Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
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.
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.
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.
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…
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.
Finding Optimal Flows Efficiently
- M. Mhalla, S. Perdrix
- Computer ScienceInternational Colloquium on Automata, Languages…
- 17 September 2007
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.
Extended Measurement Calculus
Computational Depth Complexity of Measurement-Based Quantum Computation
- D. Browne, E. Kashefi, S. Perdrix
- Computer ScienceTheory of Quantum Computation, Communication, and…
- 25 September 2009
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.
Classically controlled quantum computation
This work introduces a Classically controlled Quantum Turing Machine (CQTM), which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for formalised classical control, and proves that any classical Turing machine can be simulated by a CQTM without loss of efficiency.
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.