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

• URL: http://arxiv.org/abs/2604.25494v1
• Date: Tue, 28 Apr 2026 10:54:42 GMT
• Title: Sector-dominant graph-local drivers for path-window barrier Hamiltonians on the Boolean hypercube
• Abstract summary: We study finite-size adiabatic state preparation on Boolean hypercubes.<n>We use graph-local drivers built from sector/path coordinates related to monotone Gray-code representatives.<n>We provide code, finite certificates, CSV files, validation logs, and reproduction scripts to make the finite-size claims traceable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \((w,α,ε)=(8,0.50,0.15)\), 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.

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