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7
votes
2 answers
How does quantum teleportation work with mixed shared states?
I am given the scenario that instead of the two parties (A & B) sharing the bell state $|\phi_+\rangle$ they share the mixture $\rho_\lambda = \lambda|\phi_+\rangle\langle\phi_+|+(1-\lambda)\frac{\mathbb{1}}{2}\otimes \frac{\mathbb{1}}{2}$ in the…
Luca Ion
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7
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1 answer
Is this single qubit gate in the Clifford hierarchy?
For a single qubit, the Clifford hierarchy is defined to be
$$
\mathcal C^{(k)} = \Big\{ U \in \mathbf U(2)
\mathrel{\Big\vert} \forall P \in \mathcal C^{(1)} : U P U^\dagger
\in \mathcal C^{(k-1)} \Big\}.
$$
Is it true that all elements of $…
Ian Gershon Teixeira
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7
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3 answers
Show that, averaging over uniformly random unitaries, $\mathbb{E}[UXU^\dagger]=\operatorname{Tr}(X)\frac{I}{d}$
As mentioned e.g. in this answer, if we compute the average
$$\Phi(X)\equiv \mathbb{E}_U[UXU^\dagger] \equiv \int_{\mathbf U(d)} d\mu(U) UXU^\dagger,$$
where $d\mu(U)$ is the Haar measure over the unitary group $\mathbf U(d)$, we get…
glS
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7
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1 answer
Publicly available samples for quantum circuits and/or simulators
With Yosi Rinott and Tomer Shoham we studied various statistical aspects of samples coming from NISQ computers.
My question is about available data consisting of samples from NISQ computers
We would be very happy to get samples from runs of quantum…
Gil Kalai
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7
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1 answer
What are the 2022 Nobel Prize winning papers of Alain Aspect, John Clauser, and Anton Zeilinger, and how do they fit into the timeline of QIS?
The 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for "experiments with entangled photons... pioneering quantum information science".
Presumably there were noteworthy publications of each.
Are there…
Mark Spinelli
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7
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2 answers
How to intuitively understand why $T$ gate can't be implemented transversally?
Suppose we have all to all connectivity and can implement fault-tolerant logical gates in the Clifford group. Why can't we just apply a physical $T$ gate to every physical qubit in the code block? (Suppose we have stabilizer generators like a bunch…
Jiakai Wang
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7
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2 answers
How are quantum circuits run on real quantum computers?
Sorry if this question sounds trivial, however I'm struggling to get the intuition of how quantum circuits are actually run on real quantum hardware.
As far as I know, in a simulated environment, circuits are transpiled, compiled and assembled so…
mpro
- 527
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7
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1 answer
How to check if a $n$-qubit unitary is the tensor product of single-qubit unitaries
Let's assume I give you the expression of a unitary matrix acting on two qubits that is:
$$U=\sum_{i} A_i \otimes B_i$$
for some operators $A_i$ and $B_i$.
Is there a simple criterion allowing you to find out if it is actually simply…
Marco Fellous-Asiani
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7
votes
1 answer
What arguments point towards D-Wave devices being potentially useful?
I'm looking for any evidence pointing towards D-Wave's approach to quantum computation being promising to achieve any sort of computational advantage with respect to classical devices.
Note that I'm not asking about quantum annealing in general. As…
glS
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7
votes
2 answers
Is there a "simple" way to tell if a stabilizer code is degenerate?
Suppose I have a stabilizer code defined by $m$ independent Pauli strings. Is there a "simple" way to check if the code is degenerate or not?
As test cases the $[[5,1,3]]$ code is not degenerate, and Shor's $[[9,1,3]]$ code is.
unknown
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6 answers
What would be an informative introduction to quantum computing software?
I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc).
In the question below they are looking for courses on the subject, which I am also interested in, and do plan on…
user3088
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7
votes
1 answer
Shor code: phase flip error
For Shor's error correcting code, what is the intuition behind saying that the following circuit corrects the phase flip error?
I realize that the circuit is trying to compare phases of the three 3-qubit blocks, two at a time. But I don't…
BlackHat18
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7
votes
1 answer
Does a fully working quantum computer solve a specific problem at varying speeds every time?
Lets say we have a fully working quantum computer. I give it a problem to solve and measure how long it takes to solve it. I repeat the process. Would it take the exact same time to solve the same problem?
I have read that a quantum computer's…
Nightwolf
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7
votes
2 answers
Breakthroughs in quantum computing using non-standard quanta
It seems that quantum computers can be classified by the type of quantum they operate on. Not entirely sure what category most common current systems fall into (eg. D-Wave, Google, IBM, Microsoft). Photonic computing seems to be one of the more…
user820789
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7
votes
2 answers
In amplitude amplification, how are the amplitudes of qubits changed?
I am relatively new to quantum computing and I feel like I don't fully understand the power of quantum computing due to a lack of understanding of how amplitude amplification works.
What is confusing me is that the amplitude of the qubit is the…
Eric Li
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