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1500 questions
6
votes
1 answer
Are nearly all pure two-qubit state entangled?
I am using the code below, utilizing QETLAB's RandomStateVector(4) and IsPPT, to generate a random state and to judge whether the state is entangled or separable:
clear all; clc;
for i = 1:30000
psi = RandomStateVector(4);
rho = psi*psi';
…
Sherlock
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6
votes
1 answer
Definition of magic $T$ and $H$ states: are there different definitions for them?
I am a bit confused by the definition of magic $T$ and $H$ states and I would like to check if their name is actually not uniformously spread in the litterature (or if I am not understanding something).
In the original paper about them, they are…
Marco Fellous-Asiani
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0 answers
Projective measurements: aftermath and restoration
I have some practical difficulties with projective measurements, so I'd welcome inspiration from others. This is beyond the question "Are true Projective Measurements possible experimentally?" in that I'm not aiming for perfection but for something…
agaitaarino
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6
votes
0 answers
Does Randomized Benchmarking characterize decoherence error?
In my understanding, Randomized Benchmarking (RB) generates a sequence of Clifford gates with different lengths and then characterizes the average error. Since RB is not sensitive to SPAM error, it doesn't characterize it.
My question is, does the…
peachnuts
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6
votes
1 answer
BHT algorithm implementation
Summary of Method
Amplitude Amplification Summary
The BHT algorithm uses amplitude amplification, a nice generalisation of Grover's algorithm, where there is a subset $G\subset X$ of good elements in the orthonormal basis $X$. Below is a brief…
Chris Long
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6
votes
1 answer
Uniformly distributed state in the Weyl basis
The Weyl basis (also known as Weyl-Heisenberg) is an orthonormal, unitary, and non-Hermitian basis for the Hilbert space of dimension $d$. The basis elements are given by
$$ U_{ab} = \sqrt{\omega^{ab}}X^aZ^b, $$
where $X,Z$ are the shift and clock…
Mateus Araújo
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6
votes
1 answer
What is the basic hardware gate library in the IBM & google?
I need to know what is the basic hardware gate library in hardware IBM and Google? I mean, which one of the gates can be implemented directly in the hardware. I would be very grateful if everyone helps me.
Moein sarvaghad
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6
votes
2 answers
What is the role of entanglement in quantum-computational speed-up?
The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is responsible for the exponential speed-up that quantum…
Ognyan Tsvetkov
- 127
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6
votes
1 answer
Proving that with probability 1 $NP \nsubseteq BQP$ with respect to random oracles
In the paper Strength and Weakneses of Quantum Computers (https://arxiv.org/abs/quant-ph/9701001) by Bennet, Bernstein, Brassard and Vazirani, it is shown the statement in the title (Theorem 3.5 in the Arxiv version). I'm confused on the logic of…
Apo
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6
votes
1 answer
Entanglement distillation by local operations and post-selection using one entanglement pair
Consider the state $|X\rangle = \sqrt{0.9} |00\rangle + \sqrt{0.1} |11\rangle$, shared between Alice and Bob, who are located far apart.
Alice brings in an ancilla qubit at her location (left-most qubit in the kets): $|X\rangle = \sqrt{0.9}…
user120404
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6
votes
1 answer
Confusion about random sampling of integers in Shor's algorithm
My understanding of Shor's algorithm is that you have to carry out the following steps if you are trying to factor $N$:
Chose a random number less than $N$. Let's call it $a$.
Calculate the period of $a^x \ \text{mod} \ N$. Let's call the period…
John Mathew
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6
votes
2 answers
How does using a superposition of 0 and 1 improve the processing capabilities of a quantum computer compared to classical computers?
Whenever I learn about quantum computing and qubits, it always talks about the superposition principle and that the qubits can be in both states 0 and 1 simultaneously, thus claiming that quantum computers have processing capability way more than…
revittrk
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6
votes
2 answers
Can one always find purifications which preserve equality of statistical mixtures?
When pure states $|\psi_1⟩$, $|\psi_2⟩$ and $|\phi_1⟩$, $|\phi_2⟩$ in $\mathcal{H}_A \otimes \mathcal{H}_B$ have identical statistical mixtures
$$\frac{1}{2}(|\psi_1⟩⟨\psi_1| + |\psi_2⟩⟨\psi_2|) = \frac{1}{2}(|\phi_1⟩⟨\phi_1| + |\phi_2⟩⟨\phi_2|)…
Gv26
- 103
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6
votes
2 answers
What are the conditions ensuring a two-qubit density matrix is positive semidefinite?
I've seen some papers writing
$$\rho=\frac{1}{4}\left(\mathbb{I} \otimes \mathbb{I}+\sum_{k=1}^{3} a_{k} \sigma_{k} \otimes \mathbb{I}+\sum_{l=1}^{3} b_{l} \mathbb{I} \otimes \sigma_{l}+\sum_{k, l=1}^{3} E_{k l} \sigma_{k} \otimes…
narip
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6
votes
1 answer
How is the state preparation Unitary in initialize selected?
Normally, in order to prepare the Bell state $\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$, we can simply make a circuit with a Hadamard gate on $|0\rangle$ followed by a CNOT gate on $|1\rangle$. However, initializing the Bell state and then using…
sven
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