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Curriculum reinforcement learning for quantum architecture search under hardware errors
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Proposes CRLQAS, a curriculum-based RL quantum architecture search method with a 3D binary circuit encoding, random halting, illegal actions, and an Adam-SPSA optimizer, plus a PTM-based GPU simulator for noisy VQE circuit search.
Problem
Quantum architecture search for variational quantum eigensolver (VQE) circuits under hardware noise and shot noise, where prior QAS methods were largely developed for noiseless, all-to-all connected devices.
Approach
Combines a DDQN agent with a tensor-based 3D binary circuit encoding, illegal-action pruning, random episode halting (negative binomial episode length), feedback-driven moving-threshold curriculum, and a multi-stage Adam-SPSA optimizer with continuously decaying hyperparameters; noisy simulation is accelerated by precomputed Pauli-transfer matrices in JAX.
Key results
- On H2-4 in noiseless settings, CRLQAS reaches energy error 7.2e-8 with 21 gates versus 1.9e-2 with 38 gates for modified qubit-ADAPT-VQE.
- For LiH-6 noiseless, CRLQAS reaches energy error 6.7e-4 with 67 gates, compared with 2.9e-4 with 132 gates for quantumDARTS; CRLQAS is more compact on that molecule, not more accurate.
- In noisy H2-4 with IBM Ourense noise, CRLQAS reaches -1.136 Ha versus -0.963 Ha reported by QCAS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CRLQAS instead of quantumDARTS | VQE architecture search · H2-4 noiseless | energy error: 4.3 \times 10^{-6} -> 7.2 \times 10^{-8} | Helped |
| Use CRLQAS instead of quantumDARTS | VQE architecture search · LiH-4 noiseless | energy error: 1.7 \times 10^{-4} -> 2.6 \times 10^{-6} | Helped |
| Use CRLQAS instead of quantumDARTS | VQE architecture search · LiH-6 noiseless | energy error: 2.9 \times 10^{-4} -> 6.7 \times 10^{-4} | Hurt |
| Use CRLQAS instead of quantumDARTS | VQE architecture search · H2O-8 noiseless | energy error: 3.1 \times 10^{-4} -> 1.8 \times 10^{-4} | Helped |
| Add illegal actions to CRLQAS (ablation) | CRLQAS · LiH-6 noiseless | noiseless error: 0.0037 -> 0.0008 | Helped |
| Add illegal actions to CRLQAS (ablation) | CRLQAS without random halting · H2-4 noisy, Ourense | noiseless error: 0.0004 -> 0.0001 | Helped |
| Add random halting to CRLQAS with illegal actions (ablation) | CRLQAS · LiH-6 noiseless | noiseless error: 0.0008 -> 0.0012 | Hurt |
| Add random halting to CRLQAS with illegal actions (ablation) | CRLQAS · H2-4 noisy, Ourense | noiseless error: 0.0001 -> 0.0002 | Hurt |
| Add shot noise (ablation) | CRLQAS with illegal actions and random halting · LiH-4 noisy, Mumbai Median | noiseless error: 0.0024 -> 0.0038 | Hurt |
| Use CRLQAS instead of QCAS | VQE architecture search · H2-4 noiseless | noiseless energy error: 1.9\times10^{-2} -> 8\times10^{-5} | Helped |
Surprising findings
- Minimizing the noisy energy does not necessarily minimize the noiseless energy; the noiseless error can pass chemical accuracy while the noisy curve is well above it.
- In noisy LiH-4 settings with heavier noise, the agent failed to reach chemical accuracy.
Limitations
- Noisy experiments are limited to about four qubits due to computational cost; larger systems were studied only noiselessly.
- No validation on real quantum hardware; noise simulations assume no drift.
- Training from scratch is computationally demanding and sample-inefficient.
Experimental setup
Datasets: molecular Hamiltonians (H2, LiH, H2O in STO-3G) IBM device noise profiles (IBM Mumbai, IBM Ourense)
Benchmarks: VQE ground-state energy of H2-2/3/4, LiH-4/6, H2O-8
Metrics: energy error number of gates circuit depth number of parameters
Baselines: QCAS quantumDARTS modified qubit-ADAPT-VQE COBYLA
Builds on: double deep q-network feedback-driven curriculum learning qubit-ADAPT-VQE SPSA Adam
Closest papers by meaning
- TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search (NeurIPS 2025 · similarity 0.92)
- Training-Free Quantum Architecture Search (AAAI 2024 · similarity 0.92)
- Replay-buffer engineering for noise-robust quantum circuit optimization (NeurIPS 2026 · similarity 0.88)
- AI-Powered Algorithm-Centric Quantum Processor Topology Design (AAAI 2025 · similarity 0.88)
- PALQO: Physics-informed model for Accelerating Large-scale Quantum Optimization (NeurIPS 2025 · similarity 0.88)
- Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms (AAAI 2025 · similarity 0.87)
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