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.
We have the following costs: • Vψm : ( 1, 2, ϵψ + 4 √ ( N k+1) |Si k| log ( 1 ϵψ )√√ϵs +√ϵm ) projected unitary encoding, using √ ( N k+1) |Si k| log ( 1 ϵψ ) × [UUni + Omi 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.