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1500 questions
7
votes
1 answer
Resources for QRAM implemented as a subroutine for quantum algorithm
I am currently working on a project on a higher version of amplitude amplification and for that we want to store the initial state (which will be some sort of superposition) into a QRAM. Now we want to simulate the working of the algorithm and I am…
Parmeet Singh EP 066
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7
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1 answer
Are projective measurements the only optimal measurements to discriminate between two states?
Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one.
There is an optimal measurement to distinguish between these two states --- the…
BlackHat18
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7
votes
0 answers
How large can we make the fidelity between mixed states by allowing unitaries?
For pure states, it is known that one can always find a unitary that relates the two i.e. for any choice of states $\vert\psi\rangle$ and $\vert\phi\rangle$, there exists a unitary $U$ such that $U\vert\psi\rangle = \vert\phi\rangle$. Hence, we have…
JRT
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7
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2 answers
Why are there eight $T$ magic state and twelve $H$ magic states?
I am learning magic state distillation.
We can define the following two states:
$$ |T\rangle \langle T | = \frac{1}{2}(I+\frac{1}{\sqrt{3}}(\sigma_x+\sigma_y+\sigma_z))$$
$$ |H\rangle \langle H | =…
Marco Fellous-Asiani
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7
votes
1 answer
What is the rank of a quantum channel?
I read the following sentence in a paper:
We consider a quantum channel $\mathcal{E}_{\omega}(\rho)=\sum_{i=1}^{r} K_{i} \rho K_{i}^{\dagger}$ where $r$ is the rank of the channel.
I didn't find the definition of the rank of the quantum channel…
Sherlock
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7
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1 answer
Good references to learn magic state distillation for fault tolerance
I need to learn magic state distillation procedure and their application to fault-tolerance.
One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf
I am wondering if there are more recent and pedagogic…
Marco Fellous-Asiani
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7
votes
2 answers
How universal is the Toffoli gate for classical reversible computing?
It is easy to see that no finite set of classical reversible gates can be strictly universal (without ancilla) for classical reversible computation: for any reversible gate on $n$ bits, in its action on $n+1$ bits it induces an even permutation, and…
Dylan Thurston
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7
votes
2 answers
ZX-calculus: pi-copy rule not required for completeness?
In ZX-calculus, the $\pi$-copy rule is quite famous, and is used for instance here:
However, this paper never introduces this rule, and says that this set is enough to prove the Clifford completeness of the ZX calculus:
Is it just that they forgot…
Léo Colisson
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7
votes
1 answer
How to avoid error when applying certain combinations of degree of freedom rotations using a quantum circuit?
When applying each of the six degree of freedom rotations (or certain combinations of them) in an SO(4) using quantum gates, the results I expected are produced. For example, the following circuit in Craig Gidney's Quirk tool demonstrates rotations…
JavaFXpert
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7
votes
2 answers
Why are Bell states the maximally entangled ones?
I just want to know why actually Bell states are examples of maximally entangled states and significance of that "maximal" term. Is there anything for proving that?
user18115
7
votes
1 answer
Are anti-unitary gates possible?
According to Wigner’s theorem, every symmetry operation must be represented in quantum mechanics by an unitary or an anti-unitary operator. To see this, we can see that given any two states $|\psi\rangle$ and $|\psi'\rangle$, you would like to…
Mauricio
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7
votes
1 answer
Elementary question: is $\langle a|b \rangle$ the same as $\langle a||b\rangle$?
In trying to learn more about quantum computing, one of the first things encountered is a definition of the inner product $\langle a|b\rangle$. If I interpret it correctly, and looking near the bottom of page 15 of the 2011 book by Rieffel and…
mhucka
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7
votes
1 answer
Why does job.running in QISKit output False, even if the job is still running?
I submitted a job in the 0.5.0 version of QISKit using
job = execute(qc, 'ibmqx5', shots=shots)
This just submits the job, and does not wait for a result.
I then immediately tested whether the job was still running using
print(job.running)
This…
James Wootton
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7
votes
1 answer
Translation of color/toric code to a small network of solid-state spins
Within Quantum Error Correction and stabilizer codes, toric codes/surface codes are very tempting, mainly for their high error threshold. For more background please check up, in our Physics sister (aunt?) site: Quantum Error Correction: Surface code…
agaitaarino
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7
votes
1 answer
Threshold and practical requirements for initial state preparation?
At the beginning of a quantum computational process we generally want to start in a perfectly known initial state, and evolve from there. This cannot be done perfectly, for fundamental reasons, but I strongly suspect there has to be a practical…
agaitaarino
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