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Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings
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Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings
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We introduce a $0.611$-approximation algorithm for Quantum MaxCut and a $\frac{1+\sqrt{5}}{4} \approx 0.809$-approximation algorithm for the EPR Hamiltonian of [arXiv:2209.02589]. A novel ingredient in both of these algorithms is to partially entangle pairs of qubits associated to edges in a matching, while preserving the direction of their single-qubit Bloch vectors. This allows us to interpolate between product states and matching-based states with a tunable parameter.
Forward citations
Cited by 3 Pith papers
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Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra
Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
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Sharp Bounds on Ground State Energy of the SYK Model
For super-constant k = o(√n), the expected operator norm of the k-SYK Hamiltonian equals (1−o(1))√(2n)/k, via a twisted-boson operator whose moments match SYK trace moments exactly.
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Quantum Cut Sparsifiers
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
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