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

TL;DR

This paper introduces a parallelized quantum amplitude estimation algorithm that achieves near-Heisenberg scaling with logarithmic circuit depth, enabling efficient distributed quantum computing.

Contribution

The paper presents a novel parallel amplitude estimation algorithm combining global GHZ states and low-depth Grover circuits, optimizing trade-offs for near-Heisenberg scaling.

Findings

Achieves near-Heisenberg scaling in total queries

Attains sub-linear circuit depth in estimation precision

Proves near-optimal trade-off using parallel quantum adversary method

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.