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6
votes
1 answer
Why does $x\sqrt{1-x^2}$ enhance the ability to approximate analytical functions in quantum circuit learning?
In the paper Quantum Circuit Learning (arXiv) they say that the ability of a quantum circuit to approximate a function can be enhanced by terms like $x\sqrt{1-x^2}$ ($x\in[-1,1])$.
Given inputs $\{x,f(x)\}$, it aims to approximate an analytical…
raycosine
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6
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Decomposition of any 2-level matrix into single qubit and CNOT gates
I saw an example which takes a 2 level matrix. Which is a $8\times8$ matrix that acts non trivially only on 2 levels of only states $|000\rangle$ and $|111\rangle$. The way they do it is by using a gray code from $|000\rangle$ to $|111\rangle$ and…
bilanush
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6
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How does a $2 \pi$ pulse in Cirac Zoller give a -1 sign to the state?
I understand the first step in the Cirac-Zoller controlled-phase gate; about how to move the state from the electronic state to the vibrational mode state. However, I am unable to understand how a $2\pi$ pulse gives the -1 sign to the state and how…
Tech Solver
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Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?
Context:
Three coins on the table. Each is either heads or tails. You can
uncover any one of the three coins, revealing whether it is heads or
tails but then you choose two the other two coins disappear --- you'll
never know whetehr those…
Sanchayan Dutta
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6
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1 answer
How to create the oracle matrix in Grover's algorithm?
I'm trying to implement Grover's algorithm in pyQuil, but I'm having trouble creating the oracle matrix given the function $f$, where $f(x)=1$ if $x=w$ and $f(x)=0$ otherwise. In most of the implementations I've seen, either a mysterious oracle…
user5694
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Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?
This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention:
In their paper[1] conjecturing that holographic space-time and quantum
error correction are one…
Sanchayan Dutta
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6
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1 answer
Do weak measurements (with/without weak values) have any application in quantum computation?
I have seen their applications in quantum state tomography but not in computation as such.
RAMAN CHOUDHARY
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6
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How can pure state ensemble decompositions not be unique?
Apparently, the decomposition of a state into an ensemble of pure states is not unique. I can't understand why, as if I understood correctly a "pure state ensemble decomposition" is just the diagonalization of the density…
user2723984
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How to construct a quantum circuit (QIP system) for the graph non-isomorphism problem?
I'm having some trouble understanding quantum interactive proof systems (QIP systems) and the related circuit constructions. Interactive proof systems model these type of situations:
Interactive proof systems:
To say a promise problem…
Sanchayan Dutta
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6
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2 answers
Does quantum computing relate to stochastic computing in any way?
I'm a bit familiar with the concept of stochastic computing, where numbers are stored in large bit streams called "Stochastic Numbers", which represent numbers in the domain $[0,1]$ typically.
The Wikipedia article on stochastic computing summarizes…
DanBC
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6
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2 answers
Defining entanglement for systems with more than two qubits
Introductory textbooks I've read define entanglement as when your product state cannot be factored into the tensor product of individual quantum states. But consider a three-qbit system:
$$C_{2,0}H_2|000\rangle = \begin{bmatrix} \frac{1}{\sqrt{2}}…
ahelwer
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6
votes
3 answers
When can a matrix be "extended" into a unitary?
DaftWulie's answer to Extending a square matrix to a unitary matrix says that extending a matrix into a unitary cannot be done unless there's constraints on the matrix. What are the constraints?
Pablo LiManni
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6
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Extending a square matrix to a unitary matrix
Suppose we have a square matrix $M$ of size $n\times n$. It is given that any element $M_{ij}$ of $M$ is a real number and satisfies $0 \leq M_{ij} \leq 1$, $\forall$ $i,j$. No other property for $M$ is known. Is it possible to create a new matrix…
new2quantum
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2 answers
Efficient implementation of the Clifford group for $n$ qubits
I'm looking for an efficient implementation of the Clifford group $\mathcal{C}_n$
of $n$ qubits.
The Clifford group $\mathcal{C}_n$ has stucture $(2_+^{1+2n} \circ C_8).Sp(2,n)$,
where $2_+^{1+2n}$ denotes an extraspecial 2 group of $+$ type,…
Martin Seysen
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2 answers
What is the correspondence between adiabatic phase and a topological phase?
In the adiabatic model, we have a system acquiring a Berry phase due to cyclic slow periodic evolution under a Hamiltonian. While in the topological phases, we talk about systems such as anyons which acquire fractional phases under permutation or…
Siddhant Singh
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