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arXiv · 2603.01358

Quantum framework for parameterizing partial differential equations via diagonal block-encoding

Hiroshi Yano·Yuki Sato
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Abstract

We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal matrices, or diagonal block-encodings, can be used to represent spatially varying coefficients with structured, potentially complicated profiles. This encoding enables efficient quantum simulation of forward PDEs and extends naturally to parameter-dependent settings. Such simulations are a key primitive for quantum algorithms for PDE-constrained optimization, where the goal is to identify optimal design parameters. We illustrate the framework numerically through forward simulation and parameter design for the two-dimensional wave equation with a Gaussian parameter profile.

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Hiroshi Yano, Yuki Sato. 2026-03-02. Quantum framework for parameterizing partial differential equations via diagonal block-encoding. https://arxiv.org/abs/2603.01358

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