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arXiv · 2508.06121

Near-Heisenberg-limited parallel amplitude estimation with logarithmic depth circuit

Kohei Oshio·Kaito Wada·Naoki Yamamoto
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Abstract

Quantum amplitude estimation is one of the core subroutines in quantum algorithms. This paper gives a parallelized amplitude estimation (PAE) algorithm that simultaneously achieves near-Heisenberg scaling in the total number of queries and sub-linear scaling in the circuit depth, with respect to the estimation precision. The algorithm is composed of a global GHZ state followed by separated low-depth Grover circuits optimized by quantum signal processing techniques; the number of qubits in the GHZ state and the depth of each circuit is tunable as a trade-off way, which particularly enables even near-Heisenberg-limited and logarithmic-depth algorithm for amplitude estimation. We prove that this trade-off scaling is nearly optimal with use of the parallel quantum adversary method, against folklore on the impossibility of efficient parallelization in amplitude estimation. The proposed algorithm has a form of distributed quantum computing, which may be suitable for device implementation.

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Kohei Oshio, Kaito Wada, Naoki Yamamoto. 2025-08-08. Near-Heisenberg-limited parallel amplitude estimation with logarithmic depth circuit. https://arxiv.org/abs/2508.06121

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