Operator-Algebraic Methods for Asymptotic-Preserving Quantum Simulation of Open Systems

• URL: http://arxiv.org/abs/2605.18886v1
• Date: Sat, 16 May 2026 19:27:58 GMT
• Title: Operator-Algebraic Methods for Asymptotic-Preserving Quantum Simulation of Open Systems
• Abstract summary: We develop a mathematically rigorous framework for simulating multiscale physical systems using quantum computational resources.<n>We prove that layered quantum protocols, which implement fast-scale relaxation via native analog evolution or analytic manifold projection, converge uniformly in the diamond norm.<n>This work provides a principled mathematical bridge between classical multiscale numerical analysis and quantum simulation algorithms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We develop a mathematically rigorous framework for simulating \emph{multiscale physical systems} using quantum computational resources, by translating the \emph{language of asymptotic-preserving (AP) schemes} into the formalism of quantum channels and Lindbladian dynamics. For stiff open quantum systems governed by singularly perturbed generators $\cL_\eps = \eps^{-1}\cL_{\mathrm{fast}} + \cL_{\mathrm{slow}}$ with $\eps \to 0$, we prove that layered quantum protocols, which implement fast-scale relaxation via native analog evolution or analytic manifold projection, converge uniformly in the diamond norm to consistent discretizations of the limiting slow dynamics, with explicit error bound $\mathcal{O}(\epsΔt + Δt^2)$ independent of stiffness. We establish precise resource-complexity bounds showing that superlinear gate-count savings $Ω(κ\cdot(d_{\mathrm{tot}}/d_{\mathrm{slow}})^c)$ arise if and only if fast dynamics are resolved via (i) hardware-native analog evolution, or (ii) analytic adiabatic elimination reducing effective Hilbert space dimension. The framework is illustrated through cavity QED in the bad-cavity limit and a quantum-inspired AP discretization of kinetic equations converging to fluid limits, with quantified error propagation in trace and diamond norms. This work provides a principled mathematical bridge between classical multiscale numerical analysis and quantum simulation algorithms.

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