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1500 questions
7
votes
2 answers
Complexity of $n$-Toffoli with phase difference
I'm interested in the $n$-Toffoli gates with phase differences. I found a quadratic technique in section 7.2 of this paper.
Here's the front page of the paper.
Here's an image of the section that I'm referring to.
Does anyone know if there has…
Minh Pham
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7
votes
2 answers
How to visualize Hadamard gate as $X$-$Z$-$X$ decomposition?
In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of $R_x$, $R_z$ rotations and $e^{i\phi}$ for some angle $\phi$. I have found…
Trishant Sahu
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7
votes
2 answers
Cascade/Feedforward quantum circuits
I would like to know if it is possible implement the following situation in Qiskit (either using the simulators or real quantum computers).
Consider this illustrative toy example:
The arrows illustrate that the outcomes $\{\sigma_1,...,\sigma_i\}$…
fcrp
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7
votes
0 answers
Solving linear system $Ax=b$ with exponential speed-up via binary optimization?
The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a matrix. In case we want to know solution $|x\rangle$…
Martin Vesely
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7
votes
2 answers
If $\rho,\sigma$ are classical-quantum states, can the fidelity $F(\rho,\sigma)$ be expressed in terms of $F(\rho_i,\sigma_i)$?
Let $\rho = \sum_i \vert i\rangle\langle i\vert \otimes \rho_i$ and $\sigma = \sum_i\vert i\rangle\langle i\vert\otimes\sigma_i$ where we are using the same orthonormal basis indexed by $\vert i\rangle$ for both states.
The quantum fidelity is…
Wut
- 73
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7
votes
1 answer
Bernstein–Vazirani problem in book as exercise
I´ve solved the Exercise 7.1.1 (Bernstein–Vazirani problem) of the book "An introduction to quantum computing" (Mosca et altri). The problem is the following:
Show how to find $a \in Z_2^n$ given one application of a black box that maps…
asdf
- 503
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7
votes
2 answers
How to prove generalized Uhlmann's theorem?
I think the Uhlmann theorem should be in general of this form:
Let $\rho$ and $\sigma$ be density operators acting on $A$, with Schmidt degrees at most $r$, and let $B$ be another Hilbert space with dimension at least $r$, so that $\rho, \sigma$…
MaudPieTheRocktorate
- 301
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7
votes
2 answers
Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers
Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some studies indicating that in some cases quantum annealing…
Martin Vesely
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7
votes
1 answer
Biggest variance of $h=\sum_i H_i$?
What's the biggest variance of $h=\sum_i H_i$ where $H_i$ is the hamiltonian act on the ith qubit?
If the n qubits state is separable, i.e., the state is $\mid\psi_1\rangle\otimes\mid\psi_2\rangle\otimes\cdots\mid\psi_n\rangle$. Obviously, the…
narip
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7
votes
2 answers
Quantum teleportation of a mixed state through a pure state?
Let's assume we have a register of qubits present in a mixed state
$$\rho = \sum_i^n p_i|\psi_i\rangle \langle \psi_i|$$
and we want to teleport $\rho$ through a random pure state $|\phi\rangle$. What would be the result of this…
Thomas
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7
votes
1 answer
Is the complexity of a quantum circuit constant in the depth of the circuit?
Take a quantum circuit on $n$ qubits, you have some sequence of gates.
You can represent these gates as hermitian matrices, and then with some padding, you could take the product of these matrices, by closure would be a hermitian matrix, a quantum…
abrahimladha
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7
votes
1 answer
What is meant by "perfect state transfer"?
In discussions on many quantum algorithms especially related to quantum walks, I have seen the term "perfect state transfer" used to describe some property apparently related to the periodicities of the walk/algorithm, but I cannot quite grasp the…
Mark Spinelli
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7
votes
3 answers
Can the theory of quantum computation assist in the miniaturization of transistors?
In his inaugural lecture, Ronald de Wolf states
People are working with quantum objects, but trying to make them behave as classical as possible. (...) Instead of suppressing them to make systems behave as classically as possible, why not try to
…
Discrete lizard
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7
votes
1 answer
Why do I get this extra factor when working out the dynamics of an adiabatic quantum computation?
I was trying to revise my understanding of adiabatic quantum computation via a simple example. I'm familiar with the overall concept -- that you have an overall Hamiltonian
$$
H(s)=(1-s)H_0+s H_f
$$
where $s$ is a function of time, starting from…
DaftWullie
- 62,671
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- 140
7
votes
1 answer
Quantum capacity for serial composition of quantum channels
Recently, I have been working with quantum channel capacity for quantum-quantum channels and I was wondering if there exist some results for channel compositions.
Specifically, I have been looking for results on what happens to quantum channel…
Josu Etxezarreta Martinez
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