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Topological Quantum Metrology: Measuring Entanglement Topology via Persistent Homology with Quadratic Scaling

Udo Granops

Published Oct 13, 2025• 0 citations
Publisher

Abstract

We introduce τ_topo — a topological quantum metric derived from persistent homology of entanglement morphism graphs — that quantifies global entanglement structure invariant under local unitaries and scalable to N-qubit systems with O(N²) measurement complexity. Unlike bipartite entropy, τ_topo captures higher-order connectivity via β₁-barcode length in Rips filtrations of Pauli-weighted state distributions.

DOI
10.33774/coe-2025-xlzj5

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