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.
Fermionic Independent Set and Laplacian of an independence complex are QMA-hard
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The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.
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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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The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.