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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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Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 3): sampling
In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern:
FIG 3. Control operations for the quantum supremacy…
Sanchayan Dutta
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6
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Are inseparable states with positive partial transpose nonlocal?
In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, emphasis mine):
So, one is now faced with the problem…
glS
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6
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What is the point of building arithmetic circuits in a quantum computer?
My question simply is the following: is there any interests in building arithmetic circuits such as adders or multiplier on a quantum computer?
I'm asking this because it seems that classical computers are way better at doing arithmetic operations,…
Samuel Beaussant
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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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Non maximally entangled states for QKD
Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
Sujan Vijayaraj
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Do the eigenvalues of the Choi matrix have any direct physical interpretation?
Let $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ be a CPTP map, and let $J(\Phi)$ be its Choi representation.
As is well known, any such map can be written in a Kraus representation of the form
$$\Phi(X)=\sum_a p_a A_a X A_a^\dagger,\tag A$$
where…
glS
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6
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3 answers
Are there many practical problems for which Grover's algorithm beats the best heuristic classical algorithm?
It's well known that, given an oracle for a function $f$ from a very large set $S$ (of order $N \gg 1$) to $\{0, 1\}$, Grover's algorithm can find an element of $S$ that maps to 1 with $\sim \sqrt{N}$ oracle queries, whereas the best classical…
tparker
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Implementation of filter operation
If I want to implement the measurement operation corresponding to filtering, i.e.
$$
M_1=\left(\begin{array}{cc}1 & 0 \\ 0 & \alpha \end{array}\right)\qquad M_2=\left(\begin{array}{cc}0 & 0 \\ 0 & \sqrt{1-\alpha^2} \end{array}\right),
$$
how would I…
DaftWullie
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In what ways can qubits be used for applications that do not require entanglement?
Many good questions on this site have explored how entanglement lies at the boundary between the quantum world and the classical. For example in computational speedups, or teleportation or superdense coding, at least two qubits are entangled in some…
Mark Spinelli
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6
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A basic question on circuits and matrix representation
I have several (rather basic) questions on matrix representation of circuits and I would be very grateful to anyone that could clear up my confusion, thank you in advance.
1) When reading circuit diagrams I know that the input qubit goes in the left…
bhapi
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Maximum number of "almost orthogonal" vectors one can embed in Hilbert space
In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared to 1.
$$\left\langle V_i\middle|V_i\right\rangle…
user2669
6
votes
4 answers
Where I can read about protein folding on quantum computers with simple examples?
Where I can read about protein folding on quantum computer (Qiskit will be ideal variant) with simple examples? Thanks
mitrik_bnr
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6
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Second reflection in the Grover's algorithm
When interpreted geometrically, the second phase of the Grover's algorithm which corresponds to inversion about the mean is interpreted as reflection over the original state.
Can you explain intuitively the relationship between those two?
usercs
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6
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Can we amplify BPP algorithms with a random quantum circuit?
Suppose we are given a (univariate) polynomial $P$ of degree $d$, and we wish to determine if $P$ is identically $0$. A standard way to do this is to use a classical PRG to randomly sample $n$ bits, drawing a number $r$ uniformly from $[0,S]$; we…
Mark Spinelli
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