Sector-dominant graph-local drivers for path-window barrier Hamiltonians on the Boolean hypercube

TL;DR

This paper investigates graph-local drivers for adiabatic state preparation on Boolean hypercubes, demonstrating that hybrid drivers can significantly improve ground-state fidelity in certain barrier problems.

Contribution

It introduces sector-dominant graph-local drivers based on sector/path coordinates and shows their effectiveness in non-diagonal Hamiltonian cases with finite-size numerical validation.

Findings

Hybrid drivers improve ground-state fidelity in barrier instances.

Sector-preserving skeleton is the dominant contribution.

Reproduction code confirms a fidelity of approximately 0.9799.

Abstract

We study finite-size adiabatic state preparation on Boolean hypercubes using graph-local drivers built from sector/path coordinates related to monotone Gray-code representatives. The construction is not presented as a new all-$n$ Gray-code existence theorem; rather, it provides finite representatives, explicitly checked through the cases used in the numerical experiments, for testing problem-dependent graph-local drivers. For ordinary diagonal-cost transverse-field annealing, the ordering does not yield a robust advantage, and we include this negative result as a baseline. For non-diagonal target Hamiltonians whose geometry is expressed in the same sector/path coordinates, hybrid drivers combining sector, path-window, and small transverse-field components can substantially improve the final ground-state fidelity in centered barrier instances. Reproduction runs from the accompanying code confirm a representative centered original-window barrier value of approximately \(0.9799\) for the fixed-control hybrid parameters \((w,\alpha,\epsilon)=(8,0.50,0.15)\), while also showing that the improvement is target-class dependent. Randomized and ablation controls indicate that the dominant contribution is the sector-preserving skeleton, with strict one-bit completion acting as a secondary refinement. We provide code, finite certificates, CSV files, validation logs, and reproduction scripts to make the finite-size claims traceable.