Efficient quantum phase estimation with adaptive entanglement-assisted Hadamard test
Abstract
The entanglement-assisted Hadamard test (EHT) is a practical method for estimating a quantum phase by amplifying the phase signal. However, the feasible amplification is fundamentally limited by the accuracy of the reference phase, such that the method is inefficient in the high-precision regime. In this work, we propose an algorithm, called adaptive entanglement-assisted Hadamard test (AEHT), that iteratively refines the reference phase, enabling progressively stronger amplification as the iteration goes by. We further consider the imperfect eigenstate preparation scenario, where a systematic bias is unavoidable when estimating the quantum phase with the conventional EHT. Such a bias can be suppressed by the proposed AEHT. Moreover, taking physical implementation into consideration, we adopt device-restart count to measure the cost of quantum phase estimation, rather than shot count. The numerical experiments confirm the effectiveness of the proposed AEHT compared with conventional methods under this measure. By unlocking the full amplification power of large entangled states, this work offers an efficient method to estimate high-precision quantum phase on near-term quantum processors.
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BibTeX
@misc{chen2026efficient,
title = {{Efficient quantum phase estimation with adaptive entanglement-assisted Hadamard test}},
author = {Hengzhun Chen and Benchi Zhao and Yingzhou Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01772},
eprint = {2610.01772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01772},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient quantum phase estimation with adaptive entanglement-assisted Hadamard test
AU - Hengzhun Chen
AU - Benchi Zhao
AU - Yingzhou Li
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01772
UR - https://arxiv.org/abs/2610.01772
AB - The entanglement-assisted Hadamard test (EHT) is a practical method for estimating a quantum phase by amplifying the phase signal. However, the feasible amplification is fundamentally limited by the accuracy of the reference phase, such that the method is inefficient in the high-precision regime. In this work, we propose an algorithm, called adaptive entanglement-assisted Hadamard test (AEHT), that iteratively refines the reference phase, enabling progressively stronger amplification as the iteration goes by. We further consider the imperfect eigenstate preparation scenario, where a systematic bias is unavoidable when estimating the quantum phase with the conventional EHT. Such a bias can be suppressed by the proposed AEHT. Moreover, taking physical implementation into consideration, we adopt device-restart count to measure the cost of quantum phase estimation, rather than shot count. The numerical experiments confirm the effectiveness of the proposed AEHT compared with conventional methods under this measure. By unlocking the full amplification power of large entangled states, this work offers an efficient method to estimate high-precision quantum phase on near-term quantum processors.
ER -