Nonlinear Spectroscopy via Generalized Quantum Phase Estimation

TL;DR

This paper introduces a generalized quantum phase estimation framework that efficiently simulates nonlinear optical spectroscopy, including higher-order responses, on quantum computers, potentially transforming experimental and theoretical spectroscopy analysis.

Contribution

The work develops a novel multi-variate quantum phase estimation method for response functions, enabling efficient simulation of nonlinear spectroscopy on quantum computers.

Findings

Allows sampling of response functions of arbitrary order.

Circuit cost scales linearly with the order of response.

Includes a fault-tolerant circuit modification for early quantum computers.

Abstract

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy, having that the circuit cost grows linearly with respect to the order of the target nonlinear response. This opens up an exciting new field of applications for quantum computers with potential technological impact.