Quantum Entanglement Analysis Based on Abstract Interpretation

Paper information (2008, SAS, LNCS 5079, pp. 270–282) — Simon Perdrix. DOI; arXiv:0801.4230

Work

The paper brings abstract interpretation to quantum-program analysis, using a computable abstract domain to approximate how entanglement propagates during execution. The goal is not to reconstruct a full state vector, but to soundly mark potential entanglement relationships and provide scalable static information about a quantum program.

Contributions

An abstract-interpretation method for analyzing entanglement propagation.
A sound approximation from concrete quantum semantics to an abstract analysis.
A demonstration that static analysis can conservatively detect potential entanglement without enumerating the full state.
A connection between entanglement properties and program-analysis and verification toolchains.

Limits

Sound abstract interpretation trades precision for a conservative approximation; the analysis may report potential entanglement without distinguishing all concrete cases. The abstract domain and program model limit which operations can be handled. The method does not automatically provide exact amplitudes, hardware-noise certification of entanglement, or a complete algorithm-correctness proof.

Connections

The paper makes the static-reasoning direction in Verification Methods and Tools concrete for entanglement, and can be compared with the density-operator semantics in Quantum States and Operations. Compared with Quantum Weakest Preconditions and Floyd–Hoare Logic for Quantum Programs, it emphasizes an automated conservative dataflow approximation rather than backward postcondition rules.

Original paper

Simon Perdrix, Quantum Entanglement Analysis Based on Abstract Interpretation, in SAS 2008, LNCS 5079, 270–282, DOI: 10.1007/978-3-540-69166-2_18. arXiv:0801.4230