Quantum annealing and D-Wave quantum annealer attracted considerable attention for their ability to solve combinatorial optimization problems. In order to solve other type of optimization problems, it is necessary to apply certain kinds of mathematical transformations. However, linear constraints reduce the size of problems that can be represented in quantum annealers, owing to the sparseness of connections between qubits. For example, the quadratic assignment problem (QAP) with linear equality constraints can be solved only up to size 12 in the quantum annealer D-Wave Advantage, which has 5640 qubits. To overcome this obstacle, Ohzeki developed a method for relaxing the linear equality constraints and numerically verified the effectiveness of this method with some target problems, but others remain unsolvable. In particular, it is difficult to obtain feasible solutions to problems with hard constraints, such as the QAP. We therefore propose a method for solving the QAP with quantum annealing by applying a post-processing bit-flip heuristic algorithm to solutions obtained by the Ohzeki method. In a numerical experiment, we solved a sparse QAP by the proposed method. This sparse QAP has been used in areas such as item listing on an E-commerce website. We successfully solved a QAP of size 19 with high accuracy for the first time using D-Wave Advantage. We also confirmed that the bit-flip heuristic algorithm moves infeasible solutions to nearby feasible solutions in terms of Hamming distance with good computational efficiency.
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.
As the number of qubits available on noisy quantum computers grows, it will become necessary to efficiently select a subset of physical qubits to use in a quantum computation. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while r…
In this paper, we present a hybrid quantum/classical algorithm to solve an NP-hard combinatorial problem called the multiple target data association (MTDA) and tracking problem. We use diabatic quantum annealing (DQA) to enumerate the low energy, or high probability, feasible assignments, and we use a classical computer to find the Bayesian expected mean track estimate by summing over these assignments. We demonstrate our hybrid quantum/classical approach on a simple example. This may be the first demonstration of a Bayesian hybrid quantum-classical multiple target tracking filter. We contrast…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum, however the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small da…
Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables after they are mapped to the Ising spin Hamiltonian of quantum annealing. To account for hardware constraints of current and future physical quantum annealers, methods enabling the embedding of fully connected graphs of logical spins into a constant-degree graph of physical spins are therefore essential. Here, we compare the recently proposed embedding scheme for quantum annealing with all-to-all con…
Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise, and we analyze the code's performance using a belief-propagation decoding algorithm. Our observations may also apply to more general encoding schemes and noise models.
We introduce a novel Simulated Quantum Annealing (SQA) algorithm which employs a multispin quantum fluctuation operator. At variance with the usual transverse field, short-range two-spin flip interactions are included in the driver Hamiltonian. A Quantum Monte Carlo algorithm, capable of efficiently simulating large disordered systems, is described and tested. A first application to SQA, on a random square lattice Ising spin glass reveals that the multi-spin driver Hamiltonian improves upon the usual transverse field. This work paves the way for more systematic investigations using multi-spin …
Google（谷歌）；Institute for Solid State Physics（固体物理研究所）；University of Tokyo（东京大学）
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.
Spin Model for Quantum Annealing with Kerr Parametric Oscillators
Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Secure System Platform Research Laboratories, NEC Corporation（NEC公司安全系统平台研究实验室）；NEC-AIST Quantum Technology Cooperative Research Laboratory（NEC-AIST量子技术联合研究实验室）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
We consider a range of unconventional modifications to Quantum Annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by "transverse field chaos" in larger systems, classical and quantum methods are steered toward a false local minimum. To go from this local minimum to the global minimum, all N spins must flip, making this problem exponentially difficult to solve. We numerically study this problem by using a variety of new methods from the literature: inhomogeneous driving, adding transverse couplers, and other types of coherent o…
A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$ qubits --- is closely tracked as it becomes more and more localised near the global minimum of the classical energy. Regions where the energy gap to excited states is small (e.g. at the phase transition) are the algorithm's bottlenecks. Here I show how for large problems the complexity becomes dominated by $O(\log N)$ bottlenecks inside the spin glass phase, …
Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between the chain qubits, are applied so that the physical qubits in a chain favor taking the same value in low energy samples. Assigning a good chain-strength value is crucial for the ability of quantum annealing to solve hard problems, but there are no general methods for computing such a value and, even if an optimal value is found, it may still not be suitable b…
Practical Noise Mitigation for Quantum Annealing via Dynamical Decoupling: Toward Industry-Relevant Optimization using Trapped Ions
University of Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所-特伦托基础物理与应用研究所）；Department of Electrical Engineering and Computer Science, University of Siegen（锡根大学电气与计算机工程系）；eleQtron GmbH（eleQtron有限公司）
We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N=100 and N=80 variables, respectively. In the classical limit we employ generalized ensemble techniques and measure the time that a Markovian Monte Carlo process spends in searching classical ground states. In the quantum limit we determine the maximum finite correlation length along a quantum adiabatic trajectory determined by the linear sweep of the adiabatic control parameter in the Hamiltonian composed of the problem Hamiltonian and the …
Practical hybrid decoding scheme for parity-encoded spin systems
NEC-AIST Quantum Technology Cooperative Research Laboratory（NEC-AIST量子技术联合研究实验室）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, eq…
QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning
School of Electronic Information, Central South University（中南大学电子信息学院）；School of Computer Science and Engineering, Central South University（中南大学计算机科学与工程学院）；Beijing QBoson Quantum Technology Co. Ltd.（北京QBoson量子科技有限公司）；Institute of Artificial Intelligence (TeleAI) of China Telecom（中国电信人工智能研究院（TeleAI））
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…
Quantum devices can be used to solve constrained combinatorial optimization (COPT) problems thanks to the use of penalization methods to embed the COPT problem's constraints in its objective to obtain a quadratic unconstrained binary optimization (QUBO) reformulation of the COPT. However, the particular way in which this penalization is carried out, affects the value of the penalty parameters, as well as the number of additional binary variables that are needed to obtain the desired QUBO reformulation. In turn, these factors substantially affect the ability of quantum computers to efficiently …
In this article, we show how to map a sampling of the hardest artificial intelligence problems in space exploration onto equivalent Ising models that then can be attacked using quantum annealing implemented in D-Wave machine. We overview the existing results as well as propose new Ising model implementations for quantum annealing. We review supervised and unsupervised learning algorithms for classification and clustering with applications to feature identification and anomaly detection. We introduce algorithms for data fusion and image matching for remote sensing applications. We overview plan…
Feasibility and optimum recovery in warm-start quantum optimization for a drug-response model on a trapped-ion processor
BRAC University（布拉格大学）；University of Southern Queensland（昆士兰南部大学）；UNSW Sydney（新南威尔士大学悉尼分校）；West Moreton Health（西莫顿健康）；Imperial College London（伦敦帝国理工学院）；Technical University of Munich (TUM)（慕尼黑工业大学）；Cogninet AI；Pawsey Supercomputing Research Centre（Pawsey超级计算研究中心）
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…
United Technologies Research Center（联合技术研究中心）；SRI International（SRI国际）
Given a Boolean formula $ϕ(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the \emph{hardness} of the problem instance. Consequently, in real-world scenarios, this problem is typically infeas…
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $γ=M/N$. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (versus only energy) is used, …
