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Quantum computation and computational issues related to quantum mechanics

24 votes

Von Neumann architectures and quantum computing

What do you mean by von Neumann architecture? I'll use the Wikipedia definition, and say that it's a computer which keeps its program and its data in the same random-access memory. This works well a …
Peter Shor 's user avatar
19 votes

Rigorous security proof for Wiesner's quantum money?

The question of cloning the BB84 states was covered in the paper "Phase covariant quantum cloning" by Dagmar Bruß, Mirko Cinchetti, G. Mauro D'Ariano, and Chiara Macchiavello [Phys Rev. A, 62, 012302 …
Peter Shor 's user avatar
47 votes
Accepted

Shor's factoring algorithm help

From this we can find the convergents of the fraction $j/2^q$ , the convergents are possible values of the order $r.$ Here do we just try all the convergents $<N$ and if we don't find $r$ …
Peter Shor 's user avatar
11 votes

Universal sets of gates for SU(3)?

It's not clear to me whether you're asking about SU(3) or SU(3$^{n}$) acting on a tensor product of qudits. I'll assume you're asking about SU(3). It's not clear to me (despite what I said in a previo …
Peter Shor 's user avatar
7 votes
Accepted

Are all computational models of quantum computing equivalent?

Now you've clarified your question, I can answer it. Assuming that the seminar was talking about universal quantum computational models (and there are universal computational models for all of these p …
Peter Shor 's user avatar
5 votes
Accepted

Quantum capacity for ensemble of Pauli channels

For your question (1), the answer is yes. The 'hashing construction' for quantum encoding is independent of the quantum channel you use, so if you use this construction for encoding, you can send info …
Peter Shor 's user avatar
7 votes
Accepted

Efficient generation of permutational invariant quantum states

Yes, they can. Recall that any reversible classical function can be computed in superposition. Now, generate the state $$ \frac{1}{\sqrt{n!}}\left(\sum_{i=1}^n |i \rangle \right) \left( \sum_{i=1}^{n …
Peter Shor 's user avatar
2 votes
Accepted

How are new probabilities computed when simulating measurement on a set of qubits?

Let $$P(0) = |a|^2 + |c|^2 + |e|^3 + |g|^2.$$ This is the probability of observing $0$. Then \begin{eqnarray*} w &=& a \big/ \sqrt{P(0)}, \\ x &=& c \big/ \sqrt{P(0)}, \\ y &=& e \big/ \sqrt{P(0)}, …
Peter Shor 's user avatar
6 votes

When is a non-unitary quantum system only theoretical?

Look at John Preskill's Lecture Notes; particularly Section 3.2. As you noted, you can do a NAND gate by using a Toffoli gate and throwing away some of the output qubits. This results in decoherence, …
Peter Shor 's user avatar
6 votes

How can I get $\sum_n e^{i a_n} |n\rangle$ from $\sum_n a_n |n\rangle$?

It's not unitary, so it's impossible because all quantum transformations have to be unitary. Consider the states $$ \frac{3}{5} |0\rangle + \frac{4}{5} |1\rangle \quad \mathrm{and} \quad \frac{3}{5} …
Peter Shor 's user avatar
9 votes
Accepted

String theory based computations

No, as far as I know, there are no models that use string theory. Given that quantum field theories seem to be simulatable in polynomial time by a quantum computer (Jordan, Lee, and Preskill, 2012), …
Peter Shor 's user avatar
18 votes
Accepted

What does a tangible Quantum-Gate look like?

You seem to have the idea that a quantum gate is a physical thing rather than just a conceptual thing. It doesn't necessarily work that way. While CMOS gates are usually actual physical devices, qua …
Peter Shor 's user avatar
18 votes
Accepted

Is relation between BQP and QMA resolved?

I haven't looked at the paper carefully, but one thing I noticed is that their proof that BQP $\subsetneqq$ QMA works by their claiming that "bit commitment $\not \in$ BQP" but "bit commitment $\in$ Q …
Peter Shor 's user avatar
5 votes

On the plausability of quantum RAM

To answer your question, a QRAM is a self-consistent and interesting model of quantum computation. It appears to be more powerful (up to a polynomial factor) than the usual circuit model of quantum co …
Peter Shor 's user avatar
7 votes

Richard Feynman says that all quantum procedures are able to be simulated by quantum computa...

Since we don't know the ultimate physical laws of the universe, and we would need to know them (or at least know much more about them than we do now) to prove Feynman's conjecture, his conjecture is s …
Peter Shor 's user avatar

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