Quantum Implicit-Explicit Schemes for Multiscale Ordinary and Partial Differential Equations via Schrödingerization

• URL: http://arxiv.org/abs/2605.29423v1
• Date: Thu, 28 May 2026 06:17:33 GMT
• Title: Quantum Implicit-Explicit Schemes for Multiscale Ordinary and Partial Differential Equations via Schrödingerization
• Abstract summary: We present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations.<n>A key ingredient of our approach is a continuous-time formulation of classical IMEX schemes.<n>We employ the Schrdingerization framework to implement IMEX schemes on quantum computers.
• Score: 34.04094622012203
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of the scaling parameter $\varepsilon$. A key ingredient of our approach is a continuous-time formulation of classical IMEX schemes, which decouples the evolution time of the quantum algorithm from the physical time of the differential equation and is therefore particularly useful in multiscale settings. Building on this idea, we employ the Schrödingerization framework [Phys. Rev. Lett. 133 (2024), 230602] to implement IMEX schemes on quantum computers. Compared to previous HHL type quantum AP scheme [J. Comput. Phys. 471 (2022), 111641], this new method requires narrower -- an extra logarithmic factor -- auxiliary register numerical examples on linear heat and multiscale telegraph equations demonstrate the independence in $\varepsilon$ of the method.

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