利用快速振荡横向场的自旋玻璃问题迭代量子优化
Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields
AI总结：
本研究提出利用高频振荡横向场的迭代量子算法IST-SAT求解自旋玻璃优化问题，经基准测试验证其较经典算法和TAQC实现多项式加速，为实现优化领域量子优势提供新路径。
摘要：
在本研究中，我们提出了一种新的迭代量子算法，名为可满足性问题迭代交响隧穿（Iterative Symphonic Tunneling for Satisfiability problems, IST-SAT），该算法利用高频振荡横向场求解量子自旋玻璃优化问题。IST-SAT以迭代序列的方式运行：一次迭代返回的比特串用于设置下一次迭代中振荡横向场的自旋相关相位。经过多次迭代，该算法的全新机制会引导系统趋近问题的基态。我们通过精确态矢量模拟，在多组困难MAX-3-XORSAT问题实例上对IST-SAT进行基准测试，结果显示其相较于特洛伊化绝热量子计算（trotterized adiabatic quantum computation, TAQC）和已知最优的半贪心经典算法实现了多项式加速。当IST-SAT以足够优质的初始近似作为种子时，该算法可在多项式次数的迭代内收敛到精确解。我们的数值结果确定了临界汉明半径（critical Hamming radius, CHR），即初始近似的质量阈值：当初始近似达到该阈值时，求解时间随问题规模的变化从指数标度转变为多项式标度。将IST-SAT与未来的经典或量子近似算法结合，有望获得更大的性能提升。因此，本研究提出的机制为在优化领域实现量子优势开辟了新路径。
英文摘要：
In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over trotterized adiabatic quantum computation (TAQC) and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critial Hamming radius(CHR), or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. By combining IST-SAT with future classical or quantum approximation algorithms, larger gains may be achieved. The mechanism we present in this work thus presents a new path toward achieving quantum advantage in optimization.
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