Quantum gradient evaluation through quantum non-demolition measurements

TL;DR

This paper introduces a Quantum Non-Demolition Measurement protocol that efficiently estimates derivatives of cost functions in variational quantum circuits, reducing circuit iterations and gate counts, especially for higher-order derivatives.

Contribution

It proposes a novel QNDM approach for derivative estimation in quantum circuits, offering advantages over standard methods in efficiency and resource usage.

Findings

Reduces the number of circuit iterations needed for derivative estimation

Improves efficiency for higher-order derivatives

Lowers total logical gate count in variational quantum circuits

Abstract

We discuss a Quantum Non-Demolition Measurement (QNDM) protocol to estimate the derivatives of a cost function with a quantum computer. %This is a key step for the implementation of variational quantum circuits. The cost function, which is supposed to be classically hard to evaluate, is associated with the average value of a quantum operator. Then a quantum computer is used to efficiently extract information about the function and its derivative by evolving the system with a so-called variational quantum circuit. To this aim, we propose to use a quantum detector that allows us to directly estimate the derivatives of an observable, i.e., the derivative of the cost function. With respect to the standard direct measurement approach, this leads to a reduction of the number of circuit iterations needed to run the variational quantum circuits. The advantage increases if we want to estimate the higher-order derivatives. We also show that the presented approach can lead to a further advantage in terms of the number of total logical gates needed to run the variational quantum circuits. These results make the QNDM a valuable alternative to implementing the variational quantum circuits.