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Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
npj Quantum Information ( IF 7.6 ) Pub Date : 2021-06-01 , DOI: 10.1038/s41534-021-00409-y
Hirofumi Nishi , Taichi Kosugi , Yu-ichiro Matsushita

The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a “compression” method of the quantum circuit for the imaginary-time steps to further reduce the circuit depth in the QITE method. The eLA, NLA, and compression methods introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.



中文翻译:

通过引入非局部逼近在 NISQ 设备上实现量子虚时间演化方法

虚时间演化方法是一种众所周知的方法,用于在经典计算机上获得量子多体问题中的基态。最近提出的量子虚时间演化方法(QITE)面临电路深度深和在嘈杂的中尺度量子(NISQ)设备上实现困难的问题。在这项研究中,开发了一种非局部近似来解决这个困难。我们发现,通过去除将虚时间演化算子转换为酉算子时强加的局部条件或局部逼近 (LA),量子电路深度显着降低。我们提出了基于非局部条件的两步逼近方法:扩展 LA (eLA) 和非局部逼近 (NLA)。为了确认 eLA 和 NLA 的有效性,我们将它们应用于未加权 3-正则图和加权全连接图的最大割问题;我们比较评估 LA、eLA 和 NLA 的表现。eLA 和 NLA 方法需要比 LA 少得多的电路深度来保持相同水平的计算精度。此外,我们为虚时间步长开发了量子电路的“压缩”方法,以进一步减少 QITE 方法中的电路深度。本研究中介绍的 eLA、NLA 和压缩方法使我们能够显着降低由门操作引起的电路深度和误差累积,并为在 NISQ 设备上实施 QITE 方法铺平道路。eLA 和 NLA 方法需要比 LA 少得多的电路深度来保持相同水平的计算精度。此外,我们为虚时间步长开发了量子电路的“压缩”方法,以进一步减少 QITE 方法中的电路深度。本研究中介绍的 eLA、NLA 和压缩方法使我们能够显着降低由门操作引起的电路深度和误差累积,并为在 NISQ 设备上实施 QITE 方法铺平道路。eLA 和 NLA 方法需要比 LA 少得多的电路深度来保持相同水平的计算精度。此外,我们为虚时间步长开发了量子电路的“压缩”方法,以进一步减少 QITE 方法中的电路深度。本研究中介绍的 eLA、NLA 和压缩方法使我们能够显着降低由门操作引起的电路深度和误差累积,并为在 NISQ 设备上实施 QITE 方法铺平道路。

更新日期:2021-06-01
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