Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
Towards a universal gateset for qma1
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The succinct state 2-local Hamiltonian problem for qubit Hamiltonians is promise-MA-complete.
citing papers explorer
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New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes
Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
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On the Complexity of the Succinct State Local Hamiltonian Problem
The succinct state 2-local Hamiltonian problem for qubit Hamiltonians is promise-MA-complete.