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1500 questions
7
votes
2 answers
Why does a controlled gate not constitute a measurement?
I have recently listened to a talk on quantum computing and was fascinated to learn about IBM Q Experience. Between the explanations in the User Guide and in Nielsen's book, I came to the following question:
Why does a controlled gate not act as a…
DK2AX
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7
votes
1 answer
Are 20 repetitions of Sycamore's one- and 2-qubit gates sufficient to produce a uniformly random state?
In the answer to this question about random circuits, James Wootton states:
One way to see how well we [fully explore the Hilbert space] is to focus on just randomly producing $n$ qubit states. These should be picked uniformly from all possible…
Mark Spinelli
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7
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2 answers
How many ancilla qubits to use with Multiple-Control Toffoli (mct) gate in Qiskit?
The Multiple-Control Toffoli (mct) gate takes as input:
1. a register containing the control qubits,
2. the target qubits and
3. a register containing ancilla qubits.
I don't know how many ancilla qubits I need to pass in for a number of $n$…
Sorin Bolos
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7
votes
3 answers
Is there a quantum operation whose output is always orthogonal to the input?
I'm trying to show/convince myself the following statement is correct (I haven't been able to find any similar posts):
"There is no reversible quantum operation that transforms any input state to a state orthogonal to it."
I can see how this could…
fortymod
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7
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3 answers
How to prove that antipodal points on the Bloch sphere are orthogonal?
I started by assuming two antipodal states
$$
|(\theta,\psi)\rangle = \cos\dfrac{\theta}{2}|0\rangle + \sin\dfrac{\theta}{2}e^{i\psi}|1\rangle\\
|(\theta+\pi,\psi+\pi)\rangle= \cos\dfrac{\theta+\pi}{2}|0\rangle +…
apen
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7
votes
1 answer
Why use U2 and U1 gate in IBM quantum computers?
I was wondering why IBM's computer were using U1 and U2 gates as part of there basis gates since as I understood, they are particular cases of the U3 gate. Why not just use U3 gate instead ?
Thanks in advance
Samuel Beaussant
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7
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1 answer
Given $n-k$ stabiliser generators, how can we find an additional $k$ commuting generators?
I am trying to understand "Stabilizer codes construction" in Nielsen & Chuang (page 465). Below, we're working in a Hilbert space of dimension $2^n$, and $G_n$ is the $n$-qubit Pauli group.
A stabilizer group $S=\langle g_1,...,g_{n-k} \rangle…
Marco Fellous-Asiani
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7
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1 answer
Looking for papers that are pessimistic about the feasibility of a quantum computer
I'm actually searching two types of documents (could be the same):
1) A synthesis about all the main gap/problems that make the physical realisation of a quantum computer actually infeasible.
2) Something more polemical that criticizes the point of…
Ievgeni
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7
votes
1 answer
Is the diamond norm subadditive under composition?
The diamond norm distance between two operations is the maximum trace distance between their outputs for any input (including inputs entangled with qubits not being operated on).
Is it the case that the Diamond norm is subadditive under…
Craig Gidney
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7
votes
2 answers
Do the Kraus operators of a CPTP channel need to be orthogonal?
Let $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ be a CPTP map.
Any such channel admits a Kraus decomposition of the form
$$\Phi(X)=\sum_a A_a X A_a^\dagger,$$
for a set of operators $A_a\in\mathrm{Lin}(\mathcal X,\mathcal Y)$ satisfying $\sum_a…
glS
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7
votes
1 answer
How to understand a phase operation between 2 Hadamard gates?
I would like to understand this image, of a "payload preparation" gate. A single H gate will create a superposition, while the phase will rotate 45 degrees. What does the second H gate do in this commonly used subcircuit?
neutrino
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7
votes
2 answers
Derive phase damping quantum operation
I am reading about the phase damping quantum operation on page 384 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition).
Nielsen & Chuang derived the operation elements from an interaction model of two…
Conn-CaoYK
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7
votes
2 answers
No-cloning theorem does not seem precise
As per wikipedia, no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state.
But from which distribution is this unknown quantum state sampled from? What does the counterfeiter know about this…
satya
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7
votes
4 answers
How to create an Ising coupling gate with Qiskit?
I'm trying to apply a time evolution algorithm for a physical system I'm trying to simulate on QISkit, however, in order to do that, I need to use the so-called Ising coupling gate:
$I=\begin{pmatrix}
e^{ia} & 0 & 0 &0 \\
0 & e^{-ia} & 0 & 0 \\
0 &…
Jorge Rodríguez Peña
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7
votes
1 answer
Showing that Matrix Inversion is BQP-complete - HHL Algorithm
I am trying to understand an argument that Matrix Inversion is BQP-complete for certain conditions on the matrix. This is explained here on page 39 (this paper is a primer to the HHL algorithm and gives some more detailed calculations, more detail…
IntegrateThis
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