Quantum Simulation of Non-Hermitian Linear Response

• URL: http://arxiv.org/abs/2603.17342v1
• Date: Wed, 18 Mar 2026 04:13:11 GMT
• Title: Quantum Simulation of Non-Hermitian Linear Response
• Abstract summary: We present a systematic algorithmic mapping that transforms the non-unitary multi-time correlation functions into a unitary form viable for quantum hardware.<n>This approach bridges the gap between the established physical theory of non-Hermitian linear response and quantum simulation, achieving optimal state preparation cost.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Linear response theory and Green's functions provide a universal framework for understanding how macroscopic and strongly correlated systems respond to weak external perturbations. While the theoretical foundation for non-Hermitian linear response theory has been recently established to describe open quantum systems, generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the non-unitary nature of the dynamics. In this work, we present a systematic algorithmic mapping that transforms the non-unitary multi-time correlation functions into a unitary form viable for quantum hardware. By mapping the vectorization of the Lindblad master equation into a unitary Schrödinger-like equation using the continuous-variable Schrödingerization technique, we show that generalized non-Hermitian Green's functions can be systematically extracted. This approach bridges the gap between the established physical theory of non-Hermitian linear response and quantum simulation, achieving optimal state preparation cost.

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