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Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms
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Proposes Q-MAML, a classical neural network (Learner) meta-trained with MAML-inspired objectives to output initial parameters for parameterized quantum circuits in variational quantum eigensolver tasks, evaluated on Heisenberg XYZ and molecular Hamiltonians.
Problem
VQAs suffer from poor parameter initialization, barren plateaus, and limited quantum processing time, which restrict the number of optimization iterations needed for convergence.
Approach
Use a classical MLP (Learner) meta-trained across a distribution of Hamiltonian tasks, following MAML, to predict initial PQC parameters from a Hamiltonian task vector, so that the PQC converges in fewer quantum iterations during adaptation; only the PQC is updated during adaptation.
Key results
- Q-MAML-initialized PQCs converge faster than Zero, Pi, reduced-domain Uniform, and Gaussian initializations on Heisenberg XYZ and molecular Hamiltonians (per trajectory plots).
- Learner successfully learns the task-space pattern, yielding a small gap between predicted and exact ground state energies across qubit counts.
- Adaptation uses 2000 PQC iterations with Adam at learning rate 0.001, and 6 target tasks (10% of molecular dataset) and 16 random Heisenberg samples are used for evaluation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Q-MAML-learned initialization instead of conventional initialization | Q-MAML · Heisenberg XYZ Hamiltonian | convergence speed | Helped |
| Use Q-MAML-learned initialization instead of conventional initialization | Q-MAML · Molecule Hamiltonian | convergence speed | Helped |
Limitations
- Evaluated only on small Hamiltonian task sets (16 Heisenberg samples, 6 molecular samples) and a limited set of qubit counts.
- Mechanistic claims about barren plateau mitigation and gradient norms are largely qualitative and speculative in the paper.
Experimental setup
Datasets: Heisenberg XYZ Hamiltonian task space (sampled J values) Molecular Hamiltonians generated with PennyLane qml.molecular_hamiltonian
Benchmarks: Heisenberg XYZ Hamiltonian ground state energy (12 and 20 qubits) Molecule Hamiltonian ground state energy (10 and 14 qubits)
Metrics: energy gap to exact ground state energy from exact diagonali gradient norm
Baselines: Zero initialization Pi initialization Uniform reduced-domain initialization Gaussian initialization
Builds on: MAML variational quantum eigensolver Gaussian parameter initialization reduced-domain parameter initialization
Closest papers by meaning
- PALQO: Physics-informed model for Accelerating Large-scale Quantum Optimization (NeurIPS 2025 · similarity 0.89)
- On the Relation between Trainability and Dequantization of Variational Quantum Learning Models (ICLR 2025 · similarity 0.88)
- TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search (NeurIPS 2025 · similarity 0.88)
- One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective (NeurIPS 2026 · similarity 0.87)
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