We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a… Expand

This work presents a method for verifying measurement-based quantum computations, by producing a quantum circuit equivalent to a given deterministic measurement pattern via a rewriting strategy based on the generalised flow of the pattern.Expand

The ZX-Calculus is made complete for the so-called Clifford+T quantum mechanics by adding two new axioms to the language, and it is proved that the π/4-fragment of the ZX -Calculus represents exactly all the matrices over some finite dimensional extension of the ring of dyadic rationals.Expand

A new equation is introduced, for the Euler decomposition of the Hadamard gate, and it is demonstrated that Van den Nest's theorem--locally equivalent graphs represent the same entanglement--is equivalent to this new axiom.Expand

A simplification strategy for ZX-diagrams is given based on the two graph transformations of local complementation and pivoting and it is shown that the resulting reduced diagram can be transformed back into a quantum circuit.Expand

A polynomial time algorithm is introduced that outputs an optimal gflow of a given graph and thus finds an optimal correction strategy to the nondeterministic evolution due to measurements.Expand

This paper proves that the "depth of computations" in the one-way model is equivalent, up to a classical side-processing of logarithmic depth, to the quantum circuit model augmented with unbounded fanout gates, a very powerful model of quantum computation.Expand

First, it is shown that any graph is a pivot-minor of a planar graph, and even a pivot minor of a triangular grid, and then it is proved that the application of measurements in the (X,Z) plane is a universal measurementbased model of quantum computation.Expand

An angle-free version of the ZX-calculus is derived and it is shown that it is complete for real stabilizer quantum mechanics and does not imply local complementation of graph states.Expand