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TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search
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Warm-starts reinforcement-learning quantum architecture search with a DMRG-derived matrix product state mapped to a brickwork circuit, cutting CNOT counts and optimizer evaluations on molecular ground-state problems up to 12 qubits.
Problem
RL-based quantum architecture search (QAS) for variational quantum algorithms scales poorly with qubit number, circuit depth and noise, due to a large action space and expensive circuit simulation per episode.
Approach
Initialize the RL agent's search from a tensor-network-derived circuit (DMRG MPS mapped to a brickwork PQC via Riemannian optimization), either letting the agent see and modify the warm-start (trainable) or keeping it fixed as a statevector outside the RL state (fixed), so RL only adds gates on top of a physically meaningful starting point.
Key results
- TensorRL (fixed TN-init) reaches 6.8e-5 error on 6-BeH2 with 5 CNOTs and depth 7, versus 21-36 depth for baselines.
- TensorRL (fixed) reduces per-episode execution time by 98% versus CRLQAS and uses ~10^3 function evaluations per episode, up to 100x fewer than baselines.
- Under 8-H2O depolarizing noise (amplified 1%/5%), TensorRL (fixed) reaches 100% success versus 30% for CRLQAS (rerun), with depth 7 vs 22.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| warm-start RL-QAS with an MPS circuit and keep the initialization fixed | TensorRL-QAS · 8-qubit H2O noiseless | CNOT count: 9 versus 69-117 CNOTs for competing methods | Helped |
| warm-start RL-QAS with an MPS circuit and keep the initialization fixed | TensorRL-QAS · 10-qubit H2O noiseless | CNOT count: 15 versus 96 CNOTs; error 4.1 \times 10^{-4} versus 2.5\times10^{-4} | Mixed |
| warm-start RL-QAS with an MPS circuit and train the warm-start | TensorRL-QAS · 12-qubit LiH noiseless | CNOT count: 37 versus 321 CNOTs for vanilla RL | Helped |
| warm-start RL-QAS with an MPS circuit and keep the initialization fixed | TensorRL-QAS · 8-qubit H2O depolarizing noise | success probability: 30% -> 100% | Helped |
| use TensorRL instead of CRLQAS | 8-qubit H2O noisy QAS · 8-qubit H2O noisy simulation | circuit depth: 2.4× reduction | Helped |
| use TensorRL instead of CRLQAS | TensorRL-QAS · 8-qubit H2O | per-episode execution time: 80% and 98% less time | Helped |
| use fixed rather than trainable TN initialization (ablation) | TensorRL-QAS · 8-qubit H2O depolarizing noise | error: 2.48\times10^{-3} -> 9.0\times10^{-4} | Helped |
| make the TN warm-start trainable rather than fixed (ablation) | TensorRL-QAS · 12-qubit LiH noiseless | error: 2.4\times10^{-2} -> 1.0\times10^{-2} | Helped |
| increase the bond dimension to χ=3 for the trainable TN initialization (ablation) | TensorRL-QAS · 10-qubit H2O noiseless | error: 7.1 \times 10^{-4} -> 6.7 \times 10^{-4} | Helped |
| use the fixed MPS initialization instead of a zero-parameter circuit with the same structure (ablation) | TensorRL-QAS · 8-qubit H2O noiseless | error: 1.3\times 10^{-4} -> 8.9 \times 10^{-4} | Hurt |
| use the fixed MPS initialization instead of a zero-parameter circuit with the same structure (ablation) | TensorRL-QAS · 8-qubit H2O shot noise | error: 6.8\times10^{-4} -> 1.5\times10^{-4} | Helped |
Surprising findings
- Fixed TN-init variant achieves better compactness than the trainable variant, which is attributed to fewer trainable parameters and reduced RL state size.
- TN-VQE (fixed MPS warm-start plus hardware-efficient ansatz optimized by COBYLA) often fails to reach chemical accuracy, indicating RL-based construction is necessary.
Limitations
- Action space limited to RX, RY, RZ and CNOT, with scaling limits noted for larger systems.
- All hardware results are noise simulations with amplified noise rates; no training on real QPU was performed (only noiseless-trained circuits run on IBMQ-Brisbane).
- Fixed TN-init variant's reported gate counts exclude the warm-start circuit gates, which are not visible to the agent.
Experimental setup
Datasets: molecular Hamiltonians for 6-BeH2, 8-H2O, 10-H2O, 12-LiH 5-qubit Heisenberg model 6-qubit TFIM model 8-qubit H2O noisy simulation
Benchmarks: 6-BeH2 8-H2O 10-H2O 12-LiH 5-qubit Heisenberg 6-qubit TFIM 20-qubit TFIM
Metrics: energy error CNOT count circuit depth rotation count function evaluations (nfev) episode time success probability
Baselines: CRLQAS vanilla RL-QAS RA-QAS TF-QAS SA-QAS quantumDARTS TN-VQE StructureRL
Builds on: DDQN CRLQAS DMRG Riemannian optimization on the Stiefel manifold Rudolph et al. TN-PQC warm-start
Closest papers by meaning
- Curriculum reinforcement learning for quantum architecture search under hardware errors (ICLR 2024 · similarity 0.92)
- Training-Free Quantum Architecture Search (AAAI 2024 · similarity 0.91)
- AI-Powered Algorithm-Centric Quantum Processor Topology Design (AAAI 2025 · similarity 0.89)
- QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design (NeurIPS 2025 · similarity 0.89)
- Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis (NeurIPS 2026 · similarity 0.89)
- One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective (NeurIPS 2026 · similarity 0.88)
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