Finding spin glass ground states using quantum walks
Finding spin glass ground states using quantum walks
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DOI：
10.1088/1367-2630/ab5ca2
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发表时间：
2019-12-01
影响因子：
3.3
通讯作者：
Kendon, Viv
中科院分区：
文献类型：
--
作者：
Callison, Adam;Chancellor, Nicholas;Kendon, Viv
利用自然硬件哈密顿量下的连续时间演化的量子计算是一个很有前途的中短期方向，朝着功能强大的量子计算硬件发展。我们研究了连续时间量子行走作为寻找自旋玻璃基态的工具的性能，这一问题是现实优化问题的有用模型。通过进行详细的数值计算，我们揭示了解决自旋玻璃问题与将量子行走应用于搜索问题的重要不同之处。重要的是，与搜索问题不同，对于自旋玻璃基态问题，不需要精确设置量子行走的跳跃速率等参数。根据问题哈密顿量中的能量尺度确定的跳跃速率的启发式值足以获得比搜索更好的量子优势。我们揭示了两种提供量子优势的一般机制：将驱动哈密顿量与问题哈密顿量中的编码进行匹配，以及确保量子行走将在短时间尺度内找到较低能级的能量重新分配原理。这使得使用量子行走来解决难题变得可行，并为合适的量子硬件上的一系列应用打开了大门。
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better quantum advantage than for search. We uncover two general mechanisms that provide the quantum advantage: matching the driver Hamiltonian to the encoding in the problem Hamiltonian, and an energy redistribution principle that ensures a quantum walk will find a lower energy state in a short timescale. This makes it practical to use quantum walks for solving hard problems, and opens the door for a range of applications on suitable quantum hardware.