First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

TL;DR

This paper extends the first-quantized eigensolver framework to include uniform magnetic fields, enabling efficient quantum simulations of electronic systems' ground and excited states with minimal additional computational cost.

Contribution

It introduces a method to incorporate magnetic fields into FQE calculations with linear circuit depth, validated through numerical simulations and derivative circuit constructions.

Findings

Magnetic field circuits have linear depth relative to qubits.

The method accurately computes ground and excited states under magnetic fields.

Electric-current density can be derived to analyze magnetic responses.

Abstract

First-quantized eigensolver (FQE) is a recently proposed framework of quantum computation for obtaining the ground state of an interacting electronic system based on probabilistic imaginary-time evolution. In this study, we propose a method for introducing a uniform magnetic field to an FQE calculation. We demonstrate via resource estimation that the additional circuit responsible for the magnetic field can be implemented with a liner depth in terms of the number of qubits assigned to each electron, giving rise to no impact on the leading order of whole computational cost. We confirm the validity of our method via numerical simulations for ground and excited states by employing the filtration circuits for energy eigenstates. We also provide the generic construction of derivative circuits together with measurement-based formulae. As a special case of them, we can obtain the electric-current density in an electronic system to get insights into the microscopic origin of magnetic response.