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• Users: Jufa
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1. ### Recommendation for a platform for drawing computational circuits

Thank you very much!
2. ### Recommendation for a platform for drawing computational circuits

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.
3. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

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.
4. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

Just an orthogonal vector.
5. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

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(...
6. ### A Tensor product matrices order relation

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...
7. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

Oh yes. You are definitely right, I am sorry for my confusion. I will work on your idea then. Thank you very much.
8. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

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.
9. ### A Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

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...
10. ### Preparing for a Quantum Computation Course: Superconducting Qubits

Yes. I will do so as well, but I am trying to find more literature.
11. ### Preparing for a Quantum Computation Course: Superconducting Qubits

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...
12. ### The integral does not converge....

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}##...
13. ### Linear momentum of the Klein Gordon field

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.
14. ### Linear momentum of the Klein Gordon field

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...
15. ### A Concept of wavefunction and particle within Quantum Field Theory

Many thanks for your answer, it helped me a lot! Also I checked your paper and found it really interesting.
16. ### A Concept of wavefunction and particle within Quantum Field Theory

-1st: Could someone give me some insight on what a ket-state refers to when dealing with a field? To my understand it tells us the probability amplitude of having each excitation at any spacetime point, but I don't know if this is accurate. Also, we solve the free field equation not for this...
17. ### A Why we can perform normal ordering?

Many thanks for your explanation!
18. ### A Why we can perform normal ordering?

Get it, thanks!
19. ### A Why we can perform normal ordering?

As explained in the summary, it seems that the commutators of some operators (creation and anihilation) can be ignored when quantising the hamiltonian of the Klein Gordon Field. I wonder why we are allowed to do such a thing. Is that possible because we are solely within a semiquantum...
20. ### I Bipartite quantum negativity

Let as consider a system ##H = A\otimes B## I've been said that quantum negativity, i.e. taking the partial transpose w.r.t A or B and summing the magnitude of the negative eigenvalues obtained, is a measure of how entangled are the parties A and B. First question: Why is it that we do not...

Many thanks!
22. ### I Restricted Boltzmann machine uniqueness

If some moderator can explain why my text is strikethrough I would appreciate it.
23. ### I Restricted Boltzmann machine uniqueness

I am dealing with restricted Boltzmann machines to model distributuins in my final degree project and some question has come to my mind. A restricted Boltzmann machine with v visible binary neurons and h hidden neurons models a distribution in the following manner: ## f_i= e^{ \sum_k b[k]...
24. ### I Quantum negativity

May be it is a good idea to give a little bit of context of the problem I am facing. In few words, I am trying to reconstruct a GHZ state of 4-qbits by means of different tomography methods and, apart from computing the fidelities of the obtained estimators, I am really interested in seeing how...
25. ### I Quantum negativity

When I computes the negativity (with the partial transpose) of the density matrix corresponding to the GHZ I obtain zero, no matter what is the partition I choose. I've read somewhere that this is because GHZ's distillable entanglement is zero, which I don't really understand because I haven't...
26. ### I Commutation between covariant derivative and metric

Is there a way of closing the thread?

Not at all.
28. ### I Commutation between covariant derivative and metric

Well, by fixing "n" I mean that you first perform the summation and then derive, what means that you get a 1-covariant tensor for each term of the sum. In each term of the sum n is definitely fixed. That's what I mean.
29. ### I Commutation between covariant derivative and metric

It must be the partial derivative of ##A^n## if you understand ##\nabla_i g_{kn}## with ##n## fixed (a 1-covariant tensor). They are equivalent ways of seeing it. Just as the covariant derivative of a contraction can be seen just as the partial derivative of it or as the contraction of the...
30. ### I Geodesics parametrization

Great answer. Many thanks.

32. ### I Is the surface of a sphere locally flat?

I know it. I did not mean that the fact that I cannot imagine it means that it does not exist. I was just expressing my ignorance of such a coordinates system. Thanks.
33. ### I Geodesics parametrization

Let us consider a sphere of a unit radius . Therefore, by choosing the canonical spherical coordinates ##\theta## and ##\phi## we have, for the differential length element: $$dl = \sqrt{\dot{\theta}^2+sin^2(\theta)\dot{\phi}^2}$$ In order to find the geodesic we need to extremize the...
34. ### I Commutation between covariant derivative and metric

I already realized what happens. Following my reasoning in the first equation displayed I should have written the partial derivative of A, not the covariant one. This rescues it all. Indeed, it seems to me that it is a general rule that covariant derivative of a contraction, i.e. the covariant...

38. ### I Is the surface of a sphere locally flat?

Sure, I only mention the first set of coordinates in order to define the metric tensor.
39. ### I Is the surface of a sphere locally flat?

That definitely solves it. Many thanks!
40. ### I Is the surface of a sphere locally flat?

I can't imagine a set of coordinates that fulfills the non-zero first order correction condition. Indeed, once you impose that the metric is euclidean at p, the new coordinates become fixed and, thus, my choice was the only one possible to be made.
41. ### I Is the surface of a sphere locally flat?

Given a certain manifold in ##R^3## I've been told that at every location ##p## it is possible to encounter a reference frame from which the metric is the euclidean at zero order from that point and its first correction is of second order. This, nevertheless does not match with the following...
42. ### I Parallel transport general relativity

Oh. So Peter I think the result here is correct. I just needed to remember that ##\theta_0 =\pi/2##. Many thanks!
43. ### I Parallel transport general relativity

I don't think it is a needed that the vectors are unitary. Indeed the only effect of choosing a non Unit vector in the basis is a change in the metric.
44. ### I Parallel transport general relativity

It is just a way of giving a physical sense to these basis vectors. The three components are never used during during the derivacions. Actually we have ##e_\theta=(1, 0) ## and ##e_\phi =(0, 1) ## and the problem you point out is solved but the inconsestency remains.
45. ### I Parallel transport general relativity

As Romsofia suggested I tried to picture a simple example to see what's going on and I encounter something that I don't understand. Put this example: The surface of a sphere considereing the basis vectors as ## \vec{e_\theta} = \big(cos(\theta)cos(\phi), cos(\theta)sin(\phi)...
46. ### I Covariant derivative notation

Many thanks, I think I understand it now.

50. ### I Parallel transport general relativity

I don't understand this line. Is there something missing?