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MG-Net: Learn to Customize QAOA with Circuit Depth Awareness
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Analyzes QAOA convergence via representation theory and proposes MG-Net, a depth-aware estimator-generator network that customizes mixer Hamiltonians (parameter grouping and Pauli types) for Max-Cut and TFIM up to 64 qubits.
Problem
QAOA performance depends on circuit depth and the mixer Hamiltonian, but the best mixer is problem- and depth-specific and hard to design by hand; required depth often exceeds current device limits.
Approach
Theoretical link between parameter grouping in the mixer (fully, partially, non-grouped), effective dimension, and convergence; then an estimator-generator network that takes problem graph and depth, predicts a cost, and generates a mixer Hamiltonian by minimizing the frozen estimator's output, trained in two stages to avoid collecting optimal mixers.
Key results
- On 64-qubit Max-Cut, MG-Net reaches approximation ratio 0.96 versus 0.91 for Goemans-Williamson, 0.79 greedy, 0.19 standard QAOA, and 0.0 for ma-QAOA.
- MG-Net circuits reach approximation ratio r>=0.995 even at p=2, whereas standard QAOA reaches this only for p>50 on Max-Cut (p>20 for TFIM).
- At 64 qubits with p=2, gradient norm stays near 1 for MG-Net, versus about 1e-1 for FG and 1e-4 for NG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the MG-Net-generated mixer instead of the strongest listed baseline, ma-QAOA | QAOA · Max-Cut, 6 qubits | approximation ratio: 0.98± 0.004 -> 0.99± 0.0004 | Helped |
| Use the MG-Net-generated mixer instead of the strongest listed baseline, GW | QAOA · Max-Cut, 16 qubits | approximation ratio: 0.93± 0.052 -> 0.95± 0.152 | Helped |
| Use the MG-Net-generated mixer instead of the strongest listed baseline, GW | QAOA · Max-Cut, 64 qubits | approximation ratio: 0.91 -> 0.96 | Helped |
| Generate a depth-tailored mixer instead of using standard fully grouped QAOA | QAOA on Max-Cut · Max-Cut, circuit depths across tested values | approximation ratio: r≥ 0.995; p>50 | Helped |
| Generate a depth-tailored mixer instead of using standard fully grouped QAOA | QAOA on TFIM · TFIM, circuit depths across tested values | approximation ratio: r≥ 0.995; p>20 | Helped |
Surprising findings
- Under non-grouped parameters (multi-angle QAOA), performance declines when the circuit becomes excessively deep (p>42), so deeper is not always better.
- Reported ma-QAOA approximation ratio on 64-qubit Max-Cut is 0.0, indicating training failure at that scale.
Limitations
- Training the cost estimator requires a labeled dataset of QAOA minimum costs, adding resource cost.
- Approach is designed for QAOA on early fault-tolerant devices and not tested under noise or on other VQAs.
- Evaluated only on Max-Cut and TFIM with a small training set of 100 instances.
Experimental setup
Datasets: weighted 3-regular graphs (Max-Cut) with uniform edge weights 1D inhomogeneous TFIM instances
Benchmarks: weighted Max-Cut (6, 16, 64 qubits) TFIM
Metrics: approximation ratio effective dimension gradient norm trainable parameter count
Baselines: Greedy Goemans-Williamson QAOA ADAPT-QAOA ma-QAOA
Builds on: QAOA ADAPT-QAOA multi-angle QAOA
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