Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
Analyzing graph structure via linear measurements , booktitle =
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
A new algorithm finds a matroid basis in tilde O(n to the 3/7) adaptive rounds via independence oracle.
Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.
citing papers explorer
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A Near-Optimal Parallel Algorithm for Finding Matroid Bases
Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
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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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An $\widetilde{O} (n^{3/7})$ Round Parallel Algorithm for Matroid Bases
A new algorithm finds a matroid basis in tilde O(n to the 3/7) adaptive rounds via independence oracle.
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Many Hamiltonians Are Sparsifiable
Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.