# Verifying the Smallest Interesting Colour Code with Quantomatic

@inproceedings{Garvie2017VerifyingTS, title={Verifying the Smallest Interesting Colour Code with Quantomatic}, author={Liam Garvie and Ross Duncan}, booktitle={QPL}, year={2017} }

In this paper we present a Quantomatic case study, verifying the basic properties of the Smallest Interesting Colour Code error detecting code.

## 21 Citations

### Optimising Clifford Circuits with Quantomatic

- Computer ScienceQPL
- 2018

It is proved that the system always reduces Clifford circuits of one or two qubits to their minimal form, and numerical results demonstrating its performance on larger Clifford circuits are given.

### Graphical Structures for Design and Verification of Quantum Error Correction

- Computer Science
- 2016

A high-level graphical framework for the design, analysis, and verification of quantum error correcting codes, and a framework in which large classes of such codes can be both analytically and numerically discovered is introduced.

### Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions

- Computer ScienceMFCS
- 2022

A family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions are introduced, and it is proved that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations.

### A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics

- MathematicsLICS
- 2018

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.

### Towards Large-scale Functional Verification of Universal Quantum Circuits

- Computer Science, PhysicsQPL
- 2018

A framework for the formal specification and verification of quantum circuits based on the Feynman path integral is introduced, and the algorithm is shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits.

### A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness

- Mathematics2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

It is shown that the axiomatisation for the ZX-calculus is also complete for any fragment of dyadic angles, and that a simple new rule (called cancellation) is necessary and sufficient otherwise.

### Formal Methods in Quantum Circuit Design

- Computer Science
- 2019

The development of a formal model of quantum circuits with ancillary bits based on the Feynman path integral, along with a concrete verification algorithm, which doubles as a natural specification language for quantum computations.

### Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics

- PhysicsLICS
- 2018

It is shown that the axiomatisation for Clifford+T is not complete in general but can be completed by adding a single (non linear) axiom, providing a simpler axiom atisation of the ZX-calculus for pure quantum mechanics than the one recently introduced by Ng&Wang.

### Fe b 20 18 Diagrammatic Reasoning beyond Clifford + T Quantum Mechanics

- Physics
- 2018

The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. An axiomatisation has recently been proven to be complete for an…

### The ZX-Calculus is a powerful graphical language for quantum reasoning and quantum computing introduced

- Computer Science
- 2019

This work improves on the known-to-be-complete presentation for the so-called Clifford fragment of the ZX-Calculus and provides a complete axiomatisation for an altered version of the language which involves an additional generator, making the presentation simpler.

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