Time Evolution of Quantum Systems

Yusuke Nishiya, Hirofumi Nishi, Yannick Couzinié +2 more

We propose an adiabatic time evolution (ATE) method for obtaining the ground state of a quantum many-electron system on a quantum circuit based on first quantization. As a striking feature of the ATE method, it consists of only unitary operations representing real-time evolution, which means that it does not require any ancillary qubits, nor controlled real-time evolution operators. Especially, we explored the first-quantized formalism of ATE method in this study since the implementation of first-quantized real-time evolution on quantum circuits is known to be efficient. However, when realizing the ATE quantum circuit in first-quantization formalism, obstacles are how to set the adiabatic Hamiltonian and how to prepare the corresponding initial ground state. We provide a way to prepare an antisymmetrized and nondegenerate initial ground state that is suitable as an input to an ATE circuit, which allows our ATE method to be applied to systems with any number of electrons. In addition, by considering a first-quantized Hamiltonian for quantum-mechanical electron system and classical nuclear system, we design a quantum circuit for optimal structure search based on ATE. Numerical simulations are demonstrated for simple systems, and it is confirmed that the ground state of the electronic system and optimal structure can be obtained by our method.

LAI YUN-ZHONG, Liang Jiu-Qing, (1)山西大学物理系,太原030006; (2)太原重型机械学院基础部,太原030024

We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi

瑞娟 赵

非厄米量子系统哈密顿量因具有不同的对称性，在量子态快速演化、量子态区分、量子精密测量等方面展现出超越标准量子力学系统的优势和新奇特性，近二十多年来受到持续关注，成为前沿领域。量子模拟非厄米系统是主要方向之一，又是研究非厄米系统的重要手段。典型的非厄米系统包括宇称–时间(Party-Time，简称PT)对称系统和赝厄米对称系统等。已有研究集中于对非厄米系统的时间演化开展量子模拟。文章围绕非厄米系统的虚时演化算符进行研究，通过计算非厄米系统的虚时演化算符，为开展典型非厄米系统的虚时演化量子模拟理论研究打下基础。我们的研究从理论上拓展了量子计算机可模拟新奇系统的范畴，并将虚时演化拓展至非厄米系统。基于我们对非厄米系统的虚时演化理论研究，对利用不同的量子系统和量子真机开展实验研究具有指导作用。The Hamiltonian of non-Hermitian quantum systems, due to its different symmetries, has shown advantages and novel properties beyond standard quantum mechanical systems in terms of rapid quantum state evolution, quantum state differentiation, quantum precision measurement, etc., which has attracted continuous attention and become a frontier field in the past two decades. Quantum simulation of non-Hermitian systems is one of the main directions and an important means to study non-Hermitian systems. Typical non-Hermitian systems include parity-time (PT) symmetric systems and pseudo Hermitian symmetric systems. Previous studies have focused on the quantum simulation of the time evolution of non-Hermitian systems. In this paper, the virtual time evolution operators of non-Hermitian systems are studied. By calculating the virtual time evolution operators of non-Hermitian systems, it lays a foundation for the theoretical study of virtual time evolution of typical non-Hermitian systems. Our research theoretically expands the range of novel systems that quantum computers can simulate, and extends virtual time evolution to non-Hermitian systems. Based on our research on the virtual time evolution theory of non-Hermitian systems, it has a guiding role to carry out experimental research with different quantum systems and quantum real machines.