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Results tagged with quantum-computer
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user 8983
The quantum computing tag is relevant for computing that uses quantum states such as superposition and/or entanglement to locate low energy states as solutions to complex problems (rather than laboriously enumerating and checking solutions as would be done with non-quantum traditional computing).
1
vote
Controlled-measurement of a quantum register
Such an operation is indeed physically realizable. Suppose you wish to measure qubit $b$ if qubit $a$ is in the 1 state. Then just measure $a$, and if you get 1 then measure $b$ (e.g. the lab assist …
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0
votes
Accepted
When is an operator subspace the span of Kraus operators?
Consider a space $\textrm{span}_j\{L_j\}$ with the $\{L_j\}$ linearly independent. This is a span of Kraus operators if it can be written as $\textrm{span}_i\{K_i\}$ with the $K_i$ being Kraus operat …
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2
votes
Quantum gate: Phase shift
A phase gate will not map between the two vectors you give. A phase gate changes the phase of the $\left|1\right>$ component, which is not what you want since for your example all components are real …
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4
votes
Examples of number theory showing up in physics
There are many theorems in quantum information which only apply to qudits of prime dimension. In particular, this seems to happen with graph states. In that case many theorems rely on the fact that …
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1
vote
Does quantum fingerprinting really argue for the exponential size of wavefunctions?
That fingerprinting argues for an exponential sized state is dubious, but not for quite the reason you outline.
First off, the orthogonality test. While you are correct that you can't with certainty …
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5
votes
1
answer
327
views
When is an operator subspace the span of Kraus operators?
Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span …
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7
votes
Accepted
How can you distinguish between projections of quantum states?
There is a circuit which returns a "1" measurement outcome with probability $\frac{1}{2} \left(1-\left|\left<\phi_1|\phi_2\right>\right|^2\right)$, so this does what you ask with $p=\frac{1-\alpha}{2} …
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6
votes
Accepted
How to derive quantum Fourier transform from discrete Fourier transform (DFT)?
Mathematically, QFT and DFT are exactly the same thing. You can verify this by comparing the first equation on each of the Wikipedia pages. On Wikipedia these two differ by a minus sign in the expon …
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2
votes
partial trace with sparse matrices
If you want something specific to Mathematica then I don't know, but in general:
Let $\sigma = \rho_{AD} = \textrm{Tr}_{BC}(\rho)$. $\rho$ is an operator on four subsystems, so it has four inputs an …
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