Hybrid Quantum Annealing for Larger-than-QPU Lattice-structured Problems

Abstract

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open-source D-Wave Hybrid framework, uses a QPU coprocessor operating with generic parameters. Performance is evaluated for standard spin-glass problems on two lattice types with up to 11616 spin variables, double the size that is directly programmable on any available QPU. The proposed method is shown to converge to low-energy solutions faster than an open-source simulated annealing method that is either directly employed or substituted as a coprocessor in the hybrid method. Using newer Advantage QPUs in place of D-Wave 2000Q QPUs is shown to enhance convergence of the hybrid method to low energies and to achieve a lower final energy.

Quantum annealing for microstructure equilibration with long-range elastic interactions

“…Ideally, these spins should represent the same state as the individual spins, but in practise this identity can be violated. To avoid this issue and to simulate even larger systems, which are essential for higher dimensional modeling in the following sections, hybrid classical and quantum annealing approaches can be used, which combine pure QA with conventional minimization approaches 36 . The numerical results in Fig.…”

“…As in practise this approach does not always deliver the lowest energy state, especially if energetically close low energy states exist, a suitable number of repetitions is made and the configuration with the lowest detected energy is taken. If the Ising problems do not match the architecture of the QPU, a subgraph of coupled qubits, know as chains, cover one variable of the problem in the so called minor embedding 36,46 . Additionally, for huge systems hybrid quantum annealing exploits classical algorithms and the interplay with quantum annealing in areas of high computational demands using a QPU coprocessor working with generic parameters for up to 11616 spin variables on the D-Wave Advantage system 36,47 .…”

Efficient low temperature Monte Carlo sampling using quantum annealing

“…However, the development of quantum annealing is still at its beginning and progressing fast, hence it can be expected that in the future faster and highly connected machines, especially with a higher number of accessible qubits, will be available, which will allow to study also models in higher dimensions with first and second order phase transitions also at finite temperatures. In the meantime, also the use of hybrid approaches 31 , which combine QA and classical minimization methods, may turn out to be useful also for finite temperature sampling. Such approaches are in general already provided by D-Wave, but they currently require manual repeated sampling due to the lower efficiency compared to pure QA.…”

“…If the Ising problems do not match the architecture of the QPU, a subgraph of coupled qubits, know as chains, cover one variable of the problem in the so called minor embedding 31,40 . In practise, the D-Wave framework Leap 41 allows a direct formulation in terms of a problem Ising Hamiltonian.…”

Efficient low temperature Monte Carlo sampling using quantum annealing

“…However, the development of quantum annealing is still at its beginning and progressing fast, hence it can be expected that in the future faster and highly connected machines, especially with a higher number of accessible qubits, will be available, which will allow to study also models in higher dimensions with first and second order phase transitions also at finite temperatures. In the meantime, also the use of hybrid approaches 44 , which combine QA and classical minimization methods, may turn out to be useful also for finite temperature sampling. Such approaches are in general already provided by D-Wave, but they currently require manual repeated sampling due to the lower efficiency compared to pure QA.…”