What Does Basic Operations Mean in Quantum Gate Simulation?

[Amith2006]

Homework Statement

I am actually trying to reproduce the research paper on "Elementary gates for Quantum computation". With reference to that paper, According to Corollary 7.4 - On an n-bit network(where n>=7), a lambda(n-2)[sigma x] gate can be simulated by 8(n-5) lambda(2)[sigma x] gates(3 bit Toffoli gates), as well as by 48n - 204 basic operations. I am able to solve the first part of the corollary. In the 2nd part they say that out of the (8n-40) Toffoli gates, 4 gates can be simulated by 16 basic operations and the remaining (8n-36) gates can be simulated by 6 basic operations. But (4 + (8n-36)) when added does not give 8n-40. That is one part of my doubt. Another thing is that, what do they mean by basic operations? I have attached that research paper.

Homework Equations

The Attempt at a Solution

 

[KataKoniK]

Hello,

Thank you for sharing your research topic with us. It seems like you are making good progress in understanding and reproducing the results of the paper. However, I can see that you have some doubts and questions regarding the second part of Corollary 7.4 and the concept of basic operations.

Firstly, regarding the discrepancy in the number of gates mentioned in the second part of the corollary, I would suggest going through the calculations again and double-checking your results. It is possible that there may be a small error in your calculations, which is causing the difference. If you still cannot find the error, I would recommend reaching out to the authors of the paper for clarification. They would be the best source to provide an explanation for any discrepancies in their work.

Secondly, to understand the concept of basic operations, it would be helpful to refer to the definitions and terminology used in the paper. I can see that the authors have defined basic operations as single-qubit operations and two-qubit operations. These operations are used to construct more complex gates, such as the Toffoli gates, which are used in quantum computation. Therefore, by simulating a Toffoli gate using a combination of basic operations, we can reduce the number of actual Toffoli gates needed in a network.

I hope this helps clarify your doubts and guides you in your research. Keep up the good work, and don't hesitate to reach out to the authors for any clarifications. Best of luck with your project!



Quantum Scientist

 

[Mene]

I would first carefully read the research paper and try to understand the concepts and equations presented. I would then try to replicate the results and calculations to ensure that the corollary is accurate. If I encounter any discrepancies, I would reach out to the authors for clarification or further explanation.

In terms of the definition of "basic operations," I would assume that it refers to the fundamental operations needed to simulate the gates, such as single qubit rotations and controlled NOT gates. However, I would also confirm this with the authors to ensure that I have the correct understanding.

Furthermore, I would suggest exploring alternative methods or approaches to simulate the gates and see if the results match with the ones presented in the paper. This could help to further validate the findings and potentially offer new insights or improvements.

Overall, as a scientist, it is important to carefully analyze and verify research findings to ensure their accuracy and contribute to the advancement of knowledge in the field of quantum computation.