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1500 questions
6
votes
1 answer
Developing quantum circuits for specific quantum chemistry configurations
I am interested in learning more about the following: would it be possible for me to simulate a molecule consisting of copper ions through a quantum circuit?
And if so, can that circuit allow me to measure the decoherence time of that molecule?
I…
Enrique Segura
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2 answers
How to prepare a specific initial state of three qubits?
I would like to prepare the following initial state for variational quantum algorithms:
$$
\sin\theta_1 \sin\theta_2 \sin\theta_3 |000\rangle + \sin\theta_1 \sin\theta_2 \cos\theta_3 |001\rangle + \sin\theta_1 \cos\theta_2 |010\rangle + \cos\theta_1…
Ashy
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6
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Do we know anything about the computational complexity of the exchange-correlation functional?
Density functional theory is based on the Hohenberg-Kohn (HK) theorems and aims to compute the ground-state many-body wavefunction of a physical material and/or molecules.
To put it simply, the HK theorems show that there is a unique one-to-one…
Dr. T. Q. Bit
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6
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2 answers
Prove that the partial trace is equivalent to measuring and discarding
I'm trying to solve the following question:
"Prove that one way to compute $\mathrm Tr_B$ is to assume that someone has measured system
$B$ in any orthonormal basis but does not tell you the measurement outcome."
- "An Introduction to Quantum…
dylan7
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6
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1 answer
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
votes
1 answer
Extensions of product states
Given a product state $\rho_{AC} = \rho_A\otimes \rho_C$, what can we say about the structure of states $\rho_{ABC}$ that are extensions of $\rho_{A}\otimes \rho_C$? By extension I mean that $\text{tr}_B\rho_{ABC} = \rho_A \otimes \rho_C$, and I am…
Alex May
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6
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1 answer
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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4 answers
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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6
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1 answer
Why can any LOCC operation be written as $\sum_k (A_k\otimes B_k)\rho(A_k^\dagger\otimes B_k^\dagger)$?
This statement can be found in Vedral et al. 1997, eq. (1).
More precisely, given a bipartite state $\rho_{AB}$, they claim that any operation on $\rho_{AB}$ involving local operations plus classical communication can be written as
$$\sum_k…
glS
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6
votes
2 answers
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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6
votes
1 answer
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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6
votes
1 answer
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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6
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3 answers
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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1 answer
What is the unitary operator realizing a given CPTP operator
Complete Positive Trace Preserving Map (CPTP) operator is the most general operation that can be performed on a quantum system. This post mentioned that a CPTP operator is nothing but a unitary operator on the system after adding few ancilla bits. I…
satya
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