Quadratic acceleration of multi-step probabilistic algorithms for state preparation

TL;DR

This paper introduces a method combining quantum amplitude amplification with multi-step probabilistic algorithms to achieve quadratic acceleration in quantum state preparation, outperforming traditional quantum phase estimation.

Contribution

The study demonstrates a novel combination of QAA and probabilistic algorithms to significantly accelerate quantum state preparation processes.

Findings

Quadratic acceleration confirmed by PITE method

Outperforms quantum phase estimation in infidelity

Effective for non-unitary operator implementation

Abstract

For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the computational process compared to classical ones. In this study, quantum amplitude amplification (QAA) and multi-step probabilistic algorithms are combined to achieve quadratic acceleration. This method outperforms quantum phase estimation in terms of infidelity. The quadratic acceleration was confirmed by the probabilistic imaginary-time evolution (PITE) method.