Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Yeung, Richie Kissinger, Aleks Cornish, Rob |
| author_facet | Yeung, Richie Kissinger, Aleks Cornish, Rob |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis Yeung, Richie Kissinger, Aleks Cornish, Rob Quantum Physics Machine Learning 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. |
| title | Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2605.10910 |