Recent content by Jufa

Thank you very much!

Homework Statement:: I need to draw circuits involving quantum gates and quantum states I would like a platform that allowed me to draw quantum computation circuits. That is, that it provides me with the schemes and allows me to write in latex. Many thanks in advance.

Yes. Namely between ##\ket{\psi}## and ##\ket{\psi^\perp}##. These are the two vectors involved. I reckon I am stating the problem in a clear way.

Just an orthogonal vector.

I maybe should have mentioned that both ket vectors belong to ##\mathcal{C}^2## and thus the perpendicular vectors are well defined up to a global phase. My attempt is the following: In the basis ## \ket{\psi}, \ket{\varphi}## the matrix looks like a diagonal one, namely: ##M = Diag\Big(...

We mainly have to prove that this quantity## \bra{\varphi} A^{\otimes n } \ket{\varphi} \pm \bra{\varphi} B^{\otimes n } \ket{\varphi} ## is greater or equal than zero for all ##\ket{\varphi}##. Being ##\ket{\varphi}## a product state it is straightforward to demonstrate such inequality. I am...

Oh yes. You are definitely right, I am sorry for my confusion. I will work on your idea then. Thank you very much.

I guess when you say ##\ket{\phi}## you mean ##\ket{\varphi}##. I don't think it makes sense to compute the entries of the matrix in a non-orthonormal basis. I don't think the associated characteristic equation has nothing to do with the one you get when an orthonormal basis is considered.

We have a matrix ##M = \ket{\psi^{\perp}}\bra{\psi^{\perp}} + \ket{\varphi^{\perp}}\bra{\varphi^{\perp}}## The claim is that the eigenvalues of such a matrix are ##\lambda_{\pm}= 1\pm |\bra{\psi}\ket{\varphi}|## Can someone proof this claim? I have been told it is self-evident but I've been...

Yes. I will do so as well, but I am trying to find more literature.

Summary:: Looking for articles/books to prepare myself for the course: Quantum computation with superconducting qubits Hello everyone. I am about to take a course in Quantum computation with superconducting qubits and I am searching for material to prepare it. I took a first course on that...

I am asked to compute ##[\phi(x), \phi^\dagger(y)]## , with ##\phi = \int \frac{dp^3}{(2\pi)^3}e^{-ipx}\hat{a}(\vec{p})## and with z=x-y a spacelike vector. And show that this commutator does not vanish, which means that for this non-relativsitic field i.e. with ##p^0 = \frac{\vec{p}^2}{2m}##...

Yes. it is definitely not right. There's a two at the denominator missing and also the momentum p should multiply the whole expression. Thank you very much for your answer, what you told me about the expression being odd rescues everything.

The correct answer is: #P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)# But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}## I hereunder display the procedure I followed: First: ##\phi = \int...

Many thanks for your answer, it helped me a lot! Also I checked your paper and found it really interesting.