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TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQE
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Proposes TITAN, a ResNet-18 plus self-attention model that predicts which VQE parameters will be frozen at initialization, using trajectories from an adaptive freezing procedure (APFA) to cut measurement overhead.
Problem
Training VQE for large Hamiltonians is costly because parameter-shift gradients require circuit evaluations linear in parameter count, and deep circuits suffer barren plateaus.
Approach
Learn a predictor that identifies inactive (frozen) parameters at initialization from APFA freezing trajectories, with training data built from an enhanced Gaussian initialization claimed to avoid barren plateaus, and a coordinate-aware fully-convolutional self-attention encoding that generalizes across ansatz sizes.
Key results
- Abstract claims up to 3x faster convergence and 40-60% fewer circuit evaluations than baselines on TFIM, Heisenberg and molecules up to 30 qubits.
- For HEA on isotropic Heisenberg Hamiltonian, most (layers, qubits) cells show Delta E <= 0 with TITAN masks, with roughly half of cells having >=5 frozen parameters.
- On molecules, 30% to 66% of parameters are frozen a priori (e.g., 77/117 for CO) with negligible energy change under Gaussian initialization.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TITAN-predicted freezing instead of no freezing | VQE with HEA on isotropic Heisenberg Hamiltonians · HEA, L ∈ {5,…,10}, N ∈ {5,…,15} | final energy difference ΔE: more than 90% of the cells are shaded green (ΔE≤0) | Mixed |
| Use TITAN-predicted freezing instead of random freezing | VQE with HEA on anisotropic Heisenberg Hamiltonians · 8-qubit, 5-layer HEA | final energy gap ΔE: improvements reaching ΔE≈ 0.12; random-freeze absolute deviations seldom exceed |ΔE|<0.03 | Helped |
| Use TITAN-predicted freezing instead of random freezing | VQE on TFIM · TFIM, J=-3 and h = 2 | final energy: gap of ∼ 1.5–2.0 energy units at N=20 | Helped |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · H₂ | ΔE (TITAN − baseline): 0.000 | No clear effect |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · HF | ΔE (TITAN − baseline): 0.000 | No clear effect |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · LiH | ΔE (TITAN − baseline): 0.018 | Hurt |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · BeH₂ | ΔE (TITAN − baseline): 0.008 | Hurt |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · H₂O | ΔE (TITAN − baseline): 0.000 | No clear effect |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · N₂ | ΔE (TITAN − baseline): -0.007 | Helped |
| Use TITAN-predicted freezing instead of no freezing | Molecular VQE with Gaussian initialization · CO | ΔE (TITAN − baseline): -0.015 | Helped |
| Replace learned, targeted freezing with random freezing (ablation) | Molecular VQE with Gaussian initialization · H₂ | ΔE (Random − baseline): 2.248 | Hurt |
| Replace learned, targeted freezing with random freezing (ablation) | Molecular VQE with Gaussian initialization · molecular benchmarks (H₂, HF, LiH, BeH₂, H₂O, N₂, CO) | final energy: 2.248; 0.000; 0.003; 0.013; 0.004; 0.011; 0.017 | Hurt |
Surprising findings
- Random parameter freezing incurs energy penalties of 0.3-1.2 Ha in some SU2/SEL settings, suggesting targeted pruning matters.
- Uniform initialization under TITAN freezing gave large energy deviations for some molecules (e.g., +2.512 Ha for N2).
Limitations
- Experiments run on classical simulators and benchmark circuits up to about 100 qubits, not real hardware.
- Frozen-parameter prediction is specific to a Hamiltonian family and ansatz class; generalization claims rest on limited tests.
- Results on molecules show mixed sign of energy change across initializations, and freeze thresholds require tuning.
Experimental setup
Datasets: Heisenberg Hamiltonians (synthetic, 5-15 qubits) transverse-field Ising model molecular Hamiltonians (H2, HF, LiH, BeH2, H2O, N2, CO)
Benchmarks: Heisenberg models transverse-field Ising model H2 HF LiH BeH2 H2O N2 CO
Metrics: variational energy delta E vs baseline number of frozen parameters gradient l2-norm convergence speed
Baselines: Baseline (vanilla VQE) Random freeze Zero initialization Uniform initialization Gaussian initialization
Builds on: variational quantum eigensolver Gaussian initialization hardware-efficient ansatz ResNet multi-head self-attention
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