TuringTest
  • TuringTest
How can you multiply a ket by a bra in that order? (no this is not a stupid joke)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
TuringTest
  • TuringTest
I have an expression for a way to write a matrix in the for\[A=\sum_{i,j=1}^ma_{ij}|e_i \rangle\langle e_j|\]and I don't understand how to multiply the ket by the bra. @Luis_Rivera no, it comes from a quantum physics thing
TuringTest
  • TuringTest
according to my understanding, a ket can be thought of as a vertical vector, and a bra a horizontal one. Matrix multiplication is not commutative, and #rows /=#colums for each, so... how does that work?
TuringTest
  • TuringTest
somehow\[|e_i\rangle\langle e_j|\otimes|f_k\rangle\langle f_l|=(|e_i\rangle\otimes|f_k\rangle)(|e_j\rangle\otimes|f_l\rangle)\]where \(\otimes\) is the tensor product. I don't know if anyone here can help me with that.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

TuringTest
  • TuringTest
@Jemurray3 tensors?
TuringTest
  • TuringTest
reading this: https://www.edx.org/c4x/BerkeleyX/CS191x/asset/chap3.pdf
anonymous
  • anonymous
What are you trying to do? In \[ A = \sum a_{ij} \mid e_i \rangle \langle e_j \mid \] the e_i and e_j vectors are the basis vectors.
TuringTest
  • TuringTest
I'm trying to understand what \(|e_i\rangle\langle e_j|\) are doing next to each other I understand that \(\langle e_j|\) is the Hermitian conjugate of \(|e_j\rangle\), and so the inner product is \(\langle e_i|e_j\rangle\) which makes sense because e_i is a row vector and e_j is a column vector, but the other way around it would be a column vector times a row vector, which is undefined, right? Or am I just hopelessly confused?
anonymous
  • anonymous
No, a column vector times a row vector is a matrix.
anonymous
  • anonymous
for instance, \[\left(\begin{matrix}1 \\ 0\end{matrix}\right) (1 \space 0) = \left(\begin{matrix}1 &0\\ 0 & 0\end{matrix}\right)\]
TuringTest
  • TuringTest
oh crap, that is embarrassing... I was thinking too hard
TuringTest
  • TuringTest
right, of course, I need to review my linear algebra for this stuff I suppose
anonymous
  • anonymous
TuringTest
  • TuringTest
while we're on the subject, can you help me visualize the implementation of a quantum gate on a system, like a photon or hydrogen atom? I'm having trouble understanding what a unitary transformation actually does, is it just a change in basis of sorts?
TuringTest
  • TuringTest
I understand it mathematically, but what is the physical implication?
TuringTest
  • TuringTest
like a NOT gate, if a photon is in the |1> state, what does it mean, or how does it pass through this gate? and this gate will then return the photon in a |0> state? could you clarify? I don't know about you, but I find QM a bit counter-intuitive ;P
TuringTest
  • TuringTest
I know this should be in physics now, but I've got you here, so...
anonymous
  • anonymous
It is indeed. I'm not tremendously familiar with quantum computation but generally speaking the easiest thing for me to visualize is a spin-1/2 system. An electron may be either spin up or down which you can denote |0> and |1> respectively. A "not" transformation just flips the spin, i.e. takes |0> to |1> and |1> to |0>.
TuringTest
  • TuringTest
right, but *how* do we flip it? quantum gates seem to be no more than mathematical constructs. Is it similar to the measuring affect where we are collapsing the wave function? I figure not, since it always flips the outcome, as opposed to just changing the probability of measuring that state.
anonymous
  • anonymous
To the best of my understanding the primary mechanism for flipping spins and such is magnetic fields.
TuringTest
  • TuringTest
So as far as you know quantum gates are implemented physically, and are not just like a change of basis which we arbitrarily construct mathematically??
TuringTest
  • TuringTest
I don't suppose you'd be able to give an example of how we might implement the Hadamard gate then?
anonymous
  • anonymous
http://library.thinkquest.org/07aug/01632/qubitcontrol.html This may or may not be of help.
anonymous
  • anonymous
^ I realize that "may or may not" is a meaningless phrase. *This may be of help.*

Looking for something else?

Not the answer you are looking for? Search for more explanations.