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7
votes
2 answers
What does it mean to take the Choi-Jamiolkowski of a quantum channel?
The Choi-Jamiolkowski of a channel $\newcommand{\on}[1]{\operatorname{#1}}\Lambda : \on{End}(\mathcal{H_A}) \xrightarrow{} \on{End}(\mathcal{H_B})$ is obtained through an isomorphism of the form:
$$
CJ:
…
the mmmPodcast
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7
votes
2 answers
How is the ground state of a Hamiltonian defined?
I'm studying VQE, but there is something I don't get.
We know (I think) that for a given Hamiltonian the minimum eigenvalue is associated with the ground state. But if we take the Hamiltonian to be Pauli Z, then it has two eigenvalues: 1 associated…
Sorin Bolos
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7
votes
2 answers
What is a separable decomposition for the Werner state?
Consider the two-qubit Werner state, defined as
$$\rho_z = z |\Psi_-\rangle\!\langle \Psi_-| + \frac{1-z}{4}I,
\quad |\Psi_-\rangle\equiv\frac{1}{\sqrt2}(|00\rangle-|11\rangle),$$
for $z\ge0$.
Using the PPT criterion, one can see that this state is…
glS
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7
votes
3 answers
Quantum circuit to implement matrix exponential
I want to build a circuit which will implement $e^{iAt}$, where $ A=
\begin{pmatrix}
1.5 & 0.5\\
0.5 & 1.5\\
\end{pmatrix}
$ and $t= \pi/2 $.
We see that $A$ can be written as, $A=1.5I+0.5X$. Since $I$ and $X$ commute,…
Omkar
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7
votes
2 answers
How to represent an $n$-qubit circuit in matrix form?
If a given quantum circuit has $n$ qubit inputs and a certain number of gates, how can we represent the whole circuit in matrix form? Here's an example:
I am sorry, I am confused on how to express the circuit above in matrix form. Especially on…
J.Koko
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7
votes
1 answer
What limits speed of quantum gates?
I would like to check something.
Consider I am working on cQED (superconducting qubits), or ion trapped, or silicon qubits (I would like to exclude "exotic for me" quantum computing like photon based, or topological Q.C).
The fastest you perform a…
Marco Fellous-Asiani
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6
votes
1 answer
Changing qubits coefficients to trigonometric functions in Grover Algorithm
In this paper, in Appendix B.1 (Grover's Search Algorithm and Grover Operator G), it does a change of coefficients, such as what is done for the Bloch Sphere, but for a many qubits system using only two vectors.
Firstly, it separates the uniform…
Bertolino
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6
votes
1 answer
Understanding Steps in Deutsch's Algorithm
I am currently working my way through the book Quantum Computation and Quantum Information by Chuang and Nielsen. So far it has been a joy to read, however I am hung up on a couple aspects of quantum parallelism and Deutsch's algorithm that I…
user918212
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6
votes
3 answers
What is meant with "shot" in quantum computation?
What is a "shot" in relation to quantum computing? I heard it is repeating time, but I don't understand it. Additionally, why is the default number of shots 1,024 in the IBM Q Experience?
One more question - I saw the sentence for each value of the…
김동민
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6
votes
2 answers
If an auxiliary qubit is allowed, how to construct toffoli gate in easier way?
We know if we don't use auxiliary, the construction of Toffoli gate will be:
However, if now you are allowed to use one auxiliary qubit, how to realize a CCNOT in a simplier way? (Can we only use X,Y,Z,H and CNOT?)
Dingshan Liu
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6
votes
1 answer
In Dirac notation, why do we have $\langle cf|g\rangle = c^*\langle f\vert g\rangle$?
A Hilbert Space has this property
$$\langle cf,g\rangle=c\langle f,g\rangle$$
where $f$ and $g$ are the vectors in the Hilbert Space and $c$ is a complex number.
In Dirac Notation,
$$\langle cf|g\rangle = c^*\langle f\vert g\rangle$$
I am confused…
HYW
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6
votes
1 answer
Is Connes' Embedding Problem akin to the word problem for finitely presented groups?
The complexity class $\mathrm{MIP^*}$ includes the set of languages that can be efficiently verified by a classical, polynomially-bounded verifier, engaging with two quantum provers that can share (potentially infinite) entanglement, but are…
Mark Spinelli
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6
votes
2 answers
The relationship between problem structure and exponential speedups under the query model
What problem structure(s) are required to admit an exponential speedup in the universal quantum model of computation under the query model?
Intuitively, it would seem that much of the benefit of the quantum model, as is often suggested, is due to…
Greenstick
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6
votes
1 answer
How to prepare mixed states using IBM quantum experience?
I want to prepare some mixed states regarding a project that I am doing, however, I am not sure how to do that using IBM Q. Experience circuit composer. Basically, I am looking to prepare maximally mixed and non-maximally mixed quantum states.
I…
Hridey Narula
- 61
- 2
6
votes
1 answer
What is the difference between the action of $Z$ and $\exp(-i Z t)$ on a state?
What is the difference between performing $Z$ operation and performing $e^{-i Zt}$ operation on a state, given that $e^{-i Zt}= \mathbb{1} + (-i Zt) + ...$ is not equal to $Z$ for any value of $t$?
Rob
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