Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning
- B. Coecke, A. Kissinger
- Physics
- 27 April 2017
This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations.
ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
- Miriam Backens, A. Kissinger
- Computer ScienceElectronic Proceedings in Theoretical Computer…
- 6 May 2018
A new graphical calculus is presented that is sound and complete for universal quantum computation by demonstrating the reduction of any diagram to an easily describable normal form, which suggests that this calculus will be significantly more convenient for reasoning about the interplay between classical non-linear behaviour and purely quantum operations.
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
- R. Duncan, A. Kissinger, S. Perdrix, J. V. D. Wetering
- Computer ScienceQuantum
- 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.
Reducing the number of non-Clifford gates in quantum circuits
- A. Kissinger, J. J. Van De Wetering
- Computer SciencePhysical Review A
- 11 August 2020
We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations.…
PyZX: Large Scale Automated Diagrammatic Reasoning
- A. Kissinger, J. V. D. Wetering
- Computer ScienceElectronic Proceedings in Theoretical Computer…
- 9 April 2019
This paper introduces PyZX, an open source library for automated reasoning with large ZX-diagrams, and shows how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software.
CNOT circuit extraction for topologically-constrained quantum memories
- A. Kissinger, A. V. D. Griend
- Computer ScienceQuantum information & computation
- 1 April 2019
A new technique for quantum circuit mapping, based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees, is given, which significantly out-performs general-purpose routines on CNOT circuits.
The Compositional Structure of Multipartite Quantum Entanglement
- B. Coecke, A. Kissinger
- MathematicsInternational Colloquium on Automata, Languages…
- 12 February 2010
It is shown that multipartite quantum entanglement admits a compositional structure, and hence is subject to modern computer science methods, and induces a generalised graph state paradigm for measurement-based quantum computing.
Quantomatic: A proof assistant for diagrammatic reasoning
- A. Kissinger, Vladimir Zamdzhiev
- Computer ScienceCADE
- 3 March 2015
This work briefly outlines the theoretical basis of Quantomatic's rewriting engine, then gives an overview of the core features and architecture and gives a simple example project that computes normal forms for commutative bialgebras.
Strong Complementarity and Non-locality in Categorical Quantum Mechanics
- B. Coecke, R. Duncan, A. Kissinger, Quanlong Wang
- Physics27th Annual IEEE Symposium on Logic in Computer…
- 22 March 2012
The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights, and the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect.
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