# Quantum computing references

Quantum

Some articles and pointers if you wish to dig deeper into quantum topology and quantum computing.

Keywords

Quantum Computing, Quantum Field Theory

- I. Introduction
- II. Elements of quantum mechanics
- III. The electromagnetic field
- IV. The qubit
- V. Quantum gates
- VI. States and operators
- VII. Shor’s algorithm
- VIII. Quantum teleportation
- IX. The Deutsch algorithm
- X. The no-cloning theorem
- XI. About anyons
- XII. About SU(2)
- XIII. Teleportation topology
- XIV. The Simon algorithm
- XV. Superdense coding
- XVI. Chern-Simons theory
- XVII. The toric code
**REF. Some pointers**

## Software

- Liquid superseded by Q# based on C# while Liquid is a F# framework. There is strong focus on quantum chemistry and it shows in the examples and documentation.
- QuTip (Python) is probably the most complete module. It has lots of examples to simulate standard quantum mechanics.
- A long list of QC simulators including all sorts of esoteric languages.
- SymPy quantum is a namespace in Python’s symbolic math and has plenty of goodies. Including implementations of Shor’s algorithm and more.
- QISKIT is a promising new addition on the scene with the support of IBM research.

## Books

- Condensed matter field theory by A.Atlan and B.Simons is a wonderful book on condensed and solid state physics.
- Knots and physics by L.Kauffman is full of fun and deep ideas. Highly recommended.
- Quantum computing, a gentle introduction by E.Rieffel and W.Polak is sometimes not so gentle at all but a great book nonetheless.
- An introduction to quantum computing by P.Kaye et al. is more robust than the gentle intro above and contains all the standard topics of (non topological) quantum computing.
- Mathematics of quantum computation by Brylinski and Chen demands solid shoes to climb the math mountains. Not for beginners.
- Problems and solutions in quantum computing by W.Steeb and Y.Hardy is so much fun. If you need to boost your confidence (in QM computations), this is the book you need.
- Topological Aspects of Quantum Entanglement by L.Kauffman is (like all of his articles) plenty of delights and far-reaching ideas. The man can convey deep stuff and keep it fun.
- Topology and condensed matter physics by S.Mohan et al. is full of really well-written articles on how topology is used to approach condensed matter. Anyons in particular.
- Quantum field theory and the Jones polynomial by E.Witten is the origin of QFT and knots. Poetry of the (math) gods.

## Articles

- From Path Integrals to Fractional Quantum Statistics by J.Horowitz explains the origins of anyons via particles paths (i.e. path integrals).
- An anyon primer by S.Rao is an intro to anyon physics for undergraduates (which means it’s supposedly easy to follow).
- Anyons and the quantum Hall effect — A pedagogical review by A.Stern is another slow-motion article on anyons for educational purposes.
- Applications of Chern-Simons theory in knot theory by L.Tsui is concise and a lovely little thing to enjoy.
- Aspects of Chern-Simons Theory by G.Dunne could the reference on standard Chern-Simons theory.
- Basic concepts in quantum computation by AEkert et al. is just what the title says.
- Computing with quantum knots by G.Collins is an article from Scientific American and gives a layman’s overview of what TQFT is all about.
- A short introduction to Fibonacci anyons by S.Trebst et al. discussed well the fusion channels and anyonic interactions.
- Non-Abelian Anyons and Topological Quantum Computation by C.Nayak et al. is a solid overview of what is happening at Station Q at Microsoft. Well, probably a lot more than that.
- Quantum computing…with a twist by S.Simon is much like the Scientific American article above an excellent and easy to understand overview of what TQFT is about.
- Quantum random access memory by Giovanetti et al. highlights the difficulties of transposing classical concepts like RAM to the quantum realm.

## Github and more

- QuTiP lectures
- Quantum Computation and Cryptography contains plenty of slides from a Romanian workshop and is perfect to get into the subject.
- Lecture notes on quantum computing by J.Watrous collects PDF’s of a university course on quantum computing.
- jsQubit is an open source JavaScript implentation of qubits.