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arXiv:2004.03972 · Scientific Reports

Hybrid quantum annealing via molecular dynamics

Hirotaka Irie, Haozhao Liang, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda

Published Apr 19, 2021• 32 citations
arXivHTMLPDF

Abstract

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

DOI
10.1038/s41598-021-87676-z

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A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and refining it using QA. In previous studies, such variables were determined using molecular dynamics (MD) as a continuous optimization method. We propose a method that uses the simple continuous relaxation technique called linear programming (LP) relaxation. Our method demonstrated superiority through comparative experiments with the minimum vertex cover problem versus the previous MD-based approach. Furthermore, the hybrid approach of LP relaxation and simulated annealing showed advantages in accuracy and speed compared to solving with simulated annealing alone.
Ising machines have the potential to realize fast and highly accurate solvers for combinatorial optimization problems. They are classified based on their internal algorithms. Examples include simulated-annealing-based Ising machines (non-quantum-type Ising machines) and quantum-annealing-based Ising machines (quantum annealers). Herein we propose a hybrid optimization method, which utilizes the advantages of both types. In this hybrid optimization method, the preprocessing step is performed by solving the non-quantum-annealing Ising machine multiple times. Then sub-Ising models with a reduced size by spin fixing are solved using a quantum annealer. The performance of the hybrid optimization method is evaluated via simulations using Simulated Annealing (SA) as a non-quantum-type Ising machine and D-Wave Advantage as a quantum annealer. Additionally, we investigate the parameter dependence of the proposed hybrid optimization method. The hybrid optimization method outperforms the preprocessing SA and the quantum annealing machine alone in fully connected random Ising models.
The path integral Monte Carlo simulated quantum annealing algorithm is applied to the optimization of a large hard instance of the random satisfiability problem (N = 10,000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the traveling salesman problem, in the present case the linear-schedule quantum annealing performance is definitely worse than classical annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.
This paper investigates the application of quantum annealing for the combinatorial optimization challenges inherent in large-scale simulations. We demonstrate that classical algorithms frequently encounter significant computational bottlenecks when tackling complex problems such as molecular dynamics simulations, materials design, and financial modeling. Quantum annealing, leveraging quantum tunneling, offers a potential paradigm shift by providing a mechanism for directly mapping these optimization problems onto quantum hardware and exploring the solution space with enhanced efficiency. This work presents a theoretical framework outlining the approach and discusses the core principles underlying its implementation. The focus is on the potential to accelerate computationally intensive simulations, addressing a critical limitation in current simulation methodologies. We explore the challenges and opportunities associated with this emerging technology, emphasizing its role in overcoming the limitations of classical optimization techniques. The primary goal is to provide a foundational understanding of how quantum annealing can be strategically applied to significantly improve the speed and accuracy of large-scale simulations.
A combinatorial optimization problem is the problem of minimizing the energy function among many combinations of variables, which is often difficult to solve with conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. Among various methods for solving such problems using Ising machines, one prominent approach is the three-stage annealing method. The approach effectively solves a combinatorial optimization problem, utilizing an initial solution, but it performs the annealing process only once. Repeating the annealing process several times may enhance the solution more efficiently. In this paper, we propose a novel hybrid iterative annealing method that consists of an initial process using a classical computer, an annealing process using a quantum annealer, and a correction process/selection process using a classical computer. The proposed method repeats the annealing process and the correction process/selection process until the solution is sufficiently converged. In the experimental evaluations through the three types of typical combinatorial optimization problems, the proposed method shows improvements by up to 54.0% compared to the three-stage annealing method.
Abstract : Many computationally challenging problems can be reduced to Quadratic Unconstrained Binary Optimization (QUBO), which can be solved by a quantum evolution from a strong transverse field to a spin glass Hamiltonian (also known as quantum annealing or QA). We have examined open system QA, using theoretical and experimental techniques to deepen our understanding of open system QA by situating it in the context of related, well studied classical and quantum problems. We have explored and elucidated the significance of tunneling in QA with Path Integral Monte Carlo. We have also provided signatures of quantum behavior of QA against closely related simulated annealing implementations, analytically, numerically, and experimentally. We have carried out a comprehensive comparison of geometrically-local open-system QA and classical solvers for computationally hard problems such as MAX-2-SAT. We have exploited and further developed a graph-theoretical mapping between the Ising spin glass partition function and circuit model decision problems, discovered in a previous ARO Quantum Algorithms funded project. We have made significant progress on error correction techniques for QA, both theoretically and experimentally, and in demonstration of quantum speedup.