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1500 questions
8
votes
2 answers
How should we interpret these quantum logic gates as physical observables?
In quantum mechanics each operator corresponds to some physical observable, but say we have the operators $X,Y,Z,H, \operatorname{CNOT}$. I understand how these gates act on qubits, but what do they actually represent in terms of a physical…
bhapi
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8
votes
2 answers
How to show a density matrix is in a pure/mixed state?
Say we have a single qubit with some density matrix, for example lets say we have the density matrix
$$\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}.$$
I would like to know what is the procedure for checking whether this state is pure or…
bhapi
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8
votes
2 answers
Meaning of "diagonal to the computational basis"
I came across the term "diagonal to the computational basis" in my reading recently. I'm not entirely sure what this term means. I know that a diagonal matrix is one with only non-zero elements on the diagonal and I know that the computational basis…
Woody1193
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8
votes
3 answers
Composing the CNOT gate as a tensor product of two level matrices
I don't understand, why is the control not gate used so often. As far as I understand it, if you apply two 2 level operations on two qubits then you get a 4 x 4 matrix by the tensor product. So how would you express the CNOT gate as a product of…
bilanush
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8
votes
3 answers
Is there any method of adding two operators in a circuit?
I am trying to reconstruct the time evolution of a Hamiltonian on the quantum computing simulator, quirk. Ideally I would like to generalise this to any simulator. The unitary matrix is
$$U(t)=e^{-iHt}$$
and I've found a way to decompose the…
Cameron
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8
votes
1 answer
How is Grover's operator represented as a rotation matrix?
I have seen that it is possible to represent the Grover iterator as a rotation matrix $G$. My question is, how can you do that exactly?
So we say that $|\psi\rangle$ is a superposition of the states of searched and not searched elements, that can be…
user4961
8
votes
1 answer
What are XX, YY, YZ etc. couplings?
The D-wave quantum computer allows us to be able to minimize Ising models. In reading other questions and responses, particularly What would be the simplest addition that would make the D-Wave architecture universal?, XX couplings (and others have…
Jacob Wise
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8
votes
1 answer
Correspondence between the Topological model and Quantum Circuit model
For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa.
From the literature developed, it seems that they tackle fairly different kinds of problems for…
user5438
8
votes
1 answer
Is the set of classical-quantum states convex?
I read about the classical-quantum states in the textbook by Mark Wilde and there is an exercise that asks to show the set of classical-quantum states is not a convex set. But I have an argument to show it is a convex set. I wonder whether I made a…
qquery
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8
votes
1 answer
Isomorphism between the Clifford group and the quaternions
How do I find an explicit isomorphism between the elements of the Clifford group and some 24 quaternions?
The easy part:
The multiplication of matrices should correspond to multiplication of quaternions.
The identity matrix $I$ should be mapped to…
knot
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8
votes
4 answers
Non-layperson explanation of why a qubit is more useful than a bit?
I have a computer science and mathematics degree and am trying to wrap my head around quantum computing and it just doesn't seem to make sense from the very beginning. I think the problem is the definitions out there are generally watered down for…
Lee Cascio
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8
votes
2 answers
Deduce the Kraus operators of the dephasing channel using the Choi
I'm trying to deduce the Kraus representation of the dephasing channel using the Choi operator (I know the Kraus operators can be guessed in this case, I want to understand the general case).
The dephasing channel maps a density operator $\rho$…
user2723984
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8
votes
4 answers
Maximally mixed states for more than 1 qubit
For 1 qubit, the maximally mixed state is $\frac{\mathrm{I}}{2}$.
So, for two qubits, I assume the maximally mixed state is the maximally mixed state is $\frac{\mathrm{I}}{4}$?
Which is:
$\frac{1}{4} (|00\rangle \langle 00| + |01\rangle \langle…
Mahathi Vempati
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8
votes
2 answers
Transformation of a Bell state
I am relatively new and interested in quantum computing.
Specifically, I am interested in transforming an equation that I found on Wikipedia. But I did not quite understand the transformation.
$…
P_Gate
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8
votes
0 answers
How can blackholes be fast information scramblers?
I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given.
As mentioned by L. Susskind et. al, the fast scrambling property of BHs seems to say BHs are infinite…
XXDD
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