By analyzing the characteristics of hardware-native Ising Models and their performance on current and next generation quantum annealers, we provide a framework for determining the prospect of advantage utilizing adiabatic evolution compared to classical heuristics like simulated annealing. We conduct Ising Model experiments with coefficients drawn from a variety of different distributions and provide a range for the necessary moments of the distributions that lead to frustration in classical heuristics. By identifying the relationships between the linear and quadratic terms of the models, analysis can be done a priori to determine problem instance suitability on annealers. We then extend these experiments to a prototype of D-Wave's next generation device, showing further performance improvements compared to the current Advantage annealers.
By analyzing the characteristics of hardware-native Ising Models and their performance on current and next generation quantum annealers, we provide a framework for determining the prospect of advantage utilizing adiabatic evolution compared to classical heuristics like simulated annealing. We conduct Ising Model experiments with coefficients drawn from a variety of different distributions and provide a range for the necessary moments of the distributions that lead to frustration in classical heuristics. By identifying the relationships between the linear and quadratic terms of the models, analysis can be done a priori to determine problem instance suitability on annealers. We then extend these experiments to a prototype of D-Wave's next generation device, showing further performance improvements compared to the current Advantage annealers.
We investigate the performance of different annealers for power flow analysis using adiabatic computing. The annealers include D-Wave's simulated annealer Neal, D-Wave's quantum-classical hybrid annealer, D-Wave's Advantages system (QA), Fujitsu's classical simulated annealer, and Fujitsu's digital annealer V3 (DA). We implement Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations, with the latter offering finer control over complex voltage adjustments. Different test systems are experimented with to systematically evaluate the annealers. The evaluation is based on the accuracy, the annealer's capability to handle the decision variables, and the computational time needed. QA and DA show superior performance over classical annealers for our application. DA effectively manages larger test systems, whereas QA encounters difficulties embedding the problem graph onto the hardware graph because of the limited qubit connectivity. This constraint confines QA to the 14-bus system with the QUBO formulation and the 4-bus system with the Ising model formulation. The best performance is associated with different annealers across different test systems, which suggests that adjusting the threshold can improve precision if the compiler and annealer are capable of handling the number of variables involved.
We investigate the performance of different annealers for power flow analysis. The annealers are D-Wave’s simulated annealer Neal, D-Wave’s quantum-classical hybrid annealer, D-Wave’s Advantage™ system (QA), Fujitsu’s simulated annealer, and Fujitsu’s digital annealer V3 (DA). We implement Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations, with the latter offering finer control over complex voltage adjustments. We also propose a new method for the iterative and adaptive updating of complex voltages for the QUBO and Ising model formulations. Six different test systems are experimented with. QA and DA show superior performance over classical annealers. DA effectively manages the 15-bus system, whereas QA encounters difficulties in embedding the problem graph onto the hardware graph because of the limited qubit connectivity. This constraint confines QA to the 14-bus system with the QUBO formulation and the 4-bus system with the Ising model formulation. The best performance is associated with different annealers across different test systems, which suggests that adjusting the threshold can improve precision if the compiler and annealer are capable of handling the variables involved.
Quantum annealing was originally proposed as an approach for solving combinatorial optimization 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 problem, and several studies have investigated Boltzmann machine learning using a quantum annealer. Previous developments have focused on comparing the performance in the standard distance of the resulting distributions between conventional methods in classical computers and sampling by a quantum annealer. In this study, we focused on the performance of a quantum annealer as a generative model from a different aspect. To evaluate its performance, we prepared a discriminator given by a neural network trained on an a priori dataset. The evaluation results show a higher performance of quantum annealer compared with the classical approach for Boltzmann machine learning in training of the generative model. However the generation of the data suffers from the remanent quantum fluctuation in the quantum annealer. The quality of the generated images from the quantum annealer gets worse than the ideal case of the quantum annealing and the classical Monte-Carlo sampling.
In this thesis, we focus on the problem of validating and benchmarking quantum annealers. To this end, we propose two algorithms for solving real-world problems and test how they perform on the current generation of quantum annealers. The first algorithm allows for solving the dynamics of quantum systems (or, in fact, any dynamical systems). The second of the proposed algorithms is suitable for solving a particular family of railway dispatching problems. We assess the performance of those algorithms on the current generation of D-Wave quantum annealers with the assistance of two novel, classical strategies for solving an Ising model also presented in the thesis. The first, tensor network-based approach is a heuristic algorithm tailored for solving instances defined on Chimera-like graphs, thus making it ideal for providing a baseline with which the results from physical annealers can be compared. The other presented approach is a massively parallel implementation of the exhaustive (brute-force) search through the whole solution space. Although the brute-force approach is limited to moderate instance sizes, it has the advantage of being able to compute the low energy spectrum and certify the solutions. Our results suggest that present-day quantum annealers are able to solve a subset of the aforementioned problems. In particular, we show that the D-Wave annealers are capable of capturing the dynamics of a simple quantum system in a specific regime of parameters, and can be used to obtain good-quality solutions for instances of railway conflict management problems. Finally, our findings indicate that the current generation of D-Wave annealers is far from perfect. We discuss problem instances for which the annealers failed to find a good or even feasible solution. We also provide, where possible, a plausible explanation of why some of the presented problems might be hard for the annealers.
Quantum annealers are computing machines that utilize quantum effects to solve hard optimization problems. Understanding the circumstances under which quantum annealers are more efficient than other optimization methods is a challenging open problem. A clue to this conundrum comes from studying the complexity of quantum annealers. In general, the complexity of a physical system relates to how efficiently the system can be simulated by classical algorithms. One then asks: if some class of quantum annealers are hard to simulate classically, are they also more powerful optimization machines? Here, the authors study quantum annealers belonging to two different complexity classes: the so-called ``stoquastic'' systems, which can be efficiently simulated with classical algorithms, and ``nonstoquastic'' systems, currently with no efficient classical treatment. Applied to a prototypical optimization problem, the authors observe that, on average, the stoquastic systems perform better on easier instances of the problem, while the more complex nonstoquastic annealers show significant advantage when applied to the hardest instances. The authors conjecture that the performance of the nonstoquastic Hamiltonians is closely related to their internal structure during the annealing process and elucidate how properties such as magnetic frustration can play a key role in devising more powerful quantum annealers.
Ising machines are a promising approach to solve combinatorial optimization problems. They map these problems onto the Ising model and search for low-energy configurations. However, navigating the rugged energy landscapes of these systems remains difficult. To improve this navigation, classical adiabatic annealing has been proposed in the literature as a heuristic optimization method for classical Ising machines. Using this technique, the Hamiltonian of the Ising machine is gradually transformed from an easily solvable Hamiltonian to the target Hamiltonian. However, its purported effectiveness is primarily motivated by an analogy to quantum adiabatic annealing, and systematic benchmarking has remained limited.
In this work, we analyze the classical adiabatic annealing technique using continuation methods. Motivated by insights from this analysis, we propose an optimized annealing strategy we refer to as hybrid classical adiabatic annealing. We benchmark our proposed strategy using MaxCut instances with up to 800 spins and problems with external fields, for which it achieves a marginal improvement for a limited set of problems. We conclude that, although theoretically motivated and occasionally beneficial, the hybrid strategy does not offer a sufficient practical advantage over simpler, existing techniques.