Optimizing quantum circuits with Riemannian gradient flow

TL;DR

This paper explores a Riemannian gradient flow approach for optimizing variational quantum circuits, leveraging the special unitary group's structure to improve optimization, especially for deep circuits, with near-term hardware implementation feasibility.

Contribution

It introduces a Riemannian optimization scheme tailored for the special unitary group, offering a novel perspective beyond traditional Euclidean methods for quantum circuit optimization.

Findings

Riemannian gradient flow shows favorable optimization properties for deep circuits.

An approximate Riemannian algorithm can be implemented on near-term quantum hardware.

The approach leverages the geometry of the special unitary group for improved optimization.

Abstract

Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that updates parameters in Euclidean geometry. Since quantum circuits are elements of the special unitary group, we can consider an alternative optimization perspective that depends on the structure of this group. In this work, we investigate a Riemannian optimization scheme over the special unitary group and we discuss its implementation on a quantum computer. We illustrate that the resulting Riemannian gradient-flow algorithm has favorable optimization properties for deep circuits and that an approximate version of this algorithm can be performed on near-term hardware.