Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis
A qubit-relabeling-equivariant, size-agnostic reinforcement learning agent synthesizes near-optimal Clifford circuits across qubit counts, outperforming Qiskit on large instances.
Published 2026Sydney Poster Session 5 · Thu, Dec 10, 10:00 AM–1:00 PM local time · Hall 1-4arXiv ↗OpenReview ↗
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The paper delivers a striking equivariant, size-agnostic policy that finds near-optimal Clifford circuits at scale, though its reliance on all-to-all connectivity, absence of ablation, and lack of non-Clifford or topological benchmarks leave its practical synthesis value…
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.