Recent content by Ricardo Belchior

Ok but how I⊗Z look like? It should be a 4x4 matrix right?

Thank you for your help. I think I figure it out ... I was looking wrong to the picture that you gave me earlier. Ok now, how can we describe this single qubit operation with algebra since the qubits are entangled? I.e how do I apply Z to: [1 0 0 1]' Given that Z is one qubit gate and that...

Thanks again for your patience. So the amplitude re-arrange that toffoli gate does is this right? : If I change the phase of amplitude of |1> and apply again the toffoli gate I have: Then, in the end, we have -|0>. Then I don't understand how do we get back to the input. Cheers

Thanks. I will read the post for sure. That's the point. The toffoli negates the qubit but the phase goes with it. Just like in X case: [0 1; 1 0]' * [a b]' = [b a]' , with a and b as complex numbers. the numbers exchange with each other, and the phases too. and if you get: |psi> = |0> +...

Thanks for your reply. But I have a question: How to "save" that, in this case, |11111> have some phase shift? Lets see: Am I thinking right? In the end, if you apply hadamard gate you'll get |psi> = -|0> - |1> - |2> - ... - |2^5> and not |psi> = |0> + |1> + |2> + ... - |2^5> What am I...

Hi! So I'm studying Gover's Algorithm and I have this doubt: Does 'Phase inversion gate' grows exponentially? I mean, if I want to signal the one combination that is the answer, I must be able to represent all 2^N states, where N is the number of qubits in the system. How do I do this without...

Ok I get it. But i still have some hard times to understand the phase-estimation. I think the bottom question is : How do I implement the controlled-U to implement ax mod N?

Hello again, So I have another question. In Shor algorithm it is applied the deffered measurment principle, right? I mean, if i did the measurment at the beginning, the results would be the same? cheers

Thanks for the great answer. Exactly, that state cannot be computed. But if I throw away the second register, the first one will have the same probabilities for all values, just like the output of hadamard gates, right? What do you mean by that? I think my biggest struggle is to...

Hello! So I'm working to try to understand shor algorithm and I have some doubts. So, after the hadamard gates we apply the unitary gate that construct the function yk mod N. Next we do a measurement in the second register to get some function value. So, when I do this measurement on the...

Ok Thanks, I think I got it.

Thanks a lot! That schemes where very helpful. But I still don't get that superposition thing. If I don't know the control qubit value, how do I do it? I suppose you assume some value? I think that I do not get that superposition part.

Hello everyone! So I was looking at Shor Algorithm for prime factorization and I have some doubts in the arithmetic part. Let's define a function f that : f(x) = ax mod N. The middle step in shor algorithm is to calculate, simultaneously, all values of f. In some papers and books, I saw some...