Literature suggestions please (Topological Quantum Computers)

In summary, the conversation discusses the individual's research on topological quantum computing, specifically focusing on non-abelian anyons and the work of A. Yu. Kitaev. To fully understand this theory, they plan to develop a background in the braiding group, fault tolerance in quantum computers, and condensed matter. Although they have taken courses in relevant topics such as HEP, quantum information, and group theory, they have not specifically studied topology. They are struggling to find resources on this relatively new research and hope to find guidance. Some suggested books in the field are Z. Wang's "Topological Quantum Computation" (2010) and A. Khare's "Fractional Statistics and Quantum Theory" (2005).
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Hi, I will be starting my research in topological QC (based on non abelian anyons following the work of A. Yu. Kitaev). To begin understanding this theory, I need to develop a background in the braiding group used to describe anyons, fault tolerance in quantum computers and probably condensed matter as well (to review fractional quantum hall effect in detail).

I have taken courses in HEP, Quantum information and Group theory but not explicitly in topology.
I have tried finding resources but this is a relatively new research so getting in on this research is a bit tedious specially when I don't have a proper background, I hope someone can guide me through it.
Thank you for your time.
 
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  • #2
Some standard books in the field:
Z. Wang, Topological Quantum Computation (2010)
A. Khare, Fractional Statistics and Quantum Theory (2005)
 

1. What is a Topological Quantum Computer?

A Topological Quantum Computer (TQC) is a type of quantum computer that is based on topological qubits, or qubits that are made up of non-local properties of quantum systems. These qubits are less susceptible to errors and can potentially be used to create more stable and powerful quantum computers.

2. How does a Topological Quantum Computer differ from a traditional Quantum Computer?

Traditional quantum computers use qubits that are based on the physical properties of particles, such as the spin of an electron. These qubits are prone to errors and require complex error correction methods. TQCs use topological qubits, which are based on the topology of a system, making them more stable and less susceptible to errors.

3. What are the potential applications of Topological Quantum Computers?

TQCs have the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence. They can also be used to solve complex optimization problems and simulate quantum systems, allowing for advancements in fields such as material science and chemistry.

4. How close are we to developing a fully functional Topological Quantum Computer?

While there has been significant progress in the development of TQCs, we are still in the early stages of research and development. Many challenges still need to be overcome, such as improving the stability and scalability of topological qubits. It is difficult to predict an exact timeline, but experts estimate that it may take several more years before a fully functional TQC is realized.

5. Are there any potential drawbacks or limitations to Topological Quantum Computers?

One potential limitation of TQCs is that they require extremely low temperatures to operate, which can be costly and challenging to maintain. Additionally, the technology is still in its early stages, so there may be unforeseen challenges or limitations that arise as research and development continues. However, the potential benefits and advancements that TQCs could bring make them a promising area of study and development in the field of quantum computing.

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