Time Evolution of Quantum State

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.

Michael Rose, David A. Mazziotti

We introduce the correlation-efficient time-evolution (CETE) algorithm for simulating quantum many-body dynamics. CETE recasts each step of time evolution as a time-independent correlation problem: the ansatz begins from a mean-field single Slater determinant and is then correlated to capture the true time-evolved state. We derive this exact ansatz from a contraction of the time-dependent Schrödinger equation onto the space of two electrons. Unlike conventional evolution by sequential short-time propagators, which must both correlate and decorrelate the state as the degree of correlation fluctuates in time, CETE correlates only once. This substantially reduces circuit depth, extending accessible simulation times on near-term quantum devices. We demonstrate the approach by simulating the time evolution of the hydrogen molecule's electronic wavefunction, highlighting the potential for the CETE algorithm to simulate strongly correlated systems on near-term devices.

Satoru Shoji, Kosuke Ito, Yukihiro Shimizu +1 more

Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time evolution operator itself. In this paper, we propose Variational Quantum Operator Simulation (VQOS), a method to realize time evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time evolution operator for closed systems in a quantum circuit that is up to 5 times shallower than the Trotterization. By providing a more practical way to implement time evolution operators, VQOS increases the applicability of near-term quantum computers.