Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine
Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine
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DOI：
10.1103/physrevresearch.4.013009
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发表时间：
2022-01-03
影响因子：
4.2
通讯作者：
Yamamoto, Yoshihisa
中科院分区：
文献类型：
--
作者：
Ng, Edwin;Onodera, Tatsuhiro;Yamamoto, Yoshihisa
我们表明，在量子噪声的存在下，基于测量反馈的相干伊辛机（MFB-CIM）的非线性随机动力学可以被利用来采样简并地面和低能量自旋配置的伊辛模型。我们制定了一个通用的离散时间高斯状态模型的MFB-CIM，它忠实地捕捉非线性动力学系统阈值和以上。该模型克服了忽略量子噪声的平均场模型和假设长光子寿命的连续时间模型的局限性。我们的模型的数值模拟表明，当MFB-CIM在具有短光子寿命的量子噪声主导的区域（即，低腔精细度），系统的零差监测可以有效地产生低能量伊辛自旋配置的样品，需要比建立的高精细度连续时间模型所建议的少得多的往返采样。我们发现，采样性能是鲁棒的，甚至通过关闭或完全反转参数驱动的符号来改善，但在没有光学非线性的情况下，性能严重降低。对于具有二进制带符号边权重的MAX-CUT问题类，足以完全采样所有自旋构型直到第一激发伊辛能量（包括所有简并）的往返次数与问题大小N成比例为1.08（N）。在N = 100时，每个实例有几十个（中位数类似于20个）这样的期望配置，我们发现中位数足够的采样时间为6 x 10（6）个往返;在具有10 GHz重复率的MFB-CIM的实验实施中，这对应于60 ms的挂钟采样时间。
We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising model. We formulate a general discrete-time Gaussian-state model of the MFB-CIM, which faithfully captures the nonlinear dynamics present at and above system threshold. This model overcomes the limitations of both mean-field models, which neglect quantum noise, and continuous-time models, which assume long photon lifetimes. Numerical simulations of our model show that when the MFB-CIM is operated in a quantum-noise-dominated regime with short photon lifetimes (i.e., low cavity finesse), homodyne monitoring of the system can efficiently produce samples of low-energy Ising spin configurations, requiring many fewer roundtrips to sample than suggested by established high-finesse, continuous-time models. We find that sampling performance is robust to, or even improved by, turning off or altogether reversing the sign of the parametric drive, but performance is critically reduced in the absence of optical nonlinearity. For the class of MAX-CUT problems with binary-signed edge weights, the number of roundtrips sufficient to fully sample all spin configurations up to the first-excited Ising energy, including all degeneracies, scales with the problem size N as 1.08(N). At N = 100 with a few dozen (median similar to 20) such desired configurations per instance, we have found median sufficient sampling times of 6 x 10(6) roundtrips; in an experimental implementation of an MFB-CIM with a 10 GHz repetition rate, this corresponds to a wall-clock sampling time of 60 ms.