First O(n^{2-1/(2h-2)} polylog n) algorithm for diameter and eccentricity in real-weighted K_h-minor-free digraphs via randomized search-to-decision reduction on VC-dimension.
Valiant and Vijay V
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Constructs quantum filtered oracle for Valiant-Vazirani theorem reducing SAT to UNIQUE SAT, enabling polynomial-time NP solution via torsion nonlinearity in noise-free limit but not #P.
Nonlinear Hamiltonians on ancilla qubits enable efficient solution of UNIQUE SAT with ⟨σ^z⟩σ^z, 3SAT with ⟨σ^x⟩σ^y - ⟨σ^y⟩σ^x, and #SAT with ⟨σ^y⟩⟨σ^z⟩σ^x - ⟨σ^x⟩⟨σ^z⟩σ^y nonlinearity.
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Quantum algorithm for Valiant-Vazirani reduction
Constructs quantum filtered oracle for Valiant-Vazirani theorem reducing SAT to UNIQUE SAT, enabling polynomial-time NP solution via torsion nonlinearity in noise-free limit but not #P.
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Nonlinear Hamiltonians and Boolean satisfiability
Nonlinear Hamiltonians on ancilla qubits enable efficient solution of UNIQUE SAT with ⟨σ^z⟩σ^z, 3SAT with ⟨σ^x⟩σ^y - ⟨σ^y⟩σ^x, and #SAT with ⟨σ^y⟩⟨σ^z⟩σ^x - ⟨σ^x⟩⟨σ^z⟩σ^y nonlinearity.