐CoV‐2 active cases while retaining the average global economic factor, Gross Domestic Product, in contrast to the scenario with no lockdown.

Large number factorization is not only the most critical entry point for Rivest–Shamir–Adleman (RSA) security analysis, but also the most direct means of attacking the asymmetric encryption algorithm RSA. In this paper, the factorization methods of large numbers are summarized and analysed: classical integer factoring algorithms, Shor's circuit model algorithm, quantum adiabatic methods (integer factorization based on a quantum nuclear magnetic resonance (NMR) platform and D-Wave quantum annealing), and hybrid quantum-classical computing. Finally, the feasibility of integer factorization based on quantum adiabatics is discussed. In this paper, quantum annealing is regarded as a quantum attack method that is completely different from the famous Shor algorithm, and the potential of D-Wave factorization of large numbers to crack RSA cryptography is verified, which provides a new idea for a quantum attack on RSA public key cryptography. [ABSTRACT FROM AUTHOR]

Thin-film optical diodes are important elements for miniaturizing photonic systems. However, the design of optical diodes relies on empirical and heuristic approaches. This poses a significant challenge for identifying optimal structural models of optical diodes at given wavelengths. Here, we leverage a quantum annealing-enhanced active learning scheme to automatically identify optimal designs of 130 nm-thick optical diodes. An optical diode is a stratified volume diffractive film discretized into rectangular pixels, where each pixel is assigned to either a metal or dielectric. The proposed scheme identifies the optimal material states of each pixel, maximizing the quality of optical isolation at given wavelengths. Consequently, we successfully identify optimal structures at three specific wavelengths (600, 800, and 1000 nm). In the best-case scenario, when the forward transmissivity is 85%, the backward transmissivity is 0.1%. Electromagnetic field profiles reveal that the designed diode strongly supports surface plasmons coupled across counterintuitive metal–dielectric pixel arrays. Thereby, it yields the transmission of first-order diffracted light with a high amplitude. In contrast, backward transmission has decoupled surface plasmons that redirect Poynting vectors back to the incident medium, resulting in near attenuation of its transmission. In addition, we experimentally verify the optical isolation function of the optical diode. [ABSTRACT FROM AUTHOR]

In this study, the portfolio optimization problem is explored, using a combination of classical and quantum computing techniques. The portfolio optimization problem with specific objectives or constraints is often a quadratic optimization problem, due to the quadratic nature of, for example, risk measures. Quantum computing is a promising solution for quadratic optimization problems, as it can leverage quantum annealing and quantum approximate optimization algorithms, which are expected to tackle these problems more efficiently. Quantum computing takes advantage of quantum phenomena like superposition and entanglement. In this paper, a specific problem is introduced, where a portfolio of loans need to be optimized for 2030, considering 'Return on Capital' and 'Concentration Risk' objectives, as well as a carbon footprint constraint. This paper introduces the formulation of the problem and how it can be optimized using quantum computing, using a reformulation of the problem as a quadratic unconstrained binary optimization (QUBO) problem. Two QUBO formulations are presented, each addressing different aspects of the problem. The QUBO formulation succeeded in finding solutions that met the emission constraint, although classical simulated annealing still outperformed quantum annealing in solving this QUBO, in terms of solutions close to the Pareto frontier. Overall, this paper provides insights into how quantum computing can address complex optimization problems in the financial sector. It also highlights the potential of quantum computing for providing more efficient and robust solutions for portfolio management. [ABSTRACT FROM AUTHOR]

In image processing, image segmentation is the process of partitioning a digital image into multiple image segments. Among state‐of‐the‐art methods, Markov random fields can be used to model dependencies between pixels and achieve a segmentation by minimising an associated cost function. Currently, finding the optimal set of segments for a given image modelled as a Markov random fields appears to be NP‐hard. The authors aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of synthetic aperture radar images. For that purpose, the authors propose a hybrid quantum annealing classical optimisation expectation maximisation algorithm to obtain optimal sets of segments. After proposing suitable formulations, the authors discuss the performances and the scalability of authors' approach on the D‐Wave quantum computer. The authors also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimisation problems. [ABSTRACT FROM AUTHOR]

Protein–ligand docking plays a significant role in structure-based drug discovery. This methodology aims to estimate the binding mode and binding free energy between the drug-targeted protein and candidate chemical compounds, utilizing protein tertiary structure information. Reformulation of this docking as a quadratic unconstrained binary optimization (QUBO) problem to obtain solutions via quantum annealing has been attempted. However, previous studies did not consider the internal degrees of freedom of the compound that is mandatory and essential. In this study, we formulated fragment-based protein–ligand flexible docking, considering the internal degrees of freedom of the compound by focusing on fragments (rigid chemical substructures of compounds) as a QUBO problem. We introduced four factors essential for fragment–based docking in the Hamiltonian: (1) interaction energy between the target protein and each fragment, (2) clashes between fragments, (3) covalent bonds between fragments, and (4) the constraint that each fragment of the compound is selected for a single placement. We also implemented a proof-of-concept system and conducted redocking for the protein–compound complex structure of Aldose reductase (a drug target protein) using SQBM+, which is a simulated quantum annealer. The predicted binding pose reconstructed from the best solution was near-native (RMSD = 1.26 Å), which can be further improved (RMSD = 0.27 Å) using conventional energy minimization. The results indicate the validity of our QUBO problem formulation. [ABSTRACT FROM AUTHOR]

Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has attracted a lot of attention to the NISQ era. Several numerical benchmarks try to compare these two metaheuristics, however, classical computational power highly limits the performance insights. In this work, we introduce a parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop a tight Lieb–Robinson bound for regular graphs, achieving the best-known numerical value to analyze QA locally. Studying MaxCut over cubic graph as a benchmark optimization problem, we show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms. [ABSTRACT FROM AUTHOR]

As the Internet of Things (IoT) becomes more integral across diverse sectors, including healthcare, energy provision and industrial automation, the exposure to cyber vulnerabilities and potential attacks increases accordingly. Facing these challenges, the essential function of an Information Security Management System (ISMS) in safeguarding vital information assets comes to the fore. Within this framework, risk management is key, tasked with the responsibility of adequately restoring the system in the event of a cybersecurity incident and evaluating potential response options. To achieve this, the ISMS must evaluate what is the best response. The time to implement a course of action must be considered, as the period required to restore the ISMS is a crucial factor. However, in an environmentally conscious world, the sustainability dimension should also be considered to choose more sustainable responses. This paper marks a notable advancement in the fields of risk management and incident response, integrating security measures with the wider goals of sustainability and corporate responsibility. It introduces a strategy for handling cybersecurity incidents that considers both the response time and sustainability. This approach provides the flexibility to prioritize either the response time, sustainability or a balanced mix of both, according to specific preferences, and subsequently identifies the most suitable actions to re-secure the system. Employing a quantum methodology, it guarantees reliable and consistent response times, independent of the incident volume. The practical application of this novel method through our framework, MARISMA, is demonstrated in real-world scenarios, underscoring its efficacy and significance in the contemporary landscape of risk management. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Data assimilation is a crucial component in the Earth science field, enabling the integration of observation data with numerical models. In the context of numerical weather prediction (NWP), data assimilation is particularly vital for improving initial conditions and subsequent predictions. However, the computational demands imposed by conventional approaches, which employ iterative processes to minimize cost functions, pose notable challenges in computational time. The emergence of quantum computing provides promising opportunities to address these computation challenges by harnessing the inherent parallelism and optimization capabilities of quantum annealing machines. In this investigation, we propose a novel approach termed quantum data assimilation, which solves the data assimilation problem using quantum annealers. Our data assimilation experiments using the 40-variable Lorenz model were highly promising, showing that the quantum annealers produced an analysis with comparable accuracy to conventional data assimilation approaches. In particular, the D-Wave Systems physical quantum annealing machine achieved a significant reduction in execution time. [ABSTRACT FROM AUTHOR]

We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with p = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms (ZZZ terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of the heavy-hex lattice. QAOA and QA are both compared against simulated annealing and the optimal solutions are computed exactly using CPLEX. The noiseless mean QAOA expectation values for p = 1, 2 are computed using classical light-cone based simulations. We find QA outperforms QAOA on the evaluated devices. [ABSTRACT FROM AUTHOR]

The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation, but also demonstrate the potential of quantum computation in effectively solving the bin packing problem, particularly as more reliable quantum technology becomes available. [ABSTRACT FROM AUTHOR]

The Integrated Side Lobe Ratio (ISLR) problem the authors consider here consists in finding optimal sequences of phase shifts in order to minimise the mean squared cross‐correlation side lobes of a transmitted radar signal and a mismatched replica. Currently, ISLR does not seem to be easier than the general polynomial unconstrained binary problem, which is NP‐hard. In their work, the authors aim to take advantage of the scalability of quantum computing to find new optima, by solving the ISLR problem on a quantum annealer. This quantum device is designed to solve quadratic optimisation problems with binary variables (QUBO). After proposing suitable formulation for different instances of the ISLR, the authors discuss the performances and the scalability of their approach on the D‐Wave quantum computer. More broadly, their work enlightens the limits and potential of the adiabatic quantum computation for the solving of large instances of combinatorial optimisation problems. [ABSTRACT FROM AUTHOR]

This paper builds on top of a paper we have published very recently, in which we have proposed a novel approach to prime factorization (PF) by quantum annealing, where 8, 219, 999 = 32, 749 × 251 was the highest prime product we were able to factorize—which, to the best of our knowledge is the largest number which was ever factorized by means of a quantum device. The series of annealing experiments which led us to these results, however, did not follow a straight-line path; rather, they involved a convoluted trial-and-error process, full of failed or partially-failed attempts and backtracks, which only in the end drove us to find the successful annealing strategies. In this paper, we delve into the reasoning behind our experimental decisions and provide an account of some of the attempts we have taken before conceiving the final strategies that allowed us to achieve the results. This involves also a bunch of ideas, techniques, and strategies we investigated which, although turned out to be inferior wrt. those we adopted in the end, may instead provide insights to a more-specialized audience of D-Wave users and practitioners. In particular, we show the following insights: (i) different initialization techniques affect performances, among which flux biases are effective when targeting locally-structured embeddings; (ii) chain strengths have a lower impact in locally-structured embeddings compared to problem relying on global embeddings; (iii) there is a trade-off between broken chain and excited CFAs, suggesting an incremental annealing offset remedy approach based on the modules instead of single qubits. Thus, by sharing the details of our experiences, we aim to provide insights into the evolving landscape of quantum annealing, and help people access and effectively use D-Wave quantum annealers.

Resource allocation of wide-area internet networks is inherently a combinatorial optimization problem that if solved quickly, could provide near real-time adaptive control of internet-protocol traffic ensuring increased network efficacy and robustness, while minimizing energy requirements coming from power-hungry transceivers. In recent works we demonstrated how such a problem could be cast as a quadratic unconstrained binary optimization (QUBO) problem that can be embedded onto the D-Wave Advantage™ quantum annealer system, demonstrating proof of principle. Our initial studies left open the possibility for improvement of D-Wave solutions via judicious choices of system run parameters. Here we report on our investigations for optimizing these system parameters, and how we incorporate machine learning (ML) techniques to further improve on the quality of solutions. In particular, we use the Hamming distance to investigate correlations between various system-run parameters and solution vectors. We then apply a decision tree neural network (NN) to learn these correlations, with the goal of using the neural network to provide further guesses to solution vectors. We successfully implement this NN in a simple integer linear programming (ILP) example, demonstrating how the NN can fully map out the solution space that was not captured by D-Wave. We find, however, for the 3-node network problem the NN is not able to enhance the quality of space of solutions.