Methodology for replacing indirect measurements with direct measurements

TL;DR

This paper develops a general methodology to replace indirect quantum measurements with direct measurements, reducing circuit depth and enabling more efficient quantum algorithms on near-term hardware.

Contribution

It introduces a systematic approach for substituting indirect measurements with sequential direct measurements in quantum circuits, applicable to various derivative evaluations and correlator measurements.

Findings

Reduces quantum circuit depth by eliminating controlled operations.

Enables direct measurement of derivatives and correlators in quantum states.

Applicable to near-term quantum algorithms and hybrid quantum-classical methods.

Abstract

In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here we investigate in what cases such a replacement is possible and develop a general methodology for trading an indirect measurement with sequential direct measurements. The results can be applied to construct quantum circuits to evaluate the analytical gradient, metric tensor, Hessian, and even higher order derivatives of a parametrized quantum state. Also, we propose a new method to measure the out-of-time-order correlator based on the presented protocol. Our protocols can reduce the depth of the quantum circuit significantly by making the controlled operation unnecessary and hence are suitable for quantum-classical hybrid algorithms on near-term quantum computers.