There's a small mistake in 16:10 where Peter defines a unitary matrix as a matrix whose "conjugate transpose is the same as the original matrix". This definition is in fact the definition of an hermitian matrix. A unitary matrix is a matrix that when multiplied with its conjugate transpose gives the identity matrix. Formally, a matrix U is unitary iff UU†=U†U=I.
At 22:08, I wished he explained more of what was meant by "since the measurement gives the same answer for both elements of the superposition, the superposition is not destroyed." Like, at 20:16, how do you measure "which bit is different?" in practice?
Unclear to me the first part of his remark, as the amplitudes alpha and beta switch state. Regarding the second comment, you need to have syndrome measurement operators that measurement which bit is different and correct the state appropriately en.wikipedia.org/wiki/Quantum_error_correction qiskit.org/documentation/stable/0.28/tutorials/noise/6_repetition_code.html
Can someone tell me if there is anything wrong with slide 26? Around 27:14, where the logical |0> and |1> are encoded using only 4 basis each? I thought they were 8 basis for each of the logical state?
Many thanks for posting this talk. It is great to see one of the founders of quantum error correction explain some of the concepts.
Thank you so much, I couldn't believe what I just found on youtube!
There's a small mistake in 16:10 where Peter defines a unitary matrix as a matrix whose "conjugate transpose is the same as the original matrix". This definition is in fact the definition of an hermitian matrix. A unitary matrix is a matrix that when multiplied with its conjugate transpose gives the identity matrix.
Formally, a matrix U is unitary iff UU†=U†U=I.
At 22:08, I wished he explained more of what was meant by "since the measurement gives the same answer for both elements of the superposition, the superposition is not destroyed."
Like, at 20:16, how do you measure "which bit is different?" in practice?
Unclear to me the first part of his remark, as the amplitudes alpha and beta switch state.
Regarding the second comment, you need to have syndrome measurement operators that measurement which bit is different and correct the state appropriately
en.wikipedia.org/wiki/Quantum_error_correction
qiskit.org/documentation/stable/0.28/tutorials/noise/6_repetition_code.html
Can someone tell me if there is anything wrong with slide 26? Around 27:14, where the logical |0> and |1> are encoded using only 4 basis each? I thought they were 8 basis for each of the logical state?
At 25:06 it is not obvious what he applied H to, to get the new code. He had time and space to do so.
Awesome guest but this is some of the worst hosting I've seen