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PALQO: Physics-informed model for Accelerating Large-scale Quantum Optimization
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Proposes PALQO, which reformulates VQA parameter-update dynamics as a nonlinear PDE and trains a PINN on a few quantum-device trajectory steps to predict future updates classically, reducing quantum measurement shots by about 90% on tasks up to 40 qubits.
Problem
Training variational quantum algorithms requires many quantum measurements because gradients need parameter-shift evaluations at every iteration, which becomes prohibitive for large-scale tasks.
Approach
Approximate VQA gradient-flow training dynamics with a Taylor-expanded nonlinear PDE (including QNTK and Hessian terms) and solve it with a physics-informed neural network trained on a short trajectory, so future parameter updates are predicted on classical hardware instead of measured on the quantum device.
Key results
- PALQO reduces quantum measurement shots to 1.535e8 vs 10.97e8 for vanilla VQE on 20-qubit TFIM (about 90% reduction), and 28.01e8 vs 464.3e8 on 14-qubit BeH2.
- PALQO achieves up to 30x speedup in iterations over vanilla VQE on TFIM with J/h=0.5 while keeping energy error around 1e-3.
- Ablation shows both PDE and data residual terms help performance, though neither is essential.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PALQO instead of Vanilla VQE | VQE optimization · 20-qubit TFIM with HEA | measurement shots (×10^8): 10.97 -> 1.535 | Helped |
| use PALQO instead of Vanilla VQE | VQE optimization · 20-qubit Heisenberg with HVA | measurement shots (×10^8): 21.66 -> 5.749 | Helped |
| use PALQO instead of Vanilla VQE | VQE optimization · 14-qubit BeH2 with UCCSD | measurement shots (×10^8): 464.3 -> 28.01 | Helped |
| use PALQO for parameter-update prediction | VQE optimization · TFIM with HEA, including J/h=2 | speedup ratio: up to 30x | Helped |
| add the data residual L_D (ablation) | PALQO · TFIM with HEA, n=12, 20, 28 | speedup ratio | Helped |
| add the PDE residual L_P2 (ablation) | PALQO · TFIM with HEA, n=12, 20, 28 | speedup ratio | Helped |
| increase hidden-layer width (ablation) | PALQO · TFIM with HEA | speedup ratio | Helped |
| increase network depth from 2 to 6 hidden layers (ablation) | PALQO · TFIM with HEA | speedup ratio | No clear effect |
| vary training sample count among 2, 4, and 8 (ablation) | PALQO · 12-qubit TFIM with HEA | speedup ratio | No clear effect |
Surprising findings
- Increasing the depth of the PINN did not improve speedup, while increasing width did.
- Speedup has high variance across configurations, and speedup is lower at J/h=2 due to a smaller energy gap.
Limitations
- Reduces quantum advantage by replacing quantum queries with classical prediction.
- High variance in speedup ratio across configurations.
- Scalability to regimes where quantum hardware outperforms classical methods is uncertain.
Experimental setup
Datasets: TFIM Hamiltonians Heisenberg model Hamiltonians XXZ model Hamiltonians LiH and BeH2 molecular Hamiltonians generated with OpenFermion
Benchmarks: TFIM ground state energy (up to 40 qubits) Heisenberg model ground state BeH2 ground state
Metrics: energy error |E_hat - E| speedup ratio in iterations number of quantum measurement shots
Baselines: vanilla VQE LSTM-based model QuACK
Builds on: physics-informed neural networks quantum neural tangent kernel QuACK variational quantum eigensolver
Closest papers by meaning
- Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms (AAAI 2025 · similarity 0.89)
- TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQE (NeurIPS 2025 · similarity 0.89)
- One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective (NeurIPS 2026 · similarity 0.89)
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