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How to translate between continuous variable model and discrete model?
If I understand correctly, the discrete and continuous variable (CV) version of quantum computation are equivalent. However, the continuous aspect of the CV model makes me wonder to what extent can both models be compared. Given a discrete-gate…
Mauricio
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Why is the CNOT representation $e^{i\frac{\pi}{4}\left(I-Z\right)\otimes\left(I-X\right)}$ hardly found in books?
The CNOT gate is usually written as
$|0\rangle\langle0|\otimes I + 1\rangle\langle1|\otimes X$
(with $X,Y,Z$ being the Pauli Basis and $I$ the Identity).
I have yet to stumble across the representation Wikipedia gives when looking at books on the…
manuel459
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8
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Why doesn't Shor's algorithm output a solution for some numbers?
I've been trying to mess around with Qiskit's implementation of Shor's algorithm, and while trying I've noticed that Shor(33), for example, would not output a solution (even with an absurd number of attempts). Qiskit's implementation would retry by…
Nuno Costa
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8
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What channels preserve the purity of all pure inputs?
Consider channels $\Phi$ such that $\Phi(|\psi\rangle\!\langle\psi|)$ is pure for all $|\psi\rangle$. Is there a simple way to characterise channels with this property?
Let's suppose $\Phi$ acts between input and output spaces of the same dimension.…
glS
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8
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1 answer
Why does code switching not allow for universal fault-tolerant quantum computation?
In this paper, the authors briefly mention that one proposed method to bypass the Eastin-Knill theorem is to perform code-switching. That is, given codes $C_1$ and $C_2$ which permit a complementary set of transversal gates, one can encode their…
Sergio Escobar
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Five qubits can be entangled in how many ways?
It is well-known that there are two ways to entangle three qubits and nine ways to entangle four qubits.
In page 22 of this paper I found that there are infinitely many ways to entangle five qubits, but I am not sure how to see or prove this or if…
R.G.J
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8
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Can quantum money be reliably "burned?"
One of the novel features of Bitcoin and other cryptocurrencies is that coins can be irrefutably "burned" or destroyed, by creating a transaction to send the money to a junk burn address.
Thinking similarly about quantum money - from knots, or…
Mark Spinelli
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Origin of braiding in measurement-only TQC
I have a technical question on the "measurement-only"-proposal for topological quantum computation on anyons. First some background:
Background.
While it has become a common idea that topological quantum gates could be implemented by braiding…
Urs Schreiber
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Why am I able to simulate such high qubit numbers on my laptop?
Recently I've been working on a VQE-related project, for which I'm using Qiskit's TwoLocal variational form (qiskit version 0.34.2). I noticed that I was able to simulate this circuit up to surprisingly high qubit numbers on my laptop, so I wanted…
Matthias
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Two definitions of the Clifford group and their relation
Clifford groups are used in at least 3 places I've encountered so far in QIP:
A circuit that contains only Clifford operations, which are generated from CNOT, H and P, is sufficient for a wide variety of quantum circuits, as shown here.
Clifford…
Lior
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What are the P(0) and P(1) probabilities for the T transformation in quantum computing?
I'm just starting of on quantum computing, specifically following the IBM Q Experience documentation [1]. In here, they are explaining the following experiment:
$T|+\rangle$
The expected outcomes according to the document:
Phase angle: $\pi/4$…
Thomas Hubregtsen
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2 answers
How to benchmark a quantum computer?
Using a simple puzzle game to benchmark quantum computers is the most clever approach I have seen so far.
The author of the aforementioned article, James, makes a nice analogy to buying a laptop ("more than just a single number when comparing") in…
user820789
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Construct Controlled-$G^{\dagger}$ from known Controlled-$G$
Let there be a known a scheme (quantum circuit) of Controlled-G, where unitary gate G has G$^†$ such that G≠G$^†$ and GG$^†$=I (for example S and S$^†$, T and T$^†$, V and V$^†$, but not Pauli and H gates).
My question for the experts is:
How is…
John Lancaster
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Is Quantum Cramer-Rao bound for single parameter always attainable?
First I will give some background of Quantum Cramer-Rao bound. There is an amount called Fisher Information:$F(\lambda)=\sum_x{p\left( x|\lambda \right) \left( \partial _{\lambda}\ln p\left( x|\lambda \right) \right) ^2}$ where $p\left( x|\lambda…
narip
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8
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What is "linear" in linear entropy?
Why is the linear entropy, defined by $S_L = 1 - \textrm{Tr} \rho^2$, called linear?
Rob
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