Fricke Topological Qubits

Round 1

Reviewer 1 Report

In the paper, the author used the theory of algebraic surfaces including the character variety to develop a new kind of topological quantum computing.

Fortunately, the authors are honest that they don't find any durect realization of their ideas in a new device. But alle ideas sound interesting and relevant.

At the end I have only one problem: I miss a good conclusion of the paper. What is now possible when one use these ideas? What is the main motivation to use the Fricke surface? How one can define topological qubits from the cubic surface? 

Author Response

We thank the first referee for his report.
The referee would like a conclusion. By the way, the discussion is at the same time our conclusion. 
At the moment we do not have the concept of an experiment so that we cannot discuss more. 
In the introduction,  we added a sentence (and the related references) about the status of experiments on quantum computing.

Reviewer 2 Report

  The subject of   proposing  a non-anyonic theory of a topological quantum computer   based on surfaces in a three-dimensional topological space for topological quantum computing field. Therefore, the authors should extend the part about the   implementation of quantum computation in more general way. The   implementation of quantum computation should be discussed for some real physical systems in the introduction and cited:    J. Phys. A: Math. Theor.  45 (2012) 485305; Ann. Phys. 334 (2013) 47;J.Opt. Soc.Am 30 (2013) 1178;  Quantum Inf. Process, 13 (2014) 1947;PhysicsLettersA383(2019)1247-1254;Rep. Prog. Phys. 74 (2011) 104401.

  In conclusion,  I recommend the revised version for publication in   Quantum Reports.

Author Response

We thank the second referee for his report. Following his proposal, we added a sentence (and the related references) about the status of experiments on quantum computing.

Building a quantum computer is still challenging. But progress has been performed using natural and artificial atoms \cite{Buluta2011}, superconducting technology \cite{Obada2013} 
and other physical techniques \cite{Top10,TimelineofQC}. One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. 
One possible solution is to create a topological quantum computer.

\bibitem{Buluta2011}
Natural and artificial atoms for quantum computation. Buluta, I.; Ashhab, S.; Nori, F. {\it Rep. Prog. Phys.} {\bf 2011} \emph{74} 104401. 

\bibitem{Obada2013}
A proposal for the realization of universal quantum gates via superconducting qubits inside a cavity.
Obada, A.~S.F.; Hessian, H.~A.; Mohamed, A.~B.A.; Homid, A.~H. A proposal for the realization of universal quantum gates via superconducting qubits inside a cavity.
 {\it Ann. Phys.} {\bf 2013} \emph{334} 47--57

\bibitem{Top10}
Top 10 quantum computing experiments of 2019. Avalaible online:
https://medium.com/swlh/top-quantum-computing-experiments-of-2019-1157db177611 (accessed on 1 November 2022). 

\bibitem{TimelineofQC}
Timeline of quantum computing and communication.  Avalaible online: https://en.wikipedia.org/wiki/Timeline$\_$of$\_$quantum$\_$computing$\_$and$\_$communication
(accessed on 1 November 2022).