Optimizing quantum circuits with Riemannian gradient flow

• URL: http://arxiv.org/abs/2202.06976v2
• Date: Wed, 11 May 2022 14:00:27 GMT
• Title: Optimizing quantum circuits with Riemannian gradient flow
• Authors: Roeland Wiersema, Nathan Killoran
• Abstract summary: Variational quantum algorithms are a promising class algorithms that can be performed on currently available quantum computers. We consider an alternative optimization perspective that depends on the structure of the special unitary group.
• Score: 0.5524804393257919
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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