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Adaptive Observation Cost Control for Variational Quantum Eigensolvers
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Proposes SubsCoRe, an adaptive shot-allocation method for sequential minimal optimization (NFT) of VQE that uses GP confident regions and equidistant observations to minimize total measurement shots.
Problem
VQE optimization is costly because each objective observation requires hundreds to thousands of quantum measurement shots; existing SMO (NFT) uses a fixed shot count per observation, wasting quantum budget.
Approach
Requires the GP posterior uncertainty over the 1D subspace being updated to lie within a confident region (CoRe), with the required accuracy adapted to optimization progress; proves that observing 1+2V_d equidistant points gives uniform, min-max optimal posterior uncertainty, so shots can be allocated per point via a simple variance-based rule (SubsCoRe-Center/-Bound variants).
Key results
- On a 5-qubit, 3-layer Heisenberg/Ising VQE, SubsCoRe-Center outperforms NFT, SGLBO and EMICoRe with statistical significance (Wilcoxon p<0.05) in energy and fidelity versus cumulative shots.
- Theory shows equidistant 1+2V_d observations with equal shots yield uniform posterior variance bounded by the observation noise variance.
- SubsCoRe caps shots at 1024 per data point per operator group, reflecting typical hardware limits.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SubsCoRe-Center with adaptive shot control instead of the evaluated baselines | VQE optimization · Ising Hamiltonian, L=3, Q=5 | ΔEnergy | Helped |
| use SubsCoRe-Center with adaptive shot control instead of the evaluated baselines | VQE optimization · Ising Hamiltonian, L=3, Q=5 | ΔFidelity | Helped |
| use SubsCoRe-Bound instead of SubsCoRe-Center (ablation) | SubsCoRe · Ising Hamiltonian, L=3, Q=5 | measurement-shot efficiency | Hurt |
| use SubsCoRe-Bound instead of SubsCoRe-Center (ablation) | SubsCoRe · Ising Hamiltonian, L=3, Q=5 | ΔEnergy | Hurt |
| use SubsCoRe-Bound instead of SubsCoRe-Center (ablation) | SubsCoRe · Ising Hamiltonian, L=3, Q=5 | ΔFidelity | Hurt |
Limitations
- Only simulated experiments; hardware noise is not considered.
- Results on a single small Hamiltonian (5-qubit Ising/Heisenberg).
Experimental setup
Metrics: energy error from ground truth fidelity error total shot count
Baselines: NFT SGLBO EMICoRe SubsCoRe-Bound
Builds on: Nakanishi-Fuji-Todo (NFT) EMICoRe SGLBO VQE kernel
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