Beyond Feasibility: Finite-Depth Accessibility in Constrained QAOA
Abstract
Constraint-preserving mixers keep QAOA within a feasible subspace, but feasibility and global mixer connectivity do not determine which feasible configurations are available to a particular shallow circuit. We study constrained QAOA at the level of the circuit actually executed: a specified feasible initial state, finite depth, and finite schedule of mixer interactions. We define the finite-depth accessible set Rp(M,x0) and show that the computational-basis support of the ideal QAOA circuit is contained within it. This gives a parameter-independent objective ceiling fR⋆=maxx∈ Rpf(x) and a normalized reachable-quality diagnostic QR, separating accessible volume from the objective quality contained within it. We evaluate this framework using resource-matched block-local XY mixer schedules for constrained portfolio optimization and synthetic block-constrained quadratic problems. Across 207 favorable-tail CVaR QAOA configurations, QR shows the strongest association with realized shallow-QAOA performance among the structural diagnostics considered, with Pearson and Spearman correlations of $0.7003$ and $0.8057$; the relationship remains positive under controlled and dependence-aware analyses. The distinction persists across changes in feasible initialization, portfolio size, and objective family. A compilation-only study further shows that, for the dense portfolio Hamiltonians considered here, phase-separator routing dominates the compiled two-qubit resource scale, while mixer schedules with comparable compiled two-qubit cost can exhibit markedly different finite-depth accessible quality. These results motivate objective-relevant finite-depth accessibility as a complementary diagnostic for resource-bounded constrained QAOA.
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BibTeX
@misc{ubale2026beyond,
title = {{Beyond Feasibility: Finite-Depth Accessibility in Constrained QAOA}},
author = {Rushikesh Ubale and Gregory T. Byrd and Yasar Mulani and Sangram Deshpande},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00736},
eprint = {2610.00736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00736},
}
RIS
TY - UNPB
TI - Beyond Feasibility: Finite-Depth Accessibility in Constrained QAOA
AU - Rushikesh Ubale
AU - Gregory T. Byrd
AU - Yasar Mulani
AU - Sangram Deshpande
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00736
UR - https://arxiv.org/abs/2610.00736
AB - Constraint-preserving mixers keep QAOA within a feasible subspace, but feasibility and global mixer connectivity do not determine which feasible configurations are available to a particular shallow circuit. We study constrained QAOA at the level of the circuit actually executed: a specified feasible initial state, finite depth, and finite schedule of mixer interactions. We define the finite-depth accessible set R_p(M,x_0) and show that the computational-basis support of the ideal QAOA circuit is contained within it. This gives a parameter-independent objective ceiling f_R^⋆=max_x∈ R_pf(x) and a normalized reachable-quality diagnostic Q_R, separating accessible volume from the objective quality contained within it. We evaluate this framework using resource-matched block-local XY mixer schedules for constrained portfolio optimization and synthetic block-constrained quadratic problems. Across 207 favorable-tail CVaR QAOA configurations, Q_R shows the strongest association with realized shallow-QAOA performance among the structural diagnostics considered, with Pearson and Spearman correlations of $0.7003$ and $0.8057$; the relationship remains positive under controlled and dependence-aware analyses. The distinction persists across changes in feasible initialization, portfolio size, and objective family. A compilation-only study further shows that, for the dense portfolio Hamiltonians considered here, phase-separator routing dominates the compiled two-qubit resource scale, while mixer schedules with comparable compiled two-qubit cost can exhibit markedly different finite-depth accessible quality. These results motivate objective-relevant finite-depth accessibility as a complementary diagnostic for resource-bounded constrained QAOA.
ER -