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1500 questions
9
votes
2 answers
What is the matrix of the iSwap gate?
Mostly I'm confused over whether the common convention is to use +$i$ or -$i$ along the anti-diagonal of the middle $2\times 2$ block.
Craig Gidney
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9
votes
3 answers
What are the possible Kraus operators of the identity channel?
Consider a Kraus representation $\{A_a\}_a$ of the identity channel $\mathcal{I}$ that maps any state to itself. Of course, $\{A_a\}_a$ are not the simplest Kraus operators, which would just be $\{I\}$, and they need not to be orthogonal. Is there a…
Shadumu
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9
votes
2 answers
Chronology of discovery of quantum phase estimation algorithm
I'm a bit confused about exactly when the phase estimation algorithm was discovered. The Wiki article, as well as various textbooks and papers, says that it was introduced in 1995 by Alexei Kitaev, but Shor's algorithm, which uses phase estimation,…
tomdodd4598
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9
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1 answer
Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?
This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in defining graph states using $d$-dimensional qudits,…
SLesslyTall
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9
votes
3 answers
What is D-Wave's "Pegasus" architecture?
How is D-Wave's Pegasus architecture different from the Chimera architecture?
user1271772 No more free time
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9
votes
2 answers
How to justify post quantum encryption security?
Is there some definition or theorem about what a quantum computer can achieve from which post-quantum cryptographic schemes (eg lattice cryptography, but not quantum cryptography) can justify their security? I know the period finding function is…
Joseph Johnston
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9
votes
1 answer
Phase-Shift Gate in Qiskit
How to implement the phase shift gate in qiskit or ibmq?
Phase Shift Gate : $$\begin{pmatrix}e^{ia} && 0 \\ 0 && e^{ia}\end{pmatrix} = e^{ia}I$$
Debarghya Kundu
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9
votes
2 answers
Expressing "Square root of Swap" gate in terms of CNOT
How could a $\sqrt{SWAP}$ circuit be expressed in terms of CNOT gates & single qubit rotations?
CNOT & $\sqrt{SWAP}$ Gates
Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit…
user820789
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9
votes
1 answer
Measuring ancillas in Shor's algorithm
When considering Shor's algorithm, we use ancilla qubits to effectively obtain the state
$$\sum_x \left|x,f(x)\right>$$
for the function $f(x) = a^x \mod N$.
As I have learned it, we then measure the ancilla qubits, to obtain, say $f(x) = b$ and get…
nippon
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9
votes
2 answers
Are we certain that quantum computers are more efficient than classical computers can be built?
I mean are we certain that they will be able to provide us a huge improvements (in some tasks) compared to clasical computers?
Adou
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9
votes
1 answer
Prove that adding any non Clifford gate to the Clifford group yields a universal gate set
I have seen it claimed in multiple places that adding any non Clifford gate to the Clifford group yields a universal gate set. It is, however, not easy to find an accessible proof of this fact.
The…
Ian Gershon Teixeira
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9
votes
2 answers
Calculate the period (like in Shor's algorithm) from the factors?
One of the fundamental elements of Shor's algorithm is the calculation of the function:
$$
f_a(r) = a^r (mod \ N)
$$
where $N$ is the number to be factored and $a$ is a number chosen with some limitation. The quantum circuit is able to find the…
Doriano Brogioli
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9
votes
2 answers
What is (formally) a transversal operator?
This question concerns about a formal definition of transversal operator.
I understood that transversal operator are a group of operators which are efficient in terms of circuit depth and can be used as logical operators for stabilizer codes.…
Daniele Cuomo
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9
votes
2 answers
Given an orthogonal projection $\Pi$, is $\|\Pi(\sigma-\rho)\Pi\|_1\le\|\sigma-\rho\|_1$ true?
Suppose I have an arbitrary orthogonal projector $\Pi$ and two density operators $\rho, \sigma$. Is it true that:
$$ ||\Pi (\sigma - \rho) \Pi||_1 \le || \sigma - \rho ||_1 $$
where $||\cdot||_1$ denotes the trace norm?
NYG
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9
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1 answer
What are the differences between Qiskit's AerSimulator, QasmSimulator and StatevectorSimulator?
In Qiskit, we can see the names of available simulators with the command Aer.backends(). These include:
AerSimulator('aer_simulator')
AerSimulator('aer_simulator_statevector')
AerSimulator('aer_simulator_density_matrix')…
user3886914
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