Streamlined quantum algorithm for persistent Betti numbers with exponential qubit reduction, polynomial speedups, and a competitive quantum-inspired classical algorithm showing no evidence for exponential quantum advantage.
The membership oracle acts as Oi mk|sk⟩| a⟩ =|sk⟩| a⊕ m(sk)⟩ (C1) where we have defined the membership function m(sk) = { 1 if sk∈ Si k 0 if sk /∈ Si k
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A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits
Streamlined quantum algorithm for persistent Betti numbers with exponential qubit reduction, polynomial speedups, and a competitive quantum-inspired classical algorithm showing no evidence for exponential quantum advantage.