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1500 questions
7
votes
1 answer
Quantum teleportation with "noisy" entangled state
This is actually an exercise from Preskill (chapter 4, new version 4.4). So they are asking about the fidelity of teleporting a random pure quantum state from Bob to Alice, who both have one qubit of the following system ("noisy" entangled…
CFRedDemon
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votes
2 answers
Hidden shift problem as a benchmarking function
I encountered the hidden shift problem as a benchmarking function to test the quantum algorithm outlined in this paper / arXiv (the problem also features here / arXiv).
There are two oracle functions $f$, $f'$ : $\mathbb{F}_{2}^{n}
\rightarrow \{…
BlackHat18
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7
votes
1 answer
Understanding classical vs. quantum channel capacities
The classical channel capacity ($C_{ea}$) and the quantum channel capacity ($Q$) as defined here (eqs. 1 and 2) are given by
\begin{equation}
C_{ea} = \text{sup}_{\rho} \Big[S(\rho) + S(\Phi_t \rho) - S(\rho,t)\Big],
\end{equation}
and…
Tobias Fritzn
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7
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2 answers
Why can't a quantum computer strongly simulate itself?
We can strongly simulate a quantum circuit if we can estimate the probability of measuring $|0^n\rangle$, say, at the end to within some fixed relative error.
Now, by measurement, a quantum computer can certainly weakly simulate itself, i.e.…
wdc
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7
votes
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Proof of the optimality of Grover's algorithm
I am currently working on the proof of Grover's algorithm, which states that the runtime is optimal.
In Nielsen they say, the idea is to check whether $D_k$ is restricted and does not grow faster than $O(k^2)$. Now in Nielsen, an inductive proof is…
P_Gate
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7
votes
1 answer
Quantum teleportation of a state, from one of two bases
I'm watching Christian Schaffner's talk on quantum position-based cryptography (link here) and have a question about a particular application of teleportation.
At about the 16:40 mark, he seems to say something along these lines (notation is…
NNN
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votes
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What is maximum circuit depth and size IBM Q5 and Q16 could handle?
I'm trying to implement a couple of algorithms on ibmq_16_melbourne, so I need to know if this device is able to handle with depth and size of my current circuit or not.
For example, the circuit size is 300 and depth is 99.
C-Roux
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7
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1 answer
Quantum speedup without entanglement
Is there an instance of a quantum algorithm that is faster than its classical counterpart, but doesn't use entanglement, only superposition?
psitae
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What role do Hecke operators and ideal classes perform in “Quantum Money from Modular Forms?”
Cross-posted on MO
The original ideas from the 70's/80's - that begat the [BB84] quantum key distribution - concerned quantum money that is unforgeable by virtue of the no-cloning theorem. A limitation was that the quantum money required the bank…
Mark Spinelli
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7
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1 answer
Quantum algorithm for linear system of equations (HHL) - Final Step: How can I find my vector of solution $|x\rangle$?
I'm working on solving a linear system with the quantum algorithm HHL. I don't understand how I can recover my vector $|x\rangle$ of real solution of the system starting from the states measured with ancilla qubit in $|1\rangle$.
I found something…
Nicolò Cangini
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7
votes
1 answer
Connection between the definitions of concurrence for a two-qubit states
The concurrence for a state $\rho$ as defined here is
\begin{equation}
C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}.
\end{equation}
Where $\lambda_i$ are the eigenvalues of matrix $ \sqrt{\sqrt{\rho} \tilde{\rho} \sqrt{\rho}}$,…
Tobias Fritzn
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7
votes
1 answer
Interaction of an RF pulse with transmon qubit
When an RF pulse is interacting on resonance with a transmon qubit, it leads to rotation of the qubit around an axis in the XY plane (in a reference frame rotating in the transition frequency of the qubit). What is the exact relation between the…
Qexp
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7
votes
2 answers
A two qubit state in a special form
How can a pure two-qubit state $|\psi\rangle = a |00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$, be written in the following form
\begin{equation}
|\psi_{\alpha}\rangle = \sqrt{\alpha}|01\rangle + \sqrt{1-\alpha}…
Tobias Fritzn
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7
votes
0 answers
Construction of optimal ensemble to show quantum steerability
In Wiseman et al. (2007), in the process of deriving necessary and sufficient conditions for the steerability of some classes of states, the authors show (lemma 1, page 3) how to construct an optimal ensemble $F^\star=\{\rho_\xi^\star\mathscr…
glS
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7
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Is quantum computer equivalent to Turing machine with matrix multiplication oracle?
Since quantum computer with $n$ qubits is described by a $2^{n}\times2^{n}$ unitary matrix is it equivalent to an oracle that can do multiplication of large matrix and return $n$ numbers computed from it in a time polynomial by $n$.
And if yes how…
a user
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