Quantum mixed state compiling
Quantum mixed state compiling
复制标题
DOI：
10.1088/2058-9565/acc4e3
复制
发表时间：
2022-09
影响因子：
6.7
通讯作者：
Nic Ezzell;E. Ball;Aliza U. Siddiqui;M. Wilde;A. Sornborger;Patrick J. Coles;Zoe Holmes
中科院分区：
文献类型：
--
作者：
Nic Ezzell;E. Ball;Aliza U. Siddiqui;M. Wilde;A. Sornborger;Patrick J. Coles;Zoe Holmes
学习量子电路以准备给定的混合态的任务是基本的量子子例程。提出了一种适用于近期硬件的变分量子算法（VQA）来学习混合态。我们的算法代表了以前的VQA，旨在学习准备电路的纯状态的推广。我们考虑两种不同的ansätze编译的目标状态;第一个是基于学习一个纯化的状态，第二个表示它作为一个凸组合的纯状态。在这两种情况下，存储和操作编译状态所需的资源都随着近似值的等级而增长。因此，通过学习目标状态的较低秩近似，我们的算法提供了一种压缩状态以进行更有效处理的方法。作为我们的算法的副产品，一个有效地学习目标状态的主成分，因此我们的算法进一步提供了一个新的方法，主成分分析。我们调查我们的算法的有效性，通过广泛的数值实现，显示出典型的随机状态和热状态的许多身体系统可以学习这种方式。此外，我们演示了量子硬件如何我们的算法可以用来研究硬件噪声引起的状态。
The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.