What question did this study set out to answer?

This research aims to develop a framework for efficiently constructing qubit Hamiltonians in quantum chemistry.

July 12, 20260 citationsOpen Access

GeoVac (The Geometric Vacuum): Structurally Sparse Qubit Hamiltonians and the Discrete Spectral Triple

Key Points

This research aims to develop a framework for efficiently constructing qubit Hamiltonians in quantum chemistry.
Utilized a spectral-graph-theory approach with the discrete graph Laplacian on S^3.
Established mathematical equivalence to the Schrödinger equation and applied sparse qubit Hamiltonians.
Conducted classical validation benchmarks across various molecular systems.
Achieved O(Q^2.5) Pauli-term scaling, with reductions up to 1712x compared to Gaussian methods.
Validated performance on classical benchmarks, including He at 0.019% and H2 at 96.0% of the dissociation energy.
Developed a comprehensive library of 38 molecules compatible with major quantum frameworks.

Abstract

GeoVac is a spectral-graph-theory framework for computational quantum chemistry and mathematical physics. The discrete graph Laplacian on the three-sphere S³ is mathematically equivalent to the Schrodinger equation via Fock's 1935 conformal projection (Paper 7, 18/18 symbolic proofs), and this equivalence is exploited to build structurally sparse qubit Hamiltonians whose angular-momentum (Gaunt) selection rules enforce block-diagonal electron-repulsion integrals. The result is O (Q². 5) Pauli-term scaling, a 51x-1712x reduction versus Gaussian baselines across LiH, BeH2, and H2O (Paper 14), with a 38-molecule library exported to OpenFermion, Qiskit, and PennyLane (Paper 20). Classical validation benchmarks include He at 0. 019% and H2 at 96. 0% of the dissociation energy. Beyond quantum-computing applications, the framework's structure has been developed as a discrete almost-commutative spectral triple in the Marcolli-van Suijlekom gauge-network lineage: state-space Gromov-Hausdorff convergence of the Camporesi-Higuchi truncations is established unconditionally at explicit rate (4/pi) log (n) /n via a translation-seminorm metrization (Paper 38), a degeneracy theorem closes the natural route to a Lorentzian quantum metric on truncated Krein spectral triples (Paper 45; an earlier convergence claim is retracted, see docs/claimsᵣegister. md), and the framework's transcendental periods are classified as cyclotomic mixed-Tate at level 4 via a master Mellin engine (Papers 55-56). Developed with an AI-augmented agentic research workflow; all results validated against analytical solutions, NIST reference data, and a symbolic proof suite.

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