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Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis

NeurIPS 2026 · Reinforcement learning › Visual and representation RL · approach: In-context and adaptive RL · 0 citations (OpenAlex)

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Trains a size-agnostic, qubit-permutation-equivariant PPO policy via reverse random-walk curriculum to synthesize all-to-all Clifford circuits, matching optimal 6-qubit CZ counts on 99.2% of benchmark instances and beating Qiskit's Aaronson-Gottesman and greedy synthesizers up to 30 qubits.

Problem

Clifford circuit synthesis with all-to-all connectivity, minimizing two-qubit (CZ) gate count; existing methods are either fast but far from optimal or optimal but computationally prohibitive, and learned methods do not scale across qubit counts.

Approach

Formulates Clifford synthesis as reverse-reduction RL to the identity tableau, with random-walk curriculum, and a qubit-permutation-equivariant, size-agnostic message-passing policy over qubit-pair tableau features; continued training from 6 to 10 qubits enables transfer to up to 30 qubits.

Key results

• Matches the optimal CZ count on 995/1003 six-qubit benchmark circuits (99.2%) with extended search in ~3 hours; all 1003 solved within one CZ of optimal.
• Greedy policy decoding takes 0.83 s for the whole 1003-circuit suite and recovers 507/1003 optima; brief policy-guided search reaches within one CZ of optimal in 21 s.
• At 30 qubits and 1024 initial gates, the ten-qubit checkpoint uses 323.3 CZ gates on average, 124.2 fewer than Qiskit's Bravyi greedy and 460.1 fewer than Aaronson-Gottesman; solve rate on uniform targets falls to 59% at 30 qubits.

Surprising findings

• The six-qubit-trained checkpoint produces higher CZ counts than Qiskit's greedy and AG on the fully random 7-30 qubit targets, despite solving every target, showing a reliability-quality tradeoff.
• Ablation shows a Transformer and message-passing variants differ modestly, and an MLP that processes qubits independently is substantially worse, suggesting inter-qubit communication matters more than the exact update rule.

Limitations

• One-step action selection and rollouts scale poorly, O(n^2) actions and O(n^2) gates for large n.
• The 10-qubit checkpoint loses reliability on uniform targets beyond about 24 qubits (59% solve rate at 30).
• Six-qubit checkpoint yields worse CZ counts on large deep and fully random targets than Qiskit baselines.

Experimental setup

Datasets: random-walk generated Clifford tableaus (6 and 10 qubits)

Benchmarks: Bravyi et al. 1003 optimal six-qubit Clifford tableaus random-walk and uniform Clifford targets 7-30 qubits

Metrics: CZ count fraction of optimal solutions solve rate runtime

Baselines: Aaronson-Gottesman Bravyi et al. greedy synthesizer Bravyi et al. peephole optimizer RelTransformer Transformer MLP FlatMLP

Builds on: PPO reverse curriculum generation DeepCubeA

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