【arXiv导读】通用可区分量子神经网络（Universal discriminative quantum neural networks）【arXiv:1805.08654】

[btn type=”primary” url=”https://arxiv.org/abs/1805.08654″]原文链接[/btn]

题目：Universal discriminative quantum neural networks 通用鉴别量子神经网络

作者：H. Chen(1,2), L. Wossnig(2)*, S. Severini(2,3), H. Neven(4), and M. Mohseni(4)†

单位：

1. Department of Physics & Astronomy, University College London, London, UK
2. Department of Computer Science, University College London, London, UK
3. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
4. Google Quantum AI Laboratory, Venice, California, USA

摘要：

Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or Positive-Operator-Value-Measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary input-output mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue.

简评：

机器学习以其强大的数据处理能力在近年来的人工智能和数据挖掘等研究方向可谓搞得风生水起。加之近二三十年来量子信息技术的迅猛发展，尤其是量子计算机在特定任务下展现的超越一般计算机的能力，人们很期待机器学习的优势可以借助量子物理体系得到更深的推广和更快的提升。相应的，量子机器学习（quantum machine learning）的概念油然而生。虽然已有研究工作展现了量子机器学习的理论框架，但是，如何构建一个可以在量子计算机或量子模拟器上直接应用的具体研究方法，一直是近年来困难却又重要的研究题目。

这篇文章便是在这一研究方向上的一次尝试：通过研究机器学习的主要方法——神经网络——的量子对应，来讨论量子计算机可能完成的任务。具体来说，这篇文章研究了所谓的量子电路学习（quantum circuit learning），即通过量子电路构建一系列的幺正操作模块，而这些模块在量子测量的协助下恰可以看作处于不同层的“量子神经元”。在经典-量子混合算法（classical-quantum hybrid algorithm）的帮助下，文章给出了一套学习和反馈机制，并讨论了如何用这套机制来区分不同类别的量子态。毕竟，量子态区分（quantum state discrimination）任务在现阶段的量子信息处理中扮演着重要作用，比如量子密钥分发（quantum key distribution）中的对信号态的区分可以用来验证通信协议的安全性，再比如量子计量学（quantum metrology）中对量子态的区分决定了测量的精确程度等等。此外，由于文章讨论的量子电路需要普适量子门（universal quantum gate）才能实现，因此这一方法的验证就对实际量子计算系统的能力有了很高的要求。