Quantum

Robustness of Quantum Signal Processing and Resource-aware Polynomial Design

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Briefings

This article presents an end-to-end analysis of errors in quantum signal processing (QSP) implementations, specifically focusing on how input operator errors propagate through polynomial transformations. The authors derive a classical algorithm to compute tight bounds on the operator-Lipschitz constant $L_\star$, which governs total quantum-resource costs like $T$-gate counts. A new resource-aware polynomial-design procedure is developed to minimize these costs based solely on coefficients. The method was successfully illustrated for ground state energy estimation using the H$_6$ molecular Hamiltonian, achieving a 51.9% to 56.7% reduction in modeled $T$-gate counts compared to standard analytical approximations.

Key points

• The input error propagation in QSP is governed by the operator-Lipschitz constant $L_\star$ of the implemented function.
• A resource-aware polynomial-design procedure was developed to minimize $T$-gate counts by searching for polynomials with minimum cost based on their coefficients.

Context and limitations

The study focuses on end-to-end error analysis for QSP implementations using polynomial transformations. Results are limited to the H$_6$ molecular Hamiltonian via eigenvalue thresholding for ground state energy estimation. The analysis covers algorithmic and encoding errors but does not address hardware-specific profiles beyond the tested profiles mentioned in the abstract.

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