Hybrid algorithm for the time-dependent Hartree-Fock method using the Yang-Baxter equation on quantum computers

TL;DR

This paper introduces a hybrid quantum-classical algorithm for the time-dependent Hartree-Fock method that leverages the Yang-Baxter equation to maintain constant circuit depth, enabling efficient quantum simulations of electron dynamics.

Contribution

It presents a novel hybrid quantum algorithm for TDHF that uses YBE-based circuit compression to achieve constant depth circuits, improving quantum simulation efficiency.

Findings

Circuit depth remains constant over time due to YBE compression.

The method enables efficient quantum simulation of mean-field electron dynamics.

Provides a new application of YBE symmetry in quantum chemistry simulations.

Abstract

The time-dependent Hartree-Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single Slater determinants. One of the major advantages of performing time dynamics within Hartree-Fock theory is the free fermionic nature of the problem, which makes TDHF classically simulatable in polynomial time. Here, we present a hybrid TDHF implementation for quantum computers. This quantum circuit grows with time; but with our recent work on circuit compression via the Yang-Baxter equation (YBE), the resulting circuit is constant depth. This study provides a new way to simulate TDHF with the aid of a quantum device as well as provides a new direction for the application of YBE symmetry in quantum chemistry simulations.