Quantum digital simulations of time-domain semiconductor spectroscopy in the semi-classical approximation

Abstract

We present a digital quantum simulation framework for ultrafast optical spectroscopy of semiconductor materials. The framework is based on Brillouin-zone discretization and is designed as a quantum alternative to classical simulations based on the semiconductor Bloch equations. Its current capabilities include quantum simulations of linear absorption and optical gain, incorporating Lorentzian broadening, finite-temperature band-filling effects, and reduced-dimensionality effects. Comparison with classical simulations of GaAs within the single-particle approximation demonstrates quantitative agreement in the noiseless limit. The inclusion of realistic hardware noise characteristic of NISQ-era quantum computers effectively manifests as an additional source of scattering, resulting in increased spectral broadening. We also show that the linear optical response, including many-body interactions treated within the Hartree-Fock approximation, can be mapped onto a system of coupled classical oscillators. Under certain assumptions about the query complexity of the oscillator couplings, this system exhibits a provable quantum advantage, as demonstrated in [Phys. Rev. X 13, 041041 (2023)]. Beyond the Hartree-Fock approximation, classical simulations based on many-body quantum kinetic equations face the so-called hierarchy problem, whereas the algorithmic complexity of the quantum simulations remains unchanged, offering a promising approach to overcoming this challenge.