Quantum Signal Processing Enables Accurate PDE Solutions on IBMQ Hardware

[Submitted on 29 May 2026]

10d ago· 2 min readenNews

75/100

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Summary

This paper presents end-to-end implementations of quantum circuits for solving linear partial differential equations (PDEs) in the frequency domain, compiled to machine-level instructions and benchmarked on both numerical simulations and IBMQ quantum hardware. The authors focus on advection, wave, and Poisson equations, comparing approximate methods (first-order approximation with compact but uncontrollable error) against quantum signal processing (QSP) methods (deeper circuits with tunable algorithmic error). They experimentally demonstrate that QSP-augmented algorithms provide accurate solutions under realistic hardware constraints, and extend the method to handle non-homogeneous Dirichlet boundary conditions, verified numerically for a Poisson equation with source terms from high-fidelity plasma physics simulations.

Key quotes

· 3 pulled

Quantum algorithms offer new avenues for solving partial differential equations (PDEs).

We experimentally demonstrate that the QSP-augmented algorithm can provide accurate solutions under realistic hardware constraints.

We extend our method to address non-homogeneous Dirichlet boundary conditions and verify it numerically for a Poisson equation with source term obtained from high-fidelity physics simulations of a capacitively coupled plasma.

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Quantum algorithms offer new avenues for solving partial differential equations (PDEs). While the potential for end-to-end quantum advantage is at present not well understood, recent literature presents explicit circuit constructions for solving certain c