Characterization of the QAOA spectral-gap requirement

Determine the minimum spectral gap along the adiabatic path from the transverse-field mixer Hamiltonian to the cost Hamiltonian for the constrained robust QUBOs arising in the VANGUARD optimization problem, in order to characterize the QAOA depth required to achieve a prescribed solution accuracy.

Background

The SENTINEL framework solves each local VANGUARD subproblem by mapping its QUBO formulation to an Ising cost Hamiltonian and applying QAOA. Although the optimal QAOA energy converges to the ground-state energy as the circuit depth tends to infinity, the depth needed to obtain a specified accuracy depends on the minimum spectral gap encountered along the corresponding adiabatic path.

For the constrained robust QUBOs used by SENTINEL, the paper states that this minimum spectral gap is generally unknown and may be small. Consequently, the required finite-depth QAOA resources cannot be established analytically in general, and the paper evaluates solution quality empirically rather than providing a general depth or approximation guarantee.

References

The depth required for a given accuracy, however, depends on the minimum spectral gap along this path, which is generally unknown and may be small.

— Distributed Quantum-Assisted Robust AoII Minimization in Satellite-Ground Integrated Edge Networks  (2610.05651 - Mohammad~Arif~Hossain et al., 5 Oct 2026) in Section V, subsection “Solution Quality, Certification, and Resource Scaling”