Ancilla-mediated fixed-point quantum search using Grover iterations
Abstract
Grover's quantum search algorithm provides a fundamental quadratic speedup for unstructured datasets, reducing query complexity from 𝒪(N) to 𝒪(√N). However, the algorithm's reliance on precise iteration counts leads to the ``soufflé problem,'' where over-rotation results in a sharp decline in success probability. This limitation is particularly restrictive when the number of solution states, M, is unknown. In this work, we present an ancilla-mediated fixed-point quantum search algorithm that achieves robust convergence by mapping the solution amplitude to a dedicated ancilla qubit. Unlike existing phase-matching fixed-point methods, our approach utilizes Grover's real-plane reflections, thereby maintaining the intuitive geometric architecture of the original algorithm. We demonstrate that this method achieves a success probability of at least 92.6% with a query complexity of approximately 𝒪(√(N/M)), effectively bridging the gap between standard amplitude amplification and robust fixed-point convergence.
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BibTeX
@misc{prabhat2026ancillamediated,
title = {{Ancilla-mediated fixed-point quantum search using Grover iterations}},
author = {Yash Prabhat and Snigdha Thakur and Ankur Raina},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29839},
eprint = {2608.29839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29839},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ancilla-mediated fixed-point quantum search using Grover iterations
AU - Yash Prabhat
AU - Snigdha Thakur
AU - Ankur Raina
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29839
UR - https://arxiv.org/abs/2608.29839
AB - Grover's quantum search algorithm provides a fundamental quadratic speedup for unstructured datasets, reducing query complexity from 𝒪(N) to 𝒪(√N). However, the algorithm's reliance on precise iteration counts leads to the ``soufflé problem,'' where over-rotation results in a sharp decline in success probability. This limitation is particularly restrictive when the number of solution states, M, is unknown. In this work, we present an ancilla-mediated fixed-point quantum search algorithm that achieves robust convergence by mapping the solution amplitude to a dedicated ancilla qubit. Unlike existing phase-matching fixed-point methods, our approach utilizes Grover's real-plane reflections, thereby maintaining the intuitive geometric architecture of the original algorithm. We demonstrate that this method achieves a success probability of at least 92.6% with a query complexity of approximately 𝒪(√(N/M)), effectively bridging the gap between standard amplitude amplification and robust fixed-point convergence.
ER -