Mapping state transition susceptibility in quantum annealing

Abstract

Quantum annealing is a novel type of analog computation that aims to use quantum-mechanical fluctuations to search for optimal solutions for Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave devices, works by applying a time-dependent transverse field, which puts all qubits into a uniform state of superposition, and then applying a Hamiltonian over time, which describes a user-programed Ising problem. We present a method that utilizes two control features of D-Wave quantum annealers, namely reverse annealing and an $h$-gain schedule, to quantify the susceptibility, or the distance, between two classical states of an Ising problem. The starting state is encoded using reverse annealing, and the second state is encoded on the linear terms of a problem Hamiltonian. An $h$-gain schedule is specified, which incrementally increases the strength of the linear terms, thus allowing a quantification of the $h$-gain strength required to transition the anneal into a specific state at the final measurement. Because of the nature of quantum annealing, the state tends towards global minima, and therefore we restrict the second classical state to a minimum solution of the given Ising problem. This susceptibility mapping, when enumerated across all initial states, shows in detail the behavior of the quantum annealer during reverse annealing. The procedure is experimentally demonstrated on three small test Ising models which were embedded in parallel on the D-Wave Advantage_system4.1. Analysis of the state transition mapping shows detailed characteristics of the reverse annealing process, including intermediate state transition paths, which are visually represented as state transition networks.