Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. D-Wave Systems, Inc., manufactures quantum annealers, which are available as cloud computing resources, and allow users to program the anneal schedules used in the annealing computation. In this paper, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state. We explore two D-Wave features allowing one to encode such an initial state: the reverse annealing and the h-gain features. Reverse annealing (RA) aims to refine a known solution following an anneal path starting with a classical state representing a good solution, going backwards to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The h-gain (HG) feature allows one to put a time-dependent weighting scheme on linear ($h$) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the weighted Maximum Cut problem and the weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random spin glasses with the native connectivity of the D-Wave Chimera and Pegasus chips.

翻译：量子退火是一种专用型量子计算，旨在利用量子涨落获取组合优化问题的全局最小值解。D-Wave系统公司制造的量子退火器已作为云计算资源提供，允许用户编程控制退火计算中使用的退火调度方案。本文关注通过编码初始态来提升量子退火器输出解的质量，探索了D-Wave平台两种实现初始态编码的特性：逆向量子退火和h增益特征。逆向量子退火旨在优化已知解，其退火路径始于代表优秀解经典态的初始状态，逆向行进至存在横向场的临界点，随后通过正向退火完成计算过程。h增益特征允许在哈密顿量的线性（$h$）偏置上施加时间依赖的加权方案，本文证明该特征同样可用于引导退火过程从指定初始态开始。我们还提出一种混合方法，包含类似逆向量子退火的逆向阶段与采用h增益初始态编码的正向阶段。关键创新在于，我们研究了针对同一问题迭代应用逆向量子退火和h增益的过程，目标是在非最优初始态基础上实现单调改进。在加权最大割问题与加权最大团问题等多种输入问题上的评估表明，对于某些问题，h增益编码技术是逆向量子退火的可行替代方案。我们还基于D-Wave Chimera和Pegasus芯片的原生连接性，研究了随机自旋玻璃系统中两种初始态编码方法的迭代性能表现。