Pauli-measurement removal preserving XY measurements and causal flow

Determine whether a subset of Pauli measurements in a measurement-based quantum-computation pattern can be removed while preserving the XY-plane measurements and the causal-flow property.

Background

Graphix implements Pauli pushing and graph-complementation-based transformations to remove Pauli-measured vertices from measurement-based quantum-computation patterns. The removal procedure preserves the semantics of the reference branch and preserves generalized flows and Pauli flows when they are present, but some measurements can leave the XY plane. Because causal flow is needed for the library’s optimal space-reduction procedure, the paper identifies as unresolved whether Pauli measurements can be selectively removed while retaining both the original XY-plane measurement structure and causal flow. The authors note that, in general, all Pauli measurements on non-input nodes are removed when the initial pattern has some form of flow, but this does not settle the more restrictive preservation problem.