The quantum annealing gap and quench dynamics in the exact cover problem

TL;DR

This paper explores the relationship between quantum quench and annealing dynamics in the exact cover problem, demonstrating how quench data can predict the annealing gap and optimize quantum annealing protocols.

Contribution

It introduces a method to infer the annealing gap from quench dynamics using neural networks, aiding in designing more efficient quantum annealing strategies.

Findings

Quench parameters can reveal the minimum annealing gap.

Neural networks can predict the annealing gap from quench data.

Optimized protocols improve quantum annealing efficiency.

Abstract

Quenching and annealing are extreme opposites in the time evolution of a quantum system: Annealing explores equilibrium phases of a Hamiltonian with slowly changing parameters and can be exploited as a tool for solving complex optimization problems. In contrast, quenches are sudden changes of the Hamiltonian, producing a non-equilibrium situation. Here, we investigate the relation between the two cases. Specifically, we show that the minimum of the annealing gap, which is an important bottleneck of quantum annealing algorithms, can be revealed from a dynamical quench parameter which describes the dynamical quantum state after the quench. Combined with statistical tools including the training of a neural network, the relation between quench and annealing dynamics can be exploited to reproduce the full functional behavior of the annealing gap from the quench data. We show that the partial or full knowledge about the annealing gap which can be gained in this way can be used to design optimized quantum annealing protocols with a practical time-to-solution benefit. Our results are obtained from simulating random Ising Hamiltonians, representing hard-to-solve instances of the exact cover problem.