Quantum Simulation of Non-Hermitian Linear Response via Schr\"odingerization

TL;DR

This paper introduces a quantum algorithm that transforms non-unitary linear response functions into a unitary form suitable for quantum computers, enabling the study of open quantum systems with noise resilience.

Contribution

It presents a systematic framework using Schr"odingerization to evaluate non-Hermitian responses on quantum hardware, addressing non-unitarity challenges.

Findings

The method accurately preserves spectral information under noise.

Hardware-aware simulations demonstrate robustness against depolarizing channels.

Supports integration with quantum error mitigation protocols.

Abstract

Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been recently established to describe dissipation and fluctuation-dissipation relations (FDR), generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the intrinsically non-unitary nature of the dynamics. In this work, we present a systematic algorithmic framework that seamlessly transforms non-unitary multi-time correlation functions into a unitary form viable for digital quantum hardware. By mapping the vectorization of the Lindblad master equation into an expanded continuous-variable Liouville space, we employ the Schr\"odingerization technique to deterministically evaluate the non-Hermitian response. Furthermore, through hardware-aware simulations utilizing a 133-qubit device noise model, we demonstrate that our unitary framework robustly preserves the fundamental spectral information -- specifically the phase and oscillatory frequency -- against realistic depolarizing channels. By bypassing explicit non-unitary mid-circuit measurements, this approach intrinsically supports the integration of standard quantum error mitigation protocols, providing a scalable algorithmic blueprint for probing open-system universality on near-term hardware.