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1500 questions
6
votes
2 answers
Why do Bell states have all real coefficients?
Canonically, the four Bell or EPR states for 2-qubit systems are given by:
$|\Phi^{\pm}\rangle = \frac{1}{\sqrt{2}} \left( |00\rangle \pm |11\rangle\right)$
$|\psi^{\pm}\rangle = \frac{1}{\sqrt{2}} \left( |01\rangle \pm |10\rangle\right)$.
I'm…
QuantumExplorer
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6
votes
1 answer
Which currently known quantum algorithms cannot be derived from the QSVT algorithm?
I have just started reading the paper A Grand Unification of Quantum Algorithms. There is a claim on page 2 that "by simply adjusting the parameters of QSVT, one can construct nearly all known quantum algorithms".
On the same page, the paper states…
Miriam K.
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Does Levy's lemma hold for unitary/spherical designs?
Let $\mathcal{H}$ be a $d$-dimensional Hilbert space equipped with the Haar measure. Levy's lemma says that, for an $L$ -Lipschitz function $f$ on $\mathcal{H}$, the probability that $f(x)$ for a randomly drawn unit vector $x$ deviates from its…
Banach space fan
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2 answers
Are transversal entangling gates possible for stabilizer codes other than CSS?
It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304.3709 shows that $ CCZ $ is exactly transversal on 3…
Ian Gershon Teixeira
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6
votes
0 answers
Universal gate set for the $ [[15,1,3]] $ code
The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is an implementation of the Hadamard gate $ H $.
The…
Ian Gershon Teixeira
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6
votes
4 answers
Are there even distance color codes?
The surface code comes in both odd-distance and even-distance forms. Color codes always seem to come in odd-distance. Presumably this is due to the fact that the X and Z observables overlap at the boundary of a color code, and they must anticommute,…
Craig Gidney
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6
votes
2 answers
How many qubits are simulable with a normal computer and freely accessible simulators?
I want to simulate an arbitrary isolated quantum circuit acting on $n$ qubits (i.e. a pure state of $n$ qubits).
As I know RAM is the bottleneck for quantum simulators, you can consider a "normal" computer to have between $4$ and $8$ Gio of RAM, all…
Adrien Suau
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6
votes
1 answer
Is there a concentration inequality for the quantum gate fidelity $F(C,U)$ for a channel $C$ such that $\int dU F(C,U)=X$?
For a fixed quantum channel $N$ and a unitary channel $U$, we define $N$'s gate fidelity as
$$ F(N,U) = \int \langle \psi| U \, N(| \psi \rangle \langle \psi |) \, U^\dagger| \psi \rangle d\mu_H(\psi)$$
where $\mu_H$ is the Haar measure over…
Davide Li Calsi
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6
votes
2 answers
What are some good quantum computing simulator and visualiser?
I am looking for some good software to simulate quantum computing, visually if possible.
I know about quirk (http://algassert.com/quirk)
and IBM Q Experience (https://quantumexperience.ng.bluemix.net)
I just saw this question ( Does conditional gate…
Adrien Nivaggioli
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6
votes
2 answers
Stabilizers of the [[12, 2, 4]] "Carbon" code
In a recent experimental paper, Microsoft with IonQ claimed that they demonstrated the "repeated error correction" with both the $[[7, 1, 3]]$ Steane code and the $[[12, 2, 4]]$ "Carbon" code, both of which are self-dual CSS codes.
I am particularly…
Yunzhe
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6
votes
1 answer
Is the trace of a positive map always positive?
Obviously, positive semi-definite operators always admit a positive trace as ${\rm tr}(A)=\|A\|_1\geq 0$ whenever $A\geq 0$. This motivates the following "lifted" question:
Given any positive, linear map $\Phi:\mathbb C^{n\times n}\to\mathbb…
Frederik vom Ende
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6
votes
2 answers
If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?
Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement.
So after the measurement, Alice knows what state her qubit is…
mp12853
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6
votes
1 answer
Where does the "error propagation formula" $(\Delta \theta)^2=(\Delta M)^2/|\partial_\theta\langle M\rangle|^2$ come from, in estimation theory?
Consider the single parameter estimation setting, where we have a distribution depending on $\theta$ and we're looking for a "good" estimator for $\theta$.
A commonly mentioned strategy, found e.g. in Eq. (7) of [TA2014], is to measure some…
glS
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6
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2 answers
Anyon alternatives in topological quantum computing
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons. -Wikipedia
Are there other instances of topological quantum computing models that do not use anyons?
Are there alternative…
user820789
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votes
1 answer
Clifford group without the phase gate
The Clifford group is generated by the Hadamard gate $H$, the phase gate $S=\sqrt{Z}$, and the $\text{CNOT}$ gate. I was wondering what happens if we dropped $S$, so that all matrices are real.
I found Does the real Clifford group contain all real…
Jun_Gitef17
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