Phase-Sensitive Quantum Measurement without Controlled Operations

TL;DR

This paper presents a quantum measurement method that efficiently extracts phase information from quantum amplitudes without controlled operations, using real-time evolution and shallow circuits, suitable for noisy quantum computers.

Contribution

It introduces a novel phase-sensitive measurement algorithm that reduces circuit depth and complexity compared to traditional controlled-unitary methods.

Findings

Outperforms Hadamard test in circuit depth

Compatible with current noisy quantum hardware

Uses simple error mitigation strategies

Abstract

Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary operations. We introduce a quantum algorithm based on complex analysis that overcomes this problem for amplitudes that are a continuous function of time. Our method only requires the implementation of real-time evolution and a shallow circuit that approximates a short imaginary-time evolution. We show that the method outperforms the Hadamard test in terms of circuit depth and that it is suitable for current noisy quantum computers when combined with a simple error-mitigation strategy.