Motivated by recent experiments in which specific thermal properties of complex many-body systems were successfully reproduced on a commercially available quantum annealer, we examine the extent to which quantum annealing hardware can reliably sample from the thermal state in a specific basis associated with a target quantum Hamiltonian. We address this question by studying the diagonal thermal properties of the canonical one-dimensional transverse-field Ising model on a D-Wave 2000Q quantum annealing processor. We find that the quantum processor fails to produce the correct expectation values predicted by Quantum Monte Carlo. Comparing to master equation simulations, we find that this discrepancy is best explained by how the measurements at finite transverse fields are enacted on the device. Specifically, measurements at finite transverse field require the system to be quenched from the target Hamiltonian to a Hamiltonian with negligible transverse field, and this quench is too slow. The limitations imposed by such hardware make it an unlikely candidate for thermal sampling, and it remains an open question what thermal expectation values can be robustly estimated in general for arbitrary quantum many-body systems.
By contrasting the performance of two quantum annealers operating at different temperatures, we address recent questions related to the role of temperature in these devices and their function as `Boltzmann samplers'. Using a method to reliably calculate the degeneracies of the energy levels of large-scale spin-glass instances, we are able to estimate the instance-dependent effective temperature from the output of annealing runs. Our results show that the output distributions of the annealers do not in general correspond to classical Boltzmann distributions. For the small fraction of the instan…
The debate around the potential superiority of quantum annealers over their classical counterparts has been ongoing since the inception of the field by Kadowaki and Nishimori close to two decades ago. Recent technological breakthroughs in the field, which have led to the manufacture of experimental prototypes of quantum annealing optimizers with sizes approaching the practical regime, have reignited this discussion. However, the demonstration of quantum annealing speedups remains to this day an elusive albeit coveted goal. Here, we examine the power of quantum annealers to provide a different …
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland（马里兰大学）
Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landsc…
We present \emph{multi-qubit correction} (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels--i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value--and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum a…
We present and apply a general-purpose, multi-start algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable, since each start in the multi-start algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to…
We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on the commercially available D-Wave machin…
We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are usually much easier for the quantum annealer to solve, due to their being smaller and consisting of disconnected components. This approach significantly increases the success rate and number of observations of the best known energy value in samples obtained from the quantum annealer, when compared wi…
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究科）；Institute for Innovative Research, Tokyo Institute of Technology（东京工业大学创新研究所）；Sigma-i Co., Ltd.（Sigma-i 有限公司）
Quantum annealing was originally proposed as an approach for solving combinatorial optimisation problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and various environmental factors in the hardware hamper the determination of optimal solutions. In addition, the freezing effect in regions with weak quantum fluctuations generates outputs approximately following a Gibbs--Boltzmann distribution at an extremely low temperature. Thus, a quantum annealer may also serve as a fast sampler for the Ising spin-glass prob…
Testing Quantum and Simulated Annealers on the Drone Delivery Packing Problem
Gran Sasso Science Institute（格兰萨索科学研究所）；Quantum Computing Research Laboratory, Leonardo S.p.A.（莱昂纳多公司量子计算研究实验室）；Digital Infrastructures, Leonardo S.p.A.（莱昂纳多公司数字基础设施部门）；School of Mathematics and Maxwell Institute, University of Edinburgh（爱丁堡大学数学学院与麦克斯韦研究所）
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Stinger Ghaffarian Technologies Inc.（斯汀格·加法里安技术公司）；D-Wave Systems Inc.（D-Wave系统公司）；University of Florence（佛罗伦萨大学）；Simon Fraser University（西蒙弗雷泽大学）
The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to, and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from either a quantum or classical Boltzmann machine (QBM or BM). This setup allows quantum-assisted training of deep generative models by phy…
Machine learning applications are limited by computational power. In this paper, we gain novel insights into the application of quantum annealing (QA) to machine learning (ML) through experiments in natural language processing (NLP), seizure prediction, and linear separability testing. These experiments are performed on QA simulators and early-stage commercial QA hardware and compared to an unprecedented number of traditional ML techniques. We extend QBoost, an early implementation of a binary classifier that utilizes a quantum annealer, via resampling and ensembling of predicted probabilities…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been profoundly successful in pushing the boundaries of AI. It is thus natural to investigate potentially game changing technologies such as quantum annealers to augment the capabilities of deep learning. In this work, we explore binary neural networks, which are lightweight yet powerful models typically intended for resource constrained devices. Departing from current…
Filtering out mislabeled training instances using black-box optimization and quantum annealing
LiLz Inc.（LiLz公司）；Graduate School of Information Sciences, Tohoku University（东京大学信息科学研究生院）；Sigma-i Co., Ltd.（Sigma-i公司）；Department of Physics, Institute of Science Tokyo（科学东京系物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息学研究教育院）
The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that th…
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 distri…
Multi-particle interference is a key resource for quantum information processing, as exemplified by Boson Sampling. Hence, given its fragile nature, an essential desideratum is a solid and reliable framework for its validation. However, while several protocols have been introduced to this end, the approach is still fragmented and fails to build a big picture for future developments. In this work, we propose an operational approach to validation that encompasses and strengthens the state of the art for these protocols. To this end, we consider the Bayesian hypothesis testing and the statistical…
Quantum annealers have been designed to propose near-optimal solutions to NP-hard optimization problems. However, the accuracy of current annealers such as the ones of D-Wave Systems, Inc., is limited by environmental noise and hardware biases. One way to deal with these imperfections and to improve the quality of the annealing results is to apply a variety of pre-processing techniques such as spin reversal (SR), anneal offsets (AO), or chain weights (CW). Maximizing the effectiveness of these techniques involves performing optimizations over a large number of parameters, which would be too co…
This paper presents the details and testing of two implementations (in C++ and Python) of the hybrid quantum-classical algorithm Quantum Annealing Learning Search (QALS) on a D-Wave quantum annealer. QALS was proposed in 2019 as a novel technique to solve general QUBO problems that cannot be directly represented into the hardware architecture of a D-Wave machine. Repeated calls to the quantum machine within a classical iterative structure and a related convergence proof originate a learning mechanism to find an encoding of a given problem into the quantum architecture. The present work conside…
