Quantum annealing is a powerful alternative model of quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive demonstration of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage (such as the adiabatic formulation of Grover’s search problem) generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by experimental uncertainties and random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we explore three realistic noise channels and show that the speedup from RFQA is resilient to 1/f-like local potential fluctuations and local heating from interaction with a sufficiently low temperature bath. Another noise channel, bath-assisted quantum cooling transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. We also detail how RFQA may be implemented experimentally with current technology.

量子退火是量子计算的强大替代模型，即使没有纠错，它也可以在存在环境噪声的情况下成功实现。然而，尽管付出了很大的努力，但对于这些系统，尚未显示出量子加速的结论性证明（相对于现有技术的经典算法），并且量子优势的严格理论证明（例如，格罗弗搜索问题的绝热公式化）至少在系统的某些方面依赖于指数精度，因此保证了非物理资源会因实验不确定性和随机噪声而混乱。在这项工作中，我们提出了一种新的量子退火变体RFQA，它可以在面对噪声和适度的控制精度的情况下保持可扩展的量子加速。具体来说，我们考虑对基于通量量子位的量子退火的一种改进，其中包括随着系统的发展在横向场项方向上的低频振荡。我们证明了这种方法在格罗弗（Grover）问题和量子随机能量模型中产生了用于寻找基态的量子加速，因此应该广泛适用于其他可以公式化为量子自旋玻璃的硬优化问题。此外，我们探究了三个现实的噪声通道，并表明RFQA的加速可恢复至1 / 因此应广泛应用于可以公式化为量子自旋玻璃的其他困难的优化问题。此外，我们探究了三个现实的噪声通道，并表明RFQA的加速可恢复至1 / 因此应广泛应用于可以公式化为量子自旋玻璃的其他困难的优化问题。此外，我们探究了三个现实的噪声通道，并表明RFQA的加速可恢复至1 /类f的局部电位波动和与足够低的温度浴的相互作用引起的局部加热。另一个噪声通道，即浴辅助量子冷却过渡，实际上加速了算法，并可能胜过其他方法的负面影响。我们还将详细介绍如何使用当前技术通过实验实现RFQA。