[论文解读] Improved Boltzmann machines with error corrected quantum annealing

Richard Y. Li, Tameem Albash+1 more|arXiv (Cornell University)|Oct 3, 2019

Quantum Computing Algorithms and Architecture参考文献 64被引用 7

一句话总结

本文研究了嵌套量子退火纠错（NQAC）在通过纠错量子退火改进玻尔兹曼机训练中的应用。结果表明，即使采样偏离目标吉布斯分布，NQAC也能降低有效温度并提升在条纹与条纹及粗粒度MNIST数据集上的学习性能，表明在未完全平衡的情况下也能实现改进的训练。

ABSTRACT

Boltzmann machines are the basis of several deep learning methods that have been successfully applied to both supervised and unsupervised machine learning tasks. These models assume that a dataset is generated according to a Boltzmann distribution, and the goal of the training procedure is to learn the set of parameters that most closely match the input data distribution. Training such models is difficult due to the intractability of traditional sampling techniques, and proposals using quantum annealers for sampling hope to mitigate the sampling cost. However, real physical devices will inevitably be coupled to the environment, and the strength of this coupling affects the effective temperature of the distributions from which a quantum annealer samples. To counteract this problem, error correction schemes that can effectively reduce the temperature are needed if there is to be some benefit in using quantum annealing for problems at a larger scale, where we might expect the effective temperature of the device to not be sufficiently low. To this end, we have applied nested quantum annealing correction (NQAC) to do unsupervised learning with a small bars and stripes dataset, and to do supervised learning with a coarse-grained MNIST dataset. For both datasets we demonstrate improved training and a concomitant effective temperature reduction at higher noise levels relative to the unencoded case. We also find better performance overall with longer anneal times and offer an interpretation of the results based on a comparison to simulated quantum annealing and spin vector Monte Carlo. A counterintuitive aspect of our results is that the output distribution generally becomes less Gibbs-like with increasing nesting level and increasing anneal times, which shows that improved training performance can be achieved without equilibration to the target Gibbs distribution.

研究动机与目标

• 评估纠错量子退火，特别是嵌套量子退火纠错（NQAC），是否能够改进玻尔兹曼机的训练。
• 研究NQAC如何影响量子退火中采样分布的有效温度。
• 确定改进的机器学习性能是否与更优的向目标吉布斯分布的平衡程度相关。
• 分析退火时间与嵌套层级对性能和分布保真度的影响。
• 将量子退火结果与模拟量子退火（SQA）和自旋矢量蒙特卡罗（SVMC）进行比较，以获得物理上的深入理解。

提出的方法

• 在D-Wave 2000Q处理器上应用嵌套量子退火纠错（NQAC）来编码伊辛哈密顿量，以实现玻尔兹曼机训练。
• 利用DW2000Q的“退火时序变化”功能，在退火过程的中间点探测系统状态。
• 在两个数据集上进行训练：用于无监督学习的小型条纹与条纹数据集，以及用于有监督学习的粗粒度MNIST数据集。
• 通过与目标吉布斯分布的距离以及有效温度的降低来衡量性能。
• 与模拟量子退火（SQA）和自旋矢量蒙特卡罗（SVMC）进行比较，以验证采样行为。
• 评估解码策略，包括多数表决和自旋链丢弃，以分析其对分布保真度的影响。

实验结果

研究问题

• RQ1 NQAC是否在玻尔兹曼机训练中降低了量子退火采样分布的有效温度？
• RQ2 即使输出分布偏离目标吉布斯分布，是否仍能实现改进的学习性能？
• RQ3 退火时间如何影响NQAC编码的玻尔兹曼机的性能与分布保真度？
• RQ4 SQA和SVMC在多大程度上再现了D-Wave设备中观察到的采样动力学？
• RQ5 如多数表决等解码策略如何影响纠错量子退火中采样分布的质量？

主要发现

• NQAC成功降低了采样分布的有效温度，尤其在高噪声水平下，表明纠错能力得到提升。
• 在所有嵌套层级和更长的退火时间下均观察到改进的训练性能，尽管随着嵌套层级和退火时间增加，输出分布与吉布斯分布的相似性降低。
• 系统表现出一种准静态区域，动力学在中间退火点冻结，分布趋于稳定，与SQA和SVMC模拟结果一致。
• 性能提升并未伴随向最终哈密顿量的更好平衡，表明增强的学习性能并不要求完全热化至目标吉布斯分布。
• 丢弃断裂的自旋链显著降低了学习性能，而多数表决则引入了失真，表明解码策略是采样保真度的关键因素。
• 结果表明，NQAC可在噪声中间规模的量子退火中提供性能优势，尽管可扩展性与最优参数调优仍是待解决的挑战。