Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

中文翻译：

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受挫环模型的非绝热量子退火


量子退火（QA）是一种连续时间启发式量子算法，用于求解或近似求解经典优化问题。该算法使用时间表在具有易于准备的基态的驱动哈密顿量和其基态编码优化问题的解的问题哈密顿量之间进行插值。标准的实现依赖于绝热演化：以高概率将系统保持在瞬时基态，并且需要与瞬时基态和激发态之间的最小能隙成反比的时间尺度。然而，绝热演化可能会导致演化时间随着系统规模呈指数级增长，即使对于计算简单的问题也是如此。在这里，我们研究了具有优化退火方案的非绝热演化是否可以绕过称为受挫环模型的此类问题的指数减速。对于充分优化的退火计划和高达 39 个量子位的系统大小，我们提供了数字证据，表明我们可以避免指数减速。我们的工作强调了高度可控的质量保证在规避与质量保证标准实施相关的瓶颈方面的潜力。