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1500 questions
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3 answers
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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1 answer
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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11
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Quantum Algorithms for Convolution
I was looking into applications of Quantum Computing for machine learning and encountered the following pre-print from 2003. Quantum Convolution and Correlation Algorithms are Physically Impossible. The article doesn't appear to have been published…
DPL
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11
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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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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
votes
2 answers
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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2 answers
Why can't there be an error detecting code with fewer than 4 qubits?
Essentially this boils down to: Is it possible to encode a single logical qubit in three physical qubits so that the resulting code has distance two?
In other words, does a $[\![3,1,2]\!]$ code exist?
Comments:
No $[\![3,1,2]\!]$ stabilizer code…
Ian Gershon Teixeira
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0 answers
Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities
For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, such as the "$X$"-states, where any matrix…
Paul B. Slater
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1 answer
Why was Feynman hesitant about simulating fermions with a quantum computer?
Richard Feynman has a number of foundational publications from the early-mid 80's on quantum computing that I continue to read with awe and inspiration. As earlier discussed, the 1985 article "Quantum Mechanical Computers" is concerned with…
Mark Spinelli
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11
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1 answer
Quantum walk with binary tree
I’m trying to grok quantum walks, and would like to create an example that walks a perfect binary tree to find the one and only marked leaf node. Is this possible? If so, suppose the depth of the tree is five. Would that require a circuit with five…
JavaFXpert
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11
votes
1 answer
Are qudit graph states well-defined for non-prime dimension?
Qudit graph states are $d$-dimension generalisations of qubit graph states such that each state is represented by a weighted graph $G$ (with no self-loops) such that each edge $(i, j)$ is assigned a weight $A_{i, j} = 0,\ldots,d-1$.
The graph state…
SLesslyTall
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