Quantum algorithmic differentiation

TL;DR

This paper introduces quantum algorithmic differentiation, proposing both fully quantum and hybrid methods, potentially offering speed advantages over classical differentiation by leveraging quantum computing capabilities.

Contribution

It presents the first quantum algorithmic differentiation scheme, adaptable to existing quantum hardware, with potential speed benefits over classical methods.

Findings

The scheme can be applied using current quantum hardware.

Quantum steps like CNOT may be faster than classical counterparts.

Potential quantum advantage in differentiation tasks.

Abstract

In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid approach). Since the implementation of elementary functions is already possible on quantum computers, the scheme that we propose can be easily applied. Moreover, since some steps (such as the CNOT operator) can (or will be) faster on a quantum computer than on a classical one, our procedure may ultimately demonstrate that quantum algorithmic differentiation has an advantage relative to its classical counterpart.