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How is quantum teleportation generalized to qudits?
In an answer to a previous question, Generalization for n quantum teleportations, Craig Gidney states:
The more complicated way to generalize teleportation is figuring out how to make it work on qutrits and qudits instead of only qubits. Basically,…
user820789
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How to find the operator sum representation of the depolarizing channel?
In Nielsen and Chuang (page:379), it is shown that the operator sum representation of a depolarizing channel $\mathcal{E}(\rho) = \frac{pI}{2} + (1-p)\rho$ is easily seen by substituting the identity matrix with
$$\frac{\mathbb{I}}{2} = \frac{\rho +…
user1936752
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11
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Can quantum computing be profitable without quantum hardware?
What are the fields/business ideas that a new business can work on within quantum computing that can be profitable if this business has no access to onboard quantum setups but can access the cloud-based quantum computing platforms? What are the…
Tarek
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11
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What's an example of building a circuit $U_f$ that implements a simple function $f$?
I'd like to be able to program simple functions into simulators such as QCL. I read that any function $f$ can be implemented, but I don't know how to get say a unitary matrix that implements $f$.
$\newcommand{\qr}[1]{|#1\rangle}$
I think first I…
R. Chopin
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11
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How is computation done in a 2D surface code array?
In a 2D surface code lattice, there are some data qubits and some measurement qubits. Suppose we want to do a 2-qubit computation, for example, let say, an X-gate on qubit-1 followed by a CNOT gate with qubit-1 as the control bit and qubit-2 as the…
Edifice
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11
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Does the D-Wave 2000Q satisfy DiVincenzo's criteria?
DiVincenzo's criteria for quantum computation are the following:
A scalable physical system with well characterized qubits.
The ability to initialize the state of the qubits to a simple fiducial
state.
Long relevant decoherence times.
A…
user1271772 No more free time
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11
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2 answers
What are useful resources about the geometric of qutrits and its relation with Gell-Mann matrices?
I need some useful sources about the geometry of qutrit. Specifically related to the Gell-Mann matrix representation.
Azadeh Zohrabi
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11
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How many bits do Alice and Bob needs to compare to make sure the channel is secure in BB84?
I was trying to self-study qmc by reading the Quantum Computing A Gentle Introduction book, in section 2.4 it talks about the quantum key distribution protocol BB84. After (I thought) I understood it I went to work on exercise 2.9 and 2.10.
Ex. 2.9…
Sam
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Quantum Algorithm for God's Number
God's number is the worst case of God's algorithm which is
a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm…
user820789
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11
votes
4 answers
Minimum number of CNOTs for Toffoli with non-adjacent controls
I want to decompose a Toffoli gate into CNOTs and arbitrary single-qubit gates. I want to minimize the number of CNOTs. I have a locality constraint: because the Toffoli is occurring in a linear array, the two controls are not adjacent to each other…
Craig Gidney
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11
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The quantum complexity of implementing a permutation matrix
Suppose we are given a permutation matrix (which is unitary since it corresponds to a permutation of the basis), acting on a $2^n$-dimensional Hilbert space, which can be seen as a quantum system of $n$ qubits. Is there a way to find an efficient…
Danylo Y
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(April Fools 2024) Where can we find out more details about the recent factoring of RSA-2048?
[Note that this was originally asked on April 1, 2024, also known as April Fool's day in many Western nations]
I'm hearing some rumors that a combination of neutral atoms (Lukin's group?), in conjunction with some of the key players in…
Mark Spinelli
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11
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2 answers
Are there any uses for Shor's algorithm other than breaking public key cryptography
This question may be slightly opinion based, so I apologise if this is the incorrect place to ask.
My question is, is there any use for Shor's integer factorisation algorithm other than for breaking public key cryptography. If there isn't, then am I…
Adrien Amour
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11
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What is the complexity of determining if a state is entangled?
I have been looking around for an answer to this question but can't really come up with anything. Given some oracle, $U$, that maps $| 0 \rangle$ to $| \psi \rangle$, is there some algorithm that determines whether $| \psi \rangle$ is entangled or…
Loic Stoic
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11
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Why can all quantum circuits be converted into circuits that use only real matrices?
I know that you need to add an additional ancilla qubit to "keep track" of whether or not you are in real space or imaginary space, but how exactly does this work?
What is the proof for this? I tried looking online but I could not find a proof. I…
Rydberg
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