Matteo M. Wauters, Evert van Nieuwenburg
We provide a reusability report of the method presented by Chen et al. in "Optimizing quantum annealing schedules with Monte Carlo tree search enhanced with neural networks" and add further benchmarks on Max-Cut problems.
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New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a highe…
Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair comparisons between classical annealing, quantum annealing, and other algorithms. Here we present a heuristic approach for the optimization of annealing schedules for quantum annealing and apply it to 3D Ising spin glass problems. We find that if both classical and quantum annealing schedules are similarly optimized, classical annealing outperforms quantum anneal…
Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] have reported that Monte Carlo simulations for the Ising spin glass model on the square lattice in the physically relevant continuous-imaginary-time limit do not show superiority of quantum annealing (QA) using transverse field against classical annealing (CA). Although the QA schedule that they had used has been using conventionally, however the QA schedule mathematically has no guarantee that the used schedule is the best QA schedule for performance of optimization. We propose a new QA schedule for studying transverse-field-b…
Deep learning optimal quantum annealing schedules for random Ising models
本文提出用LSTM神经网络自动搜索正则图上随机伊辛模型的最优量子退火调度，通过局部绝热路径训练后可泛化到未见实例和更大图。
In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian which is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to the computational problem of interest, and the state overlap with this ground state gives the success probability of the annealing protocol. The form of the annealing schedule can have a significant impact on the ground state overlap at the end of the anneal, so precise control over these annealing schedules can be a powerful tool for increasing success pro…
Quantum annealing is a practical approach to approximately implement the adiabatic quantum computational model under a real-world setting. The goal of an adiabatic algorithm is to prepare the ground state of a problem-encoded Hamiltonian at the end of an annealing path. This is typically achieved by driving the dynamical evolution of a quantum system slowly to enforce adiabaticity. Properly optimized annealing schedules often significantly accelerate the computational process. Inspired by the recent success of deep reinforcement learning such as DeepMind's AlphaZero, we propose a Monte Carlo T…
The annealing schedule is optimized for a parameter in the Lechner-Hauke-Zoller (LHZ) scheme for quantum annealing designed for the all-to-all-interacting Ising model representing generic combinatorial optimization problems. We adapt the variational approach proposed by Matsuura et al. (arXiv:2003.09913) to the annealing schedule of a term representing a constraint for variables intrinsic to the LHZ scheme with the annealing schedule of other terms kept intact. Numerical results for a simple ferromagnetic model and the spin-glass problem show that nonmonotonic annealing schedules optimize the …
Designing Quantum Annealing Schedules using Bayesian Optimization
本研究提出用贝叶斯优化设计低需求的量子退火调度，在自旋模型上实现远超标准协议的保真度，还可改进混合量子算法并经中性原子量子处理器实验验证。
Trust Region Bayesian Optimization of Annealing Schedules on a Quantum Annealer
本文提出信任域贝叶斯优化（TuRBO）框架，联合优化量子退火机的退火时间和傅里叶参数化调度，在模拟中优于随机和贪婪搜索，提升能量、可行解概率并降低链断裂。
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed up classical Markov chain algorithms? In this work we consider the problem of speeding up simulated annealing algorithms, where the stationary distributions of the Markov chains are Gibbs distributions at temperatures specified according to an annealing schedule. We construct a quantum algorithm that both adaptively constructs an annealing schedule and quantu…
Schedule-dependent basin occupation and instance-specific effective scales in cycled reverse annealing on programmable quantum annealers
该研究探讨了在可编程量子退火机上运行混合反常12个量子比特Ising实例时，逆退火过程的晚期子系统自相关性在设备校准的有效温度下严格介于两个平衡参考过程之间，揭示了调度对盆地占据的影响以及反退火调度作为实例特定的盆地占据探测器的作用。
Transformer-Based Neural Quantum Digital Twins for Many-Body Spectral Reconstruction and Adaptive Quantum-Annealing Schedule Design
基于Transformer的神经量子数字孪生通过预测能级和间隙位置，优化退火调度设计，提升量子退火在真实硬件上的性能。
We study the glued-trees problem of Childs et. al. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the quantum annealing do not suffer from the so-called sign problem. Unlike the typical scenario, our schedule is efficient even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. We discuss generalizations based on initial-state randomization to avoid some slowdowns in adiabatic quantum computing due to small gaps.
The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adi…
Comparative analysis of diverse methodologies for portfolio optimization leveraging quantum annealing techniques
本文通过数值实验比较多种非常规量子退火算法在无约束单期离散均值-方差投资组合优化问题上的表现，发现部分方法在正向退火下可提高成功概率，而反向退火调度能显著改善特定算法的性能。
Diabatic Quantum Annealing for the Frustrated Ring Model
本文研究受挫环模型中非绝热量子退火能否避免标准绝热演化导致的指数级减速，并通过数值实验在最多39量子比特上证明优化退火调度可绕过该瓶颈。
Leveraging Landau-Zener-Stückelberg interference for accelerating diabatic quantum annealing
本文通过识别Landau-Zener-Stückelberg干涉机制，提出一种少参数变分调度ansatz，实现非绝热量子退火的指数级加速，并证明相干性是其关键资源。
Lower Bounds on Quantum Annealing Times
本文推导了绝热区域之外成功执行量子退火所需时间的下界，该下界在三个已知快速退火方案模型中渐近饱和并证明其具有最优标度，同时揭示了量子相干性是快速退火的计算资源。
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initia…
We develop a hybrid type of quantum annealing in which we control temperature and quantum field simultaneously. We study the efficiency of proposed quantum annealing and find a good schedule of changing thermal fluctuation and quantum fluctuation. In this paper, we focus on clustering problems which are important topics in information science and engineering. We obtain the better solution of the clustering problem than the standard simulated annealing by proposed quantum annealing.
Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
针对量子退火线性调度优化难题，提出基于CRAB算法启发的数字化量子退火和QAOA两种平滑最优调度方法，在14格点MaxCut困难实例上验证了效果并实现了数字到模拟设备的适配。
Worldline-Susceptibility Scheduling for Quantum Annealing Beyond Local-Adiabatic Evolution
研究量子退火中退火时间分布对性能的影响，提出基于世界线磁化率的低成本替代调度，通过与传统及精确调度对比，发现其在有限时间条件下表现优异，源于两种失效模式，且完整方法已在开源框架实现。
Continuous-time quantum control across an exponentially small bottleneck in a frustrated Ising ring model
针对受挫伊辛环模型中的指数小瓶颈，提出优化连续时间退火调度的方法，通过非绝热机制实现线性时间尺度下的基态制备。
Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems
本文提出利用自旋相干态路径积分设计量子绝热演化几何结构，以多项式开销构建退火协议，在SK模型和Max-2SAT等困难实例上相比线性协议将最优解测量概率提升数个数量级。
This paper studies quantum annealing (QA) for clustering, which can be seen as an extension of simulated annealing (SA). We derive a QA algorithm for clustering and propose an annealing schedule, which is crucial in practice. Experiments show the proposed QA algorithm finds better clustering assignments than SA. Furthermore, QA is as easy as SA to implement.
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundation of quantum annealing. In particular, theorems are presented for convergence conditions of quantum annealing to the target optimal state after an infinite-time evolution following the Schroedinger or stochastic (Monte Carlo) dynamics. It is proved that the same asymptotic behavior o…
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical relevance, and classical counterparts outperform them. To practically benefit from quantum architecture, one has to identify problems and algorithms with favorable scaling and improve on corresponding limitations depending on available hardware. For this reason, we developed an algorithm that solves integer linear programming problems, a classically NP-hard prob…
Demonstration of error-suppressed quantum annealing via boundary cancellation
本文推广边界消除定理至刘维尔能隙消失情形，并在量子退火硬件上实验验证其误差抑制效果，证明该协议比暂停策略对参数变化更具鲁棒性。
Trajectory-independent speed limits for controlled open quantum systems
本文研究了受控开放量子系统中与轨迹无关的速度限制，通过推广闭合量子系统中的结果，分析了相干控制与耗散之间的相互作用，并展示了该下界在热态制备中的应用。
Annealing schedule control provides new opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian fixed) for a period of time, we show it is possible to more directly probe the dissipative dynamics of the system at intermediate points along the anneal and examine thermal relaxation rates, for example, by observing the re-population of the ground state after the minimum spectral gap. We provide a detailed comparison of experiments from a D-Wave device, si…
For many optimization algorithms the time-to-solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Monte Carlo) for random Ising spin glass instances. We find power-law distributions with very heavy tails, corresponding to extremely hard instances, but far broader distributions - and thus worse performanc…
Boltzmann Machines constitute a class of neural networks with applications to image reconstruction, pattern classification and unsupervised learning in general. Their most common variants, called Restricted Boltzmann Machines (RBMs) exhibit a good trade-off between computability on existing silicon-based hardware and generality of possible applications. Still, the diffusion of RBMs is quite limited, since their training process proves to be hard. The advent of commercial Adiabatic Quantum Computers (AQCs) raised the expectation that the implementations of RBMs on such quantum devices could inc…
Tighter Lower Bounds on Quantum Annealing Times
本研究推导了不依赖退火调度、可纳入哈密顿量局部结构的量子退火时间下界，无需了解退火器动力学即可计算，在自旋系统中比现有下界多项式更紧，定性捕捉了精确退火时间随自旋数的标度关系。
We propose a quantum annealing protocol that more effectively probes the dynamics of a single qubit on D-Wave's quantum annealing hardware. This protocol uses D-Wave's h-gain schedule functionality, which allows the rapid quenching of the longitudinal magnetic field at arbitrary points during the anneal. This features enables us to distinguish between open and closed system dynamics as well as the presence or absence of longitudinal magnetic field noise. We show that both thermal and magnetic field fluctuations are key sources of noise that need to be included in an open quantum system model t…
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simultaneous spin flips at each annealing step as an analogue to quantum spin coherence as well as modifications of the Boltzmann acceptance probability to mimic quantum tunneling. We find that the use of multiple spin flips can indeed be advantageous under certain annealing schedules, but only for long anneal times.
From Exponential to Quadratic: Optimal Control for a Frustrated Ising Ring Model
针对带单个阻挫反铁磁键的伊辛环模型中传统量子退火受指数小能隙限制的问题，研究基于变分量子算法数字框架，证明QAOA可实现二次资源缩放的精确求解，并结合CRAB方法与dQA构建高精度最优数字调度。
Mapping State Transition Susceptibility in Quantum Annealing
本研究利用D-Wave量子退火器的反向退火与h增益调度特性，提出量化Ising问题经典态间易感性的方法，在Advantage_system4.1上实验验证并揭示了反向退火的详细特征与中间转移路径。
Inferring the Dynamics of the State Evolution During Quantum Annealing
本研究针对商用量子退火炉无法直接获取退火过程状态信息的问题，利用D-Wave 2000Q的自定义退火调度特性提出“切片”方法，间接推断退火状态演化动力学，可分析比特翻转规律并估算系统及单量子比特的冻结点。
Swapping Quantum Annealing Errors into a Cavity
提出腔量子退火，将退火错误交换为光子，缩短退火时间至平方根量级，并通过光子计数验证高保真结果。
We present a very general construction for quantum annealing protocols to solve Combinational Circuit Fault Diagnosis (CCFD) problems that restricts the evolution to the space of valid diagnoses. This is accomplished by using special local drivers that induce a transition graph on the space of feasible configurations that is regular and instance independent for each given circuit topology. Analysis of small instances shows that the energy gap has a generic form, and that the minimum gap occurs in the last third of the evolution. We used these features to construct an improved annealing schedul…
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima, and the classical approach of simulated annealing is predicted to have a logarithmically slow convergence to the global minimum. We show by extensive numerical analyses that quantum annealing yields a power law convergence, thus an exponential improvement over simulated annealing. The power is larger, and thus the convergence is faster, than a prediction by an…
In this work we revisit and expand on a 2015 study that used a D-Wave quantum annealer as a sampling engine to assist in the training of a Deep Neural Network. The original 2015 results were reproduced using more recent D-Wave hardware. We systematically compare this quantum-assisted training method to a wider range of classical techniques, including: Contrastive Divergence with a different choice of optimizer; Contrastive Divergence with an increased number of steps (CD-k); and Simulated Annealing (SA). We find that quantum-assisted training still outperforms the CD with Gibbs sampling-based …
We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time $t_f$. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of $t_f$ (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between ene…
Sampling diverse near-optimal solutions via algorithmic quantum annealing
本文提出一种量化 NP 难优化问题近似解多样性的新度量，并证明非均匀量子退火通过控制临界前沿和算法量子相变，能同时改善 TTS 与 TTD，在二维自旋玻璃中使解多样性提升达 40%。
Reaching states below the threshold energy in spin glasses via quantum annealing
研究通过量子退火在自旋玻璃模型中实现近似优化，发现其能快速找到低于阈值的能量状态，优于经典退火算法。
QuantumAnnealing: A Julia Package for Simulating Dynamics of Transverse Field Ising Models
QuantumAnnealing.jl是一个开源Julia包，提供在经典硬件上模拟横场伊辛模型时间演化的工具，支持复现与自定义退火时间表，用于量子设备性能验证与快速原型设计。
Learning-Driven Annealing with Adaptive Hamiltonian Modification for Solving Large-Scale Problems on Quantum Devices
本研究提出学习驱动退火（LDA）框架，通过自适应修正问题哈密顿量聚焦低能演化，构建的混合量子-经典求解器在5580量子比特自旋玻璃问题上性能优于多种经典与量子算法，推动实用量子计算发展。
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the transverse Ising model and the traveling salesman problem (TSP). Adding the transverse field to the Ising model is a simple way to introduce quantum fluctuations. The strength of the transverse field is controlled as a function of time similarly to the temperature in the conventional method. TSP can be described by the Ising spin, so that we also apply the same technique to TSP. We directory solve the time-…
Application of Quantum Annealing to Nurse Scheduling Problem
本研究利用D-Wave 2000Q量子退火设备解决带硬约束的护士排班问题，通过新颖的伊辛型哈密顿量建模，实验表明量子退火能获得满意解，且反向退火可显著提升解质量，证实其实际应用潜力。
Advanced anneal paths for improved quantum annealing
该研究利用D-Wave退火仪的反向退火、h增益功能及二者的混合调度方案，结合贝叶斯优化调参，在加权最大割等NP难问题上验证了不同技术的适用性，提出h增益可作为反向退火的可行替代方案。
Extending the computational reach of Quantum Annealing using Reverse Annealing
本文通过实验证明，结合正向和反向退火能持续提升量子退火在多种问题上的解质量和效率，且反向退火在复杂问题上优势显著，优于单纯延长退火时间。
Quantum annealing is explored as a resource for quantum information beyond solution of classical combinatorial problems. Envisaged as a generator of robust interferometric probes, we examine a Hamiltonian of $N>> 1$ uniformly-coupled spins subject to a transverse magnetic field. The discrete many-body problem is mapped onto dynamics of a single one-dimensional particle in a continuous potential. This reveals all the qualitative features of the ground state beyond typical mean-field or large classical spin models. It illustrates explicitly a graceful warping from an entangled unimodal to bi-mod…
Scheduling Quantum Annealing for Active User Detection in a NOMA Network
针对NOMA网络活跃用户检测中经典算法复杂度与性能的权衡问题，提出一种量子退火调度方法，通过通用控制函数在保证高成功概率的同时显著降低退火时间。
Quantum Annealing with chaotic driver Hamiltonians
研究在量子退火中引入基于SYK模型的混沌量子驱动哈密顿量，发现其非局域性与非对易性在MaxCut和LABS等大规模优化任务中相比传统横向场退火能实现显著加速。
Why adiabatic quantum annealing is unlikely to yield speed-up
本文研究了组合优化中的量子退火，证明由于最小谱隙位置的计算依赖于难以求解的态密度，量子加速在实际问题中不可行，并推测该结论适用于其他实例无关的横向哈密顿量。
Neural and Tensor Networks in the Study of Quantum Annealing Processors
本文提出基于张量网络的优化方法和量子退火处理器的评估框架，结合经典基线、采样和多样性指标，探讨算法性能与物理消耗的联合测量。
Diabatic quantum annealing for training energy-based generative models
利用非绝热量子退火实现温度可控的玻尔兹曼采样，提升RBMs训练效率并拓展至全连接玻尔兹曼机。
Comparing Quantum Annealing and Spiking Neuromorphic Computing for Sampling Binary Sparse Coding QUBO Problems
本研究针对二元稀疏编码QUBO问题，分别在D-Wave量子退火器和Intel Loihi 2脉冲神经形态处理器上求解，并引入迭代反向退火等方法优化，验证了两类计算的适用性且迭代反向量子退火表现最优。
Quantum Annealing Approaches to Solving the Shipment Rerouting Problems
针对 NP 难的货物改道路线问题，论文提出结合新型数学规划公式的经典算法与量子退火算法，并通过实验证明量子退火可更快获得最优或近优解。
Continuous-time quantum optimisation without the adiabatic principle
针对连续时间量子优化算法原有绝热原理动机的局限，研究以普朗克原理为物理依据，论证了非绝热量子退火单调调度的合理性，并揭示了孤立系统中反向量子退火的局限性。
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