Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis

TL;DR

This paper introduces a size-agnostic, equivariant reinforcement learning approach for synthesizing Clifford quantum circuits, achieving near-optimal results efficiently across various qubit sizes.

Contribution

It presents a novel neural network architecture that is equivariant and size-agnostic, enabling scalable and efficient Clifford circuit synthesis with reinforcement learning.

Findings

Agent finds circuits within one two-qubit gate of optimality in milliseconds.

Achieves 99.2% optimal circuits within seconds for six-qubit instances.

Outperforms existing Clifford synthesizers on large, unseen qubit instances.

Abstract

We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.