A unified framework for efficient quantum simulation of nonlinear spectroscopy

TL;DR

This paper introduces a unified quantum algorithmic framework for efficiently simulating nonlinear spectroscopic phenomena on current quantum hardware, overcoming classical limitations and enabling new insights into complex quantum systems.

Contribution

The authors develop a generalized parameter shift rule-based approach for computing nonlinear response functions, validated on IBM quantum processors with applications to spin chains and atomic systems.

Findings

Successfully simulated higher-order response functions of a 12-qubit spin chain.

Demonstrated the method's ability to resolve quasi-particle spectra in spin liquids.

Identified interaction-induced cross-peaks in atomic systems.

Abstract

Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing $n$-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain.