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.
Refined quantum algorithms for principal component analysis and solving linear system.arXiv preprint arXiv:2504.00833
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Hybrid quantum-classical method for Betti number estimation that combines classical simplex enumeration with quantum processing and claims polynomial-to-exponential speedups over existing quantum algorithms at the cost of extra ancilla qubits.
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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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Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis
Hybrid quantum-classical method for Betti number estimation that combines classical simplex enumeration with quantum processing and claims polynomial-to-exponential speedups over existing quantum algorithms at the cost of extra ancilla qubits.