Braida and Colleagues Models Log-Concavity Framework for Discrete Schrödinger Operators

Arthur Braida and colleagues at the Paris Cité University investigate computational speedups via quantum tunneling in Adiabatic Quantum Optimisation (AQO). Building on previous work with the “Hamming weight with a spike” problem, they extend the analysis to a wider range of potentials. This reveals discrete log-concavity of the ground state as a key structural property. This framework yields new spectral gap bounds, surpassing previously known limits. It also extends perturbative analysis to include convex potentials, specifically demonstrating a transition from linear to quadratic potentials. The findings sharply indicate that quantum tunneling may be more broadly applicable to convex potentials containing spikes, potentially enhancing the performance of AQO algorithms. Spectral gap bounds…