Quantum annealing with antiferromagnetic fluctuations
Quantum annealing with antiferromagnetic fluctuations
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DOI：
10.1103/physreve.85.051112
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发表时间：
2012-05-10
影响因子：
2.4
通讯作者：
Nishimori, Hidetoshi
中科院分区：
文献类型：
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作者：
Seki, Yuya;Nishimori, Hidetoshi
我们在量子退火中引入了反铁磁量子涨落。我们应用这种方法的无限范围的铁磁p-自旋模型，传统的量子退火已被证明有困难，有效地找到基态，由于一级跃迁。我们研究了这个系统的相图解析和数值。使用静态近似，我们发现，存在一个量子路径，以达到最终的基态从平凡的初始状态，避免一阶跃迁的中间值的p。我们还研究了数值的基态和第一激发态之间的能隙，并找到证据的中间值的p的时间复杂度与系统大小的多项式尺度在第二-沿着避免一阶跃迁的量子路径的沿着阶跃迁点。这些结果表明，量子退火将能够有效地解决这个问题与中间值的p，在只有简单的横向场波动的情况下。
We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of p for which the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of p efficiently, in contrast to the case with only simple transverse-field fluctuations.