Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of 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 programmed Ising problem. We present a method which utilizes two control features of D-Wave quantum annealers, 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 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. By 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's 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.

翻译：量子退火是一种新型模拟计算方式，旨在利用量子力学涨落寻找伊辛问题的最优解。基于D-Wave设备实现的横向场伊辛模型量子退火，通过施加含时横向场使所有量子比特处于均匀叠加态，再随时间施加描述用户编程伊辛问题的哈密顿量。我们提出一种方法，利用D-Wave量子退火器的两项控制功能——反向退火与h增益调度——来量化伊辛问题两个经典状态之间的跃迁敏感性（即距离）。初始状态通过反向退火编码，第二状态编码于问题哈密顿量的线性项中。通过指定逐渐增强线性项强度的h增益调度，可量化使退火过程在最终测量时跃迁至特定状态所需的h增益强度。鉴于量子退火的本质是使系统趋向全局最小值，我们将第二经典状态限定为给定伊辛问题的最小解。当对所有初始状态枚举时，这种敏感性映射能详细展示量子退火器在反向退火过程中的行为。该过程在三个嵌入D-Wave Advantage_system4.1并行运行的小型测试伊辛问题上进行了实验验证。对状态跃迁映射的分析揭示了反向退火过程的精细特征，包括中间态跃迁路径，这些路径以状态跃迁网络的可视化形式呈现。