What question did this study set out to answer?

The aim is to establish an exact and achievable performance bound for Kitaev's phase estimation algorithm.

March 22, 2026

The Exact Performance Bound for Kitaev Phase Estimation Algorithm

Key Points

The aim is to establish an exact and achievable performance bound for Kitaev's phase estimation algorithm.
Develop a theoretical framework to derive the exact performance bound.
Conduct numerical simulations to validate the theoretical findings.
Analyze the existing loose bounds and compare with the derived results.
Achieved a 60%–70% reduction over the previous best performance bounds.
Confirmed the exact bound through both theoretical proofs and numerical simulations.
Establishes the optimality of the proposed bound, indicating no further improvements are possible.

Abstract

ABSTRACT The Kitaev's phase estimation algorithm (KPEA) serves as a fundamental quantum subroutine in many quantum algorithms. However, the best existing bound for KPEA's performance remains loose, limiting its broader applicability. In this work, we demonstrate the exact, achievable bound for KPEA's performance, which cannot be further optimized in principle. Our exact bound achieves a 60%–70% reduction over the best existing bound. Both rigorous theoretical proof and numerical simulations confirm the optimality of our proposed bound.

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Cite This Study

Leng et al. (Sun,) studied this question.

synapsesocial.com/papers/69bf898bf665edcd009e9526 https://doi.org/https://doi.org/10.1002/qute.202500964

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