Classical Simulated Annealing Research Articles

A site-resolved two-dimensional quantum simulator with hundreds of trapped ions.

A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation1. As one of the leading physical platforms for quantum information processing, the ion trap has achieved a quantum simulation of tens of ions with site-resolved readout in a one-dimensional Paul trap2-4 and of hundreds of ions with global observables in a two-dimensional (2D) Penning trap5,6. However, integrating these two features into a single system is still very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner crystal and the sideband cooling of their transverse motion. We demonstrate the quantum simulation of long-range quantum Ising models with tunable coupling strengths and patterns, with or without frustration, using 300 ions. Enabled by the site resolution in the single-shot measurement, we observe rich spatial correlation patterns in the quasi-adiabatically prepared ground states, which allows us to verify quantum simulation results by comparingthe measured two-spin correlations with the calculated collective phonon modes and with classical simulated annealing. We further probe the quench dynamics of the Ising model in a transverse field to demonstrate quantum sampling tasks. Our work paves the way for simulating classically intractable quantum dynamics and for running noisy intermediate-scale quantum algorithms7,8 using 2D ion trap quantum simulators.

Relationship between synthesis method-crystal structure-melting properties in cocrystals: the case of caffeine-citric acid.

The influence of the crystal synthesis method on the crystallographic structure of caffeine-citric acid cocrystals was analyzed thanks to the synthesis of a new polymorphic form of the cocrystal. In order to compare the new form to the already known forms, the crystal structure of the new cocrystal (C8H10N4O2·C6H8O7) was solved by powder X-ray diffraction thanks to synchrotron experiments. The structure determination was performed using `GALLOP', a recently developed hybrid approach based on a local optimization with a particle swarm optimizer, particularly powerful when applied to the structure resolution of materials of pharmaceutical interest, compared to classical Monte-Carlo simulated annealing. The final structure was obtained through Rietveld refinement, and first-principles density functional theory (DFT) calculations were used to locate the H atoms. The symmetry is triclinic with the space group P-1 and contains one molecule of caffeine and one molecule of citric acid per asymmetric unit. The crystallographic structure of this cocrystal involves different hydrogen-bond associations compared to the already known structures. The analysis of these hydrogen bonds indicates that the cocrystal obtained here is less stable than the cocrystals already identified in the literature. This analysis is confirmed by the determination of the melting point of this cocrystal, which is lower than that of the previously known cocrystals.

Multi-Objective Portfolio Optimization Using a Quantum Annealer

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.

Quantum and quantum-inspired optimization for an in-core fuel management problem

Operation management of nuclear power plants consists of several computationally hard problems. Searching for an in-core fuel loading pattern is among them. The main challenge of this combinatorial optimization problem is the exponential growth of the search space with a number of loading elements. Here we study a reloading problem in a Quadratic Unconstrained Binary Optimization (QUBO) form. Such a form allows us to apply various techniques, including quantum annealing, classical simulated annealing, and quantum-inspired algorithm in order to find fuel reloading patterns for several realistic configurations of nuclear reactors. We present the results of benchmarking the in-core fuel management problem in the QUBO form using the aforementioned computational techniques. This work demonstrates potential applications of quantum computers and quantum-inspired algorithms in the energy industry.

A Method for Inverting Shallow Sea Acoustic Parameters Based on the Backward Feedback Neural Network Model

In response to the drawbacks of low efficiency, cumbersome calculation, and easy-to-fall local optimal solutions in existing shallow water acoustic parameters inversion research, this paper proposes a shallow water acoustic parameters inversion method based on a feedback (BP) neural network model. Firstly, the theoretically predicted values of the shallow water sound pressure field are obtained through the fast field method (FFM). Secondly, a relationship model between the predicted sound pressure field and the inversion of ground sound parameter values is established based on the BP neural network model. Finally, the measured sound pressure field data are brought into the neural network model to obtain the inversion results. The application results of the method indicate that, compared to the classical simulated annealing (SA) algorithm, the BP neural network model converts the data-matching process of the optimization algorithm into the construction of a relationship model between the input data and the desired parameters, avoiding repeated matching and optimization processes. Therefore, it can directly, accurately, and efficiently output the inversion results. Under the premise of setting the same accuracy, the iteration number of the BP neural network model is reduced to 2% of the SA algorithm, cutting the calculation time to 30% of the SA algorithm. It has broad application prospects in shallow sea acoustic parameters inversion algorithms.

A Novel Parallel Simulated Annealing Methodology to Solve the No-Wait Flow Shop Scheduling Problem with Earliness and Tardiness Objectives

In this paper, the no-wait flow shop problem with earliness and tardiness objectives is considered. The problem is proven to be NP-hard. Recent no-wait flow shop problem studies focused on familiar objectives, such as makespan, total flow time, and total completion time. However, the problem has limited studies with solution approaches covering the concomitant use of earliness and tardiness objectives. A novel methodology for the parallel simulated annealing algorithm is proposed to solve this problem in order to overcome the runtime drawback of classical simulated annealing and enhance its robustness. The well-known flow shop problem datasets in the literature are utilized for benchmarking the proposed algorithm, along with the classical simulated annealing, variants of tabu search, and particle swarm optimization algorithms. Statistical analyses were performed to compare the runtime and robustness of the algorithms. The results revealed the enhancement of the classical simulated annealing algorithm in terms of time consumption and solution robustness via parallelization. It is also concluded that the proposed algorithm could outperform the benchmark metaheuristics even when run in parallel. The proposed algorithm has a generic structure that can be easily adapted to many combinatorial optimization problems.

FARSI: An Early-stage Design Space Exploration Framework to Tame the Domain-specific System-on-chip Complexity

Domain-specific SoCs (DSSoCs) are an attractive solution for domains with extremely stringent power, performance, and area constraints. However, DSSoCs suffer from two fundamental complexities. On the one hand, their many specialized hardware blocks result in complex systems and thus high development effort. On the other hand, their many system knobs expand the complexity of design space, making the search for the optimal design difficult. Thus to reach prevalence, taming such complexities is necessary. To address these challenges, in this work, we identify the necessary features of an early-stage design space exploration framework that targets the complex design space of DSSoCs and provide an instance of one such framework that we refer to as FARSI. FARSI provides an agile system-level simulator with speed up and accuracy of 8,400× and 98.5% compared to Synopsys Platform Architect. FARSI also provides an efficient exploration heuristic and achieves up to 62× and 35× improvement in convergence time compared to the classic simulated annealing (SA) and modern Multi-Objective Optimistic Search. This is done by augmenting SA with architectural reasoning such as locality exploitation and bottleneck relaxation. Furthermore, we embed various co-design capabilities and show that, on average, they have a 32% impact on the convergence rate. Finally, we demonstrate that using development-cost-aware policies can lower the system complexity, both in terms of the component count and variation by as much as 60% and 82% (e.g., for Network-on-a-Chip subsystem), respectively.

Folding lattice proteins with quantum annealing

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chain-like configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to $N=30$ beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for $N=48$ and $N=64$ HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an $N=14$ HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.

An improved tabu search algorithm for solving heterogeneous fixed fleet open vehicle routing problem with time windows

The heterogeneous fixed fleet open vehicle routing problem with time windows is a very significant type of the vehicle routing problem (VRP) that aims to find the minimum fixed and variable cost of transportation for a heterogeneous fleet with a fixed number in which the capacity of every vehicle and usage of the vehicles should not be ignored. Also, in this problem, each customer has a special time window for servicing and each vehicle starts its route from the warehouse and ends up in one of the customers. We propose a mixed integer linear programming model of this problem. Since this problem, as well as open VRP and VRP with fixed heterogeneous fleet are hard NP problem, an improved tabu search algorithm is proposed to solve the problem. Our proposed algorithm uses a modified sweep algorithm to generate some initial solutions. Besides, a variable tabu list and some new mechanisms for intensification and diversification mechanisms are used. Numerical results are presented to show the correctness of our model and finally, the efficiency of the proposed algorithm is compared with an exact algorithm, classic tabu search and simulated annealing. The obtained results prove the efficiency of the proposed algorithm.

Ising Machines for Diophantine Problems in Physics

AbstractDiophantine problems arise frequently in physics, in for example anomaly cancellation conditions, string consistency conditions and so forth. We present methods to solve such problems to high order on annealers that are based on the quadratic Ising Model. This is the intrinsic framework for both quantum annealing and for common forms of classical simulated annealing. We demonstrate the method on so‐called Taxicab numbers (discovering some apparently new ones), and on the realistic problem of anomaly cancellation in U(1) extensions of the Standard Model.

Continually reactivating iterative-projection method for instantiating microstructure from two-point statistics

Processing-structure (PS) linkages play a significant role in materials development. Nevertheless, currently there is a fascinating but of bottleneck task in terms of instantiating microstructure to understand and validate PS linkages. Its challenge lies on the lack of a robust method in computation efficiency and accuracy. Inspired from several advanced techniques such as hybrid input-output (HIO) algorithm, image processing operations and different-phase neighbors-based pixel swapping rule, we proposed a continually reactivating iterative-projection process (CRIP) method to address the challenge above. The output at each iteration in CRIP is continuously improved by eliminating and moving isolated or noise pixels towards an error-reduction direction to activate the iterative-projection process of the next iteration. The performance of the method was examined on two microstructure examples. It shows at least 99.86% improvement in convergence time compared with the classical simulated annealing algorithm and around 6.14 ×10−4 reduction in error compared with the traditional HIO algorithm. More importantly, CRIP is suitable for the task of instantiating microstructure from periodic two-point statistics predicted by PS linkage, which has been demonstrated by applying it to two experimental datasets of Ni-based superalloys and dual-phase steels. Our proposed method has the advantages of high efficiency, easy operation, reliable accuracy and remarkable generalization ability.

Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement

Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially small energy gaps of the system in the annealing process. Here a time-dependent reinforcement term is added to the Hamiltonian in order to give lower energies to the most probable states of the evolving system. In this study, we take a local entropy in the configuration space for the reinforcement and apply the algorithm to a number of easy and hard optimization problems. The reinforced algorithm performs better than the standard quantum annealing algorithm in the quantum search problem, where the optimal parameters behave very differently depending on the number of solutions. Moreover, the reinforcements can change the discontinuous phase transitions of the mean-field p-spin model ($p>2$) to a continuous transition. The algorithm's performance in the binary perceptron problem is also superior to that of the standard quantum annealing algorithm, which already works better than a classical simulated annealing algorithm.

Hard-instance learning for quantum adiabatic prime factorization

Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman cryptography. With programable quantum devices, adiabatic quantum computing has been proposed as a plausible approach to solve prime factorization, having promising advantage over classical computing. Here, we find there are certain hard instances that are consistently intractable for both classical simulated annealing and unconfigured adiabatic quantum computing (AQC). Aiming at an automated architecture for optimal configuration of quantum adiabatic factorization, we apply a deep reinforcement learning (RL) method to configure the AQC algorithm. By setting the success probability of the worst-case problem instances as the reward to RL, we show the AQC performance on the hard instances is dramatically improved by RL configuration. The success probability also becomes more evenly distributed over different problem instances, meaning the configured AQC is more stable as compared to the unconfigured case. Through a technique of transfer learning, we find prominent evidence that the framework of AQC configuration is scalable---the configured AQC as trained on five qubits remains working efficiently on nine qubits with a minimal amount of additional training cost.

Toward a QUBO-Based Density Matrix Electronic Structure Method.

Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree-Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave's new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. We also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

Neutrosophic Simulated Annealing Algorithm and Its Application in Operation Optimization in Dangerous Goods Warehouse

In the classical simulated annealing algorithm (SAA), the iteration feasible solution is mainly based on a certain random probability. In the process of iteration, there is a lack of comparison between individuals and the whole population of feasible solutions, and the indicators to measure the change of state of individuals are too absolute to achieve the overall control of the algorithm. To deal with uncertain information that individuals encounter in iteration, this study introduces the idea of neutrosophic decision-making and establishes a kind of neutrosophic fuzzy set (NFS) to describe the time-varying iterative state of individuals according to the change of individual state, the change of population state, and the number of iteration. The biggest feature of this study is to propose a neutrosophic simulated annealing algorithm that combines the idea of NFS with simulated annealing. The biggest contribution of this study is to propose a novel entropy measurement method using the NFS and combine it with the simulated annealing algorithm to handle the optimization process. Finally, the effectiveness of the novel algorithm is verified by an example of warehouse optimization.

Quantum optimization of maximum independent set using Rydberg atom arrays.

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the maximum independent set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find that the problem hardness is controlled by the solution degeneracy and number of local minima, and we experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.

How to Solve Combinatorial Optimization Problems Using Real Quantum Machines: A Recent Survey

A combinatorial optimization problem (COP) is the problem of finding the optimal solution in a finite set. When the size of the feasible solution set is large, the complexity of the problem increases, and it is not easy to solve in a reasonable time with the current classical computer technology. Quantum annealing (QA) is a method that replaces classical simulated annealing (SA) methods that do not solve these cases. Therefore, several attempts have been made to solve this problem using a special-purpose quantum annealer to which the QA method is applied. In this survey, we analyze recent studies that solve real-scale COPs using quantum annealers. Through this, we discuss how to reduce the size of the COP to be input to overcome the hardware limitations of the existing quantum annealer. Additionally, we demonstrated the applicability of quantum annealer to COP on a practical scale by comparing and analyzing the results of the classical simulated annealing (SA) and QA method from each study.

Structure of amyloidogenic PAP(85-120) peptide by high-resolution NMR spectroscopy

Prostatic acid phosphatase (PAP) is an enzyme facilitating infection of cells by HIV. Its peptide fragment PAP(85-120) forms amyloid fibrils known as SEVI, which enhance attachment of the virus by viral adhesion to the host cell prior to receptor-specific binding via reducing the electrostatic repulsion between the membranes of the virus and the target cell. In this work, the PAP(85-120) peptide spatial structure was solved using nuclear magnetic resonance (NMR) spectroscopy and circular dichroism (CD) spectroscopy. The data obtained with the help of NMR (internuclear distances, dihedral angles) allow to calculate the spatial structure of PAP(85-120) using the classical simulated annealing protocol built in XPLOR-NIH. CD spectrum analysis was used to provide the information on the secondary structure of PAP(85-120) that was agreed with the calculated spatial structure. Both methods have shown that the PAP(85-120) characterized by the high flexibility with prevailing random coil structure. The PAP(85-120) peptide structure was compared with the corresponding fragment (85-120 amino acid residues) of the full-length PAP protein (PDB ID 1CVI). The compared peptide structures have turns in the same regions of amino acid residues Q101 and V109, whereas the helix number of the N-terminus and C-terminus is different.

Efficient solutions to the placement and chaining problem of User Plane Functions in 5G networks

This study attempts to solve the placement and chaining problem of 5G User Plane Functions (UPFs) in a Multi-access Edge Computing (MEC) ecosystem. The problem is formalized as a multi-objective Integer Linear Programming (ILP) model targeted at optimizing provisioning costs and quality of service. Our model takes into account several aspects of the system such as UPF-specific considerations, the Service Function Chain (SFC) requests topology (single and multiple branches), Virtual Network Function (VNF) order constraints, service demands, and physical network capacities. Since the formulated problem is NP-hard, two heuristic solutions are devised to enhance solution efficiency. Specifically, an algorithm called Priority and Cautious-UPF Placement and Chaining (PC-UPC) and a simulated annealing (SA) meta-heuristic are proposed. Through extensive simulation experiments, we evaluated the performance of the proposed solutions. The results revealed that our solutions outperformed the baselines (i.e., two greedy-based heuristics and a variant of the classical SA) and that we had obtained nearly optimal solutions with significant reductions in running time. Moreover, the PC-UPC algorithm can effectively avoid SFC rejections and improve provisioning costs by considering session requirements, current network conditions, and the effects of VNF mapping decisions. Additionally, the proposed SA approach incorporates several mechanisms (e.g., variable Markov chain length and restart–stop) that allow the improvement of not only the quality of the solutions but also their computation time.

Theories and applications of quantum annealing: A literature survey

<p indent="0mm">Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.