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Generalized flow and determinism in measurement-based quantum computation
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…
Rewriting Measurement-Based Quantum Computations with Generalised Flow
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.
A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
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.
Graph States and the Necessity of Euler Decomposition
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.
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
- R. Duncan, A. Kissinger, S. Perdrix, J. V. D. Wetering
- Computer Science, PhysicsQuantum
- 8 February 2019
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.
Finding Optimal Flows Efficiently
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.
Computational Depth Complexity of Measurement-Based Quantum Computation
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.
Extended Measurement Calculus
Graph States, Pivot Minor, and Universality of (X, Z)-Measurements
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.
Pivoting makes the ZX-calculus complete for real stabilizers
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.