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Training-Free Quantum Architecture Search
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Proposes TF-QAS, a training-free quantum architecture search that filters random PQCs by DAG path count and then ranks survivors by state-fidelity expressibility, avoiding circuit training.
Problem
Quantum architecture search (QAS) for variational quantum algorithms is computationally expensive because each candidate circuit must be trained to measure its performance.
Approach
Replace circuit training with two training-free proxies applied progressively: a zero-cost DAG path-count proxy filters out most candidates, then an expressibility (KL divergence of fidelity distribution vs Haar) proxy selects high-performing circuits from the remainder.
Key results
- TF-QAS reduces queries to reach chemical-accuracy ground state by 5 to 57 times versus PQAS and runs 6 to 17 times faster across three VQE tasks.
- Expressibility proxy achieves Spearman correlation up to 0.85 with ground-truth performance (layerwise Heisenberg), while path count correlates at 0.21 to 0.61.
- Path-based filtering retains over 55% of optimal circuits after discarding 90% of candidates.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the two-stage path and expressibility proxies instead of PQAS | TF-QAS · TFIM, Heisenberg, and BeH2 VQE | sampling efficiency: 5 to 57 times | Helped |
| Use the two-stage path and expressibility proxies instead of PQAS | TF-QAS · TFIM, Heisenberg, and BeH2 VQE | time: 6 to 17 times | Helped |
| Use TF-QAS rather than RS or PQAS | TF-QAS · TFIM VQE | probability of attaining ground state energy: 0% -> 100%; 10% -> 100% | Helped |
| Use TF-QAS rather than RS or PQAS | TF-QAS · Heisenberg layerwise VQE | probability of attaining ground state energy: 0% -> 80% | Helped |
| Use TF-QAS rather than RS or PQAS | TF-QAS · BeH2 VQE | probability of attaining ground state energy: 0% -> 50%; 10% -> 50% | Helped |
| Use only the path-based proxy rather than both proxies (ablation) | TF-QAS · TFIM | queries to ground-truth performance: 33.5 -> 104.7 | Hurt |
| Use only the expressibility-based proxy rather than both proxies (ablation) | TF-QAS · TFIM | queries to ground-truth performance: 33.5 -> 73.4 | Hurt |
| Use only the path-based proxy rather than both proxies (ablation) | TF-QAS · Heisenberg layerwise | queries to ground-truth performance: 36.5 -> 310.9 | Hurt |
| Use only the expressibility-based proxy rather than both proxies (ablation) | TF-QAS · Heisenberg layerwise | queries to ground-truth performance: 36.5 -> 85.8 | Hurt |
| Use only the path-based proxy rather than both proxies (ablation) | TF-QAS · BeH2 | queries to ground-truth performance: 110.5 -> 189.0 | Hurt |
| Use only the expressibility-based proxy rather than both proxies (ablation) | TF-QAS · BeH2 | queries to ground-truth performance: 110.5 -> 161.9 | Hurt |
| Use only the path-based proxy rather than both proxies (ablation) | TF-QAS · Heisenberg gatewise | queries to ground-truth performance: 137.9 -> 702.0 | Hurt |
Surprising findings
- The weakly correlated path-count proxy still preserves most optimal circuits when used as a 90% pre-filter, and combining the two proxies yields fewer queries than either alone.
Limitations
- Proxies do not account for trainability or barren plateaus, which the authors note as future work.
- Evaluated only on small VQE tasks (5-6 qubits) in simulation.
- Path-based proxy has weak correlation with circuit performance (0.21 to 0.61).
Experimental setup
Datasets: randomly sampled parameterized quantum circuits for TFIM, Heisenberg, and BeH2 VQE tasks
Benchmarks: 6-qubit TFIM VQE 5-qubit Heisenberg VQE 6-qubit BeH2 VQE 5-qubit Heisenberg VQE with ibmq quito topology
Metrics: number of queries to ground state wall-clock time success probability within 100 queries average energy error Spearman correlation Kendall's tau
Baselines: PQAS random sampling hardware-efficient ansatz
Builds on: PQAS training-free NAS expressibility of PQCs (Sim et al. 2019)
Closest papers by meaning
- Curriculum reinforcement learning for quantum architecture search under hardware errors (ICLR 2024 · similarity 0.92)
- TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search (NeurIPS 2025 · similarity 0.91)
- PALQO: Physics-informed model for Accelerating Large-scale Quantum Optimization (NeurIPS 2025 · similarity 0.88)
- QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design (NeurIPS 2025 · similarity 0.87)
- Q-MAML: Quantum Model-Agnostic Meta-Learning for Variational Quantum Algorithms (AAAI 2025 · similarity 0.87)
- MG-Net: Learn to Customize QAOA with Circuit Depth Awareness (NeurIPS 2024 · similarity 0.87)
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