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.
Given a projector Π = ∑dg i=1|πi⟩⟨ πi|, define|ψ⟩ as a purified maximally mixed state over a d dimensional basis (with d≥ dg), such that Π has full support on |ψ⟩
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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.