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Reinforced Learning Explicit Circuit Representations for Quantum State Characterization from Local Measurements
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Proposes QCrep, a PPO-trained Transformer-based RL agent that learns explicit surrogate state-preparation circuits from local two-qubit Pauli measurements, using a local fidelity reward, for quantum state characterization up to 100 qubits.
Problem
Quantum state characterization from few local measurements usually yields implicit neural representations that cannot be directly reconstructed into experimental state-preparation circuits, and gradient-based variational circuit learning suffers from barren plateaus.
Approach
Represent a state family by an explicit gate-sequence circuit learned by a deep RL agent (PPO) that disentangles the state toward |0>^N, rewarded by average local fidelity computed from local Pauli measurements, avoiding gradient descent over circuit parameters; a self-attention feature aggregation block with global average pooling enables zero-shot transfer across system sizes.
Key results
- On 10-qubit IQP states, QCrep reaches 0.9851 global fidelity versus 0.9174 for VQE and lower for TQS, QAOA and QAS.
- On 10-qubit Heisenberg XXZ ground states, QCrep reaches 0.9550 global fidelity and zero RMSE on the three property metrics, outperforming the other methods.
- Learned circuits for 50-qubit Ising evolution are shallower than first-order Trotter circuits, and the model transfers zero-shot to sizes 10 to 100.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use QCrep instead of VQE | 10-qubit IQP circuits · 10-qubit IQP circuits | Global Fidelity: 0.9174±0.1042 -> 0.9851±0.0208 | Helped |
| Use QCrep instead of VQE | 10-qubit IQP circuits · 10-qubit IQP circuits | R´enyi Entropy: 0.1665 -> 3.0737e-07 | Helped |
| Use QCrep instead of QAS | 10-qubit IQP circuits · 10-qubit IQP circuits | Correlations: 0.0895 -> 1.0902e-08 | Helped |
| Use QCrep instead of QAOA | 10-qubit IQP circuits · 10-qubit IQP circuits | Spin-Z: 0.1429 -> 0.0441 | Helped |
| Use QCrep instead of QAOA | 10-qubit Ising-evolved states · 10-qubit Ising-evolved states | Global Fidelity: 0.9637±0.1402 -> 0.9979±0.0012 | Helped |
| Use QCrep instead of TQS | 10-qubit Ising-evolved states · 10-qubit Ising-evolved states | R´enyi Entropy: 0.1727 -> 0.0108 | Helped |
| Use QCrep instead of QAOA | 10-qubit Ising-evolved states · 10-qubit Ising-evolved states | Correlations: 0.0382 -> 0.0227 | Helped |
| Use QCrep instead of QAOA | 10-qubit Ising-evolved states · 10-qubit Ising-evolved states | Spin-Z: 0.0513 -> 0.0231 | Helped |
| Use QCrep instead of QAOA | 10-qubit Ising ground states · 10-qubit Ising ground states | Global Fidelity: 0.9614±0.0181 -> 0.9691±0.0083 | Helped |
| Use QCrep instead of QAOA | 10-qubit Ising ground states · 10-qubit Ising ground states | R´enyi Entropy: 0.0368 -> 0.0989 | Hurt |
| Use QCrep instead of TQS | 10-qubit Ising ground states · 10-qubit Ising ground states | Correlations: 0.0958 -> 0.0947 | Helped |
| Use QCrep instead of TQS | 10-qubit Ising ground states · 10-qubit Ising ground states | Spin-Z: 0.0306 -> 0.0309 | Hurt |
Surprising findings
- Global fidelity stays near zero for roughly the first 70 steps on 50-qubit IQP states even as local fidelity rises, suggesting barren-plateau-like behavior for global fidelity rewards.
- On 10-qubit Ising ground states QAOA gets a higher global fidelity (0.9614) than QCrep (0.9691 is QCrep; QAOA is 0.9614), while QCrep is best on the rest of the metrics.
Limitations
- Experiments are limited to shallow IQP circuits and one-dimensional Hamiltonian ground states and evolutions.
- Global fidelity lower bound from Proposition 2.1 is loose, and low-entanglement assumptions are needed for good global fidelity.
- Results are from classical simulation; robustness to depolarizing noise is shown only up to p=0.2.
Experimental setup
Datasets: simulated IQP circuit output states simulated transverse-field Ising time-evolved states simulated Ising ground states simulated Heisenberg XXZ ground states
Benchmarks: IQP-generated states (N=10) Ising time-evolved states (N=10) Ising ground states (N=10) Heisenberg XXZ ground states (N=10) Hamiltonian learning on 10-qubit Ising and Heisenberg
Metrics: Rényi entropy RMSE two-point correlations RMSE spin-Z RMSE global fidelity local fidelity circuit depth
Baselines: Transformer Quantum State (TQS) VQE QAOA QAS first-order Trotter decomposition
Builds on: PPO Transformer Transformer Quantum State variational quantum eigensolver QAOA
Closest papers by meaning
- Rethink the Role of Deep Learning towards Large-scale Quantum Systems (ICML 2025 · similarity 0.87)
- TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search (NeurIPS 2025 · similarity 0.87)
- One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective (NeurIPS 2026 · similarity 0.87)
- Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis (NeurIPS 2026 · similarity 0.86)
- Replay-buffer engineering for noise-robust quantum circuit optimization (NeurIPS 2026 · similarity 0.86)
- AI-Powered Algorithm-Centric Quantum Processor Topology Design (AAAI 2025 · similarity 0.85)
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