Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis

• URL: http://arxiv.org/abs/2605.10910v1
• Date: Mon, 11 May 2026 17:49:28 GMT
• Title: Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis
• Abstract summary: We consider the problem of Clifford quantum circuits for devices with all-to-all qubit connectivity.<n>We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation.
• Score: 2.5234156040689233
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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