Evaluating analytic gradients on quantum hardware

TLDR

Near‑term quantum computing is promising for optimization tasks such as quantum chemistry, drug discovery, and machine learning, especially within parametrized or variational algorithms that combine quantum and classical processing. This work demonstrates that exact gradients of quantum circuits can be obtained by reusing the same or a very similar circuit architecture. Gradients of expectation values are estimated by running the original circuit twice with a shifted gate parameter, or by conditioning a single gate on an ancilla for more general cases.

Abstract

An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings --- most prominently in so-called parametrized or variational algorithms --- the objective function is a result of hybrid quantum-classical processing. To optimize the objective, it is useful to have access to exact gradients of quantum circuits with respect to gate parameters. This paper shows how gradients of expectation values of quantum measurements can be estimated using the same, or almost the same, architecture that executes the original circuit. It generalizes previous results for qubit-based platforms, and proposes recipes for the computation of gradients of continuous-variable circuits. Interestingly, in many important instances it is sufficient to run the original quantum circuit twice while shifting a single gate parameter to obtain the corresponding component of the gradient. More general cases can be solved by conditioning a single gate on an ancilla.