Transmutation based Quantum Simulation for Non-unitary Dynamics

Jin S, Ma C, Zuazua Iriondo E (2026)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Article in Edited Volumes

Publication year: 2026

Open Access Link: https://doi.org/10.48550/arXiv.2601.03616

Abstract

We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form A=L†L, a structure that arises naturally in standard discretizations of elliptic operators. Our main tool is the Kannai transform, which represents the diffusion semigroup e−TA as a Gaussian-weighted superposition of unitary wave propagators. This representation leads to a linear-combination-of-unitaries implementation with a Gaussian tail and yields query complexity ̃ (‖A‖Tlog(1/ε)‾‾‾‾‾‾‾‾‾‾‾‾‾√), up to standard dependence on state-preparation and output norms, improving the scaling in ‖A‖,T and ε compared with generic Hamiltonian-simulation-based methods. We instantiate the method for the heat equation and biharmonic diffusion under non-periodic physical boundary conditions, and we further use it as a subroutine for constant-coefficient linear parabolic surrogates arising in entropy-penalization schemes for viscous Hamilton--Jacobi equations. In the long-time regime, the same framework yields a structured quantum linear solver for Ax=b with A=L†L, achieving ̃ (κ3/2log2(1/ε)) queries and improving the condition-number dependence over standard quantum linear-system algorithms in this factorized setting.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Shanghai Jiao Tong University / 上海交通大学 CN China (CN) East China Normal University (ECNU) / 华东师范大学 CN China (CN)

How to cite

APA:

Jin, S., Ma, C., & Zuazua Iriondo, E. (2026). Transmutation based Quantum Simulation for Non-unitary Dynamics. (Unpublished, Submitted).

MLA:

Jin, Shi, Chuwen Ma, and Enrique Zuazua Iriondo. Transmutation based Quantum Simulation for Non-unitary Dynamics. Unpublished, Submitted. 2026.

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