Machine learning is actively being explored for its potential to design,
validate, and even hybridize with near-term quantum devices. A central question
is whether neural networks can provide a tractable representation of a given
quantum state of interest. When true, stochastic neural networks can be
employed for many unsupervised tasks, including generative modeling and state
tomography. However, to be applicable for real experiments such methods must be
able to encode quantum mixed states. Here, we parametrize a density matrix
based on a restricted Boltzmann machine that is capable of purifying a mixed
state through auxiliary degrees of freedom embedded in the latent space of its
hidden units. We implement the algorithm numerically and use it to perform
tomography on some typical states of entangled photons, achieving fidelities
competitive with standard techniques.

本研究针对机器学习在与近期量子设备设计、验证甚至混合的潜力进行了探讨，其中一个核心问题是神经网络是否能够提供量子状态的可处理表示。通过基于受限玻尔兹曼机的密度矩阵参数化，本方法能够较好地应用于混合状态的编码，可用于无监督任务的生成建模和状态测量等诸多方面。通过数值实现并应用于一些典型的纠缠光子状态，达到了与标准技术相当的保真度。

神经密度算子的潜空间净化

Latent Space Purification via Neural Density Operators

The exponential scaling of the wave function is a fundamental property of
quantum systems with far reaching implications in our ability to process
quantum information. A problem where these are particularly relevant is quantum
state tomography. State tomography, whose objective is to obtain a full
description of a quantum system, can be analysed in the framework of
computational learning theory. In this model, quantum states have been shown to
be Probably Approximately Correct (PAC)-learnable with sample complexity linear
in the number of qubits. However, it is conjectured that in general quantum
states require an exponential amount of computation to be learned. Here, using
results from the literature on the efficient classical simulation of quantum
systems, we show that stabiliser states are efficiently PAC-learnable. Our
results solve an open problem formulated by Aaronson [Proc. R. Soc. A, 2088,
(2007)] and propose learning theory as a tool for exploring the power of
quantum computation.

本文探讨了量子系统的波函数指数级放缩对于量子信息处理的重要性，提出了一种计算学习理论的方法，通过对稳定子状态的研究，解决了 Aaronson 博士提出的量子状态学习难问题，并探讨了其在量子计算中的应用。