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

• URL: http://arxiv.org/abs/2603.01358v1
• Date: Mon, 02 Mar 2026 01:36:38 GMT
• Title: Quantum framework for parameterizing partial differential equations via diagonal block-encoding
• Authors: Hiroshi Yano, Yuki Sato,
• Abstract summary: We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs)<n>For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal matrices can be used.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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