Hey all!
Sorry I haven't been very active on this blog, I'll certainly try to add things more frequently from now on. Truth be told, I've been very busy.
The UCL Physics Society has recently started an undergraduate physics colloquium. I volunteered to be its first speaker and I'm quite happy to say that the first talk was on the topic of quantum error correction. Thanks again for all those who came to it! I hope all subsequent talks are equally as good, if not better!
Anyhow, I've listed the topics which were covered and I've attached the notes I made for the talk. Blogger isn't allowing me to post the lecture slides I made, so if anyone wants to see those, just take a look at my Linkedin profile(I should be able to post it there). As a note to anyone who's interested in the lecture slides, theres this one slide about the CNOT gate which is a bit interesting. Basically, powerpoint wasn't letting me add a 4x4 matrix so I had to write it on the board. If anyones curious about it though, just search CNOT on google. If you're interested in how it changes the tensor product of two kets or how you would show that a bit more explicitly, try doing the operation yourself. So expand out something like |11> as a tensor product and multiply that 4x1 matrix with the CNOT matrix. Your end result should be the same thing as the tensor product of |10>
(control qubit flips the target qubit provided that the control qubit is 1)
I think I should probably acknowledge the resources I used to construct this material.
So thank you to Issac Chuang and Michael Nielson for their wonderful, "Quantum Computation and Quantum Information" It truly is an amazing book! Thank you to Umesh Vazirani for his invaluable lecture notes which really helped me gain an understanding of the way concepts in quantum mechanics can be thought of in a more intuitive way using unit circles and what things like tensor products mean. I can safely say, I'm quite evangelical about teaching Quantum Mechanics using the unit circle and quantum information approach now. Finally thank you to Daniel Gottesman for his talk on quantum error correction and fault tolerant quantum computation given at the Perimeter Institute for Theoretical Physics. It really allowed me to put things into context with regards to fault tolerant quantum computation.
As a sidenote to my blog readers, I'll seriously try to be more frequent with my blogposts. A friend has already encouraged me to try and take out time in order to post some things here.
Another friend and I have already decided to team up on things we can write about together. So do expect some juicy topics on PCMP!
- Shozab
P.S. Outline of the talk:
Sorry I haven't been very active on this blog, I'll certainly try to add things more frequently from now on. Truth be told, I've been very busy.
The UCL Physics Society has recently started an undergraduate physics colloquium. I volunteered to be its first speaker and I'm quite happy to say that the first talk was on the topic of quantum error correction. Thanks again for all those who came to it! I hope all subsequent talks are equally as good, if not better!
Anyhow, I've listed the topics which were covered and I've attached the notes I made for the talk. Blogger isn't allowing me to post the lecture slides I made, so if anyone wants to see those, just take a look at my Linkedin profile(I should be able to post it there). As a note to anyone who's interested in the lecture slides, theres this one slide about the CNOT gate which is a bit interesting. Basically, powerpoint wasn't letting me add a 4x4 matrix so I had to write it on the board. If anyones curious about it though, just search CNOT on google. If you're interested in how it changes the tensor product of two kets or how you would show that a bit more explicitly, try doing the operation yourself. So expand out something like |11> as a tensor product and multiply that 4x1 matrix with the CNOT matrix. Your end result should be the same thing as the tensor product of |10>
(control qubit flips the target qubit provided that the control qubit is 1)
I think I should probably acknowledge the resources I used to construct this material.
So thank you to Issac Chuang and Michael Nielson for their wonderful, "Quantum Computation and Quantum Information" It truly is an amazing book! Thank you to Umesh Vazirani for his invaluable lecture notes which really helped me gain an understanding of the way concepts in quantum mechanics can be thought of in a more intuitive way using unit circles and what things like tensor products mean. I can safely say, I'm quite evangelical about teaching Quantum Mechanics using the unit circle and quantum information approach now. Finally thank you to Daniel Gottesman for his talk on quantum error correction and fault tolerant quantum computation given at the Perimeter Institute for Theoretical Physics. It really allowed me to put things into context with regards to fault tolerant quantum computation.
As a sidenote to my blog readers, I'll seriously try to be more frequent with my blogposts. A friend has already encouraged me to try and take out time in order to post some things here.
Another friend and I have already decided to team up on things we can write about together. So do expect some juicy topics on PCMP!
- Shozab
P.S. Outline of the talk:
- Quantum mechanics through the lens of quantum information: explaining wave vectors using unit circles and transformation using linear algebra
- Two qubit composite systems: so using tensor products and relating it to entanglement. Brief mention of bell states and how they possess rotational invariance
- Quantum gates and how quantum circuits work. So operations with X, Z, Hadamard and CNOT gate
- Error correction philosophy
- Difference from classical error correction
- No cloning theorem and proof using a quantum circuit
- How we can bypass the measurement problem using ancilla Qubits
- How to correct for purely bit and phase flip errors and showing that the correction mechanisms are equivalent
- Nine qubit shoes code to correct for both kinds of errors
- Overview of fault tolerant Quantum computation, so how concatenated codes help us and an overview of how to arrive the threshold for the fault tolerance theorem
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