Quantum generative model for sampling many-body spectral functions

TL;DR

This paper introduces a quantum algorithm using phase estimation to efficiently generate samples of spectral functions in many-body quantum systems, enabling faster analysis of complex spectra such as optical conductivity and NMR.

Contribution

It presents a novel quantum circuit acting as a generative model for spectral functions, achieving polynomial-time sampling of high-rank observable spectra.

Findings

Efficient quantum circuit for spectral function sampling

Applicable to experimentally relevant spectra like structure factor and NMR

Requires doubling qubits for implementation

Abstract

Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design a circuit that acts as an efficient quantum generative model, providing samples out of the spectral function of high rank observables in polynomial time. This includes many experimentally relevant spectra such as the dynamic structure factor, the optical conductivity or the NMR spectrum. Experimental realization of the algorithm, apart from logarithmic overhead, requires doubling the number of qubits as compared to a simple analog simulator.