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7
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Why is the quantum Fisher information for pure states $F_Q[\rho,A]=4(\Delta A)^2$?
Assume that a density matrix is given in its eigenbasis as $$\rho = \sum_{k}\lambda_k |k \rangle \langle k|.$$ On page 19 of this paper, it states that the Quantum Fisher Information is given as $$F_{Q}[\rho,A] = 2…
John Doe
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7
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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
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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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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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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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2 answers
How to find the reduced density matrix of a four-qubit system?
I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix of system A.
I know I could separately extract…
meelszz
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7
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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
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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
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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
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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
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2 answers
Find the quantum operation corresponding to a given unitary evolution and projective measurement
I'm trying to (understand and) solve this problem from Nielsen and Chuang's Quantum Computation and Quantum Information.
Exercise 8.4: (Measurement) Suppose we have a single qubit principal system, interacting with a single qubit environment…
Bashir
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7
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2 answers
Using the HHL algorithm to compute $A |b \rangle$ instead of $A^{-1} |b \rangle$
In the paper "Compiling basic linear algebra subroutines for quantum computers"
here, they discuss (page 2 bottom right) using the HHL algorithm to multiply a vector by a matrix. However, after having read the HHL09 paper, what is being estimated…
IntegrateThis
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7
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Equivalent determinant condition for Peres-Horodecki criteria
The Peres-Horodecki criteria for a two-qubit state states that if the smallest eigenvalue of the partial transpose of the state is negative, it is entangled, else it is separable.
According to this paper (arXiv) page 4, left side, the following is…
Mahathi Vempati
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What is the motivation for Weyl matrices in quantum information theory?
From Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4, p. 11:
Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is the Weyl operator basis, which consists of…
Sanchayan Dutta
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