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1500 questions
6
votes
1 answer
Drawing tangent vectors to the Bloch sphere with qutip
I need to plot drawings of qubit dynamics on the Bloch sphere. I know QuTip allows to do such drawings but I specifically need to represent evolution velocities on the Bloch sphere so I need to draw tangent vectors. Is there a way I can do it with…
MrRobot
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6
votes
2 answers
Burnside Decomposition in Kuperberg's Hidden Shift
In "Another subexponential-time quantum algorithm for the dihedral hidden subgroup problem" (arXiv), Kuperberg writes that $\mathbb{C}[G]$ has a "Burnside decomposition" of
$$\mathbb{C}[G]\cong \bigoplus_{V} V^*\otimes V$$
where each $V$ is an…
Sam Jaques
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Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?
On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (arXiv), it is asserted that the Hilbert-Schmidt separability probabilities for the two-rebit,…
Paul B. Slater
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What is an example of a separable measurement that is not LOCC?
Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)?
Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM $\lbrace N_i \rbrace$ where the effects $N_i$…
MrRobot
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6
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Why is the quantum Fisher information $J_f=[f(\frac43-f)]^{-1}$ for maximally entangled qubit pairs?
I am reading paper Channel Identification and its Impact on Quantum LDPC Code Performance (arXiv) where the authors discuss the scenario where the decoder of a Quantum LDPC code uses an estimation of the depolarization probability of the channel in…
Josu Etxezarreta Martinez
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6
votes
1 answer
Phase estimation algorithm: probability bound of obtaining $m$
Note: Cross-posted on Physics SE.
Hi, I'm studying the quantum phase estimation algorithm from this book: M.A. Nielsen, I.L. Chuang, "Quantum Computation and Quantum Information", Cambridge Univ. Press (2000) [~p. 221].
He defines $b$ as the…
MementoMori
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6
votes
3 answers
Summing states of two qubit registers
I'm addressing the implementation with gates of an algorithm where there is the need of creating a qubit register $|\Psi\rangle$ starting from two input qubit registers $|a\rangle$ and $|b\rangle$, obtaining
$$|\Psi\rangle =…
Gianni
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6
votes
2 answers
How to understand the operators for watermarking schemes?
I am reading a research article (PDF) based on quantum image watermarking. The authors have defined some unitary transforms for the watermarking schemes, which is where I am having great difficulty in understanding. The operators defined…
fff
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votes
1 answer
What is the hidden subgroup in Simon's problem?
Given access to an oracle for a function $f:\{0,1\}^n\to\{0,1\}^n$ such that $f(x)=f(y)$ iff $x\oplus y\in\{0,s\}$, Simon's algorithm allows to recover $s$ in $\mathcal O(n)$ queries to the oracle.
The Wikipedia page also mentions how Simon's…
glS
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6
votes
2 answers
Implement Fredkin gate with square root of swap
I would like to implement a Fredkin gate based on square root of swap and one-qubit gates. In particular, I was hoping to find the exact gate named "?" in this circuit:
In addition, I want to avoid using C-SQSWAP. Otherwise, the solution would be…
Alex
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6
votes
0 answers
In what situation are three rounds of syndrome measurement required for fault-tolerance in the surface code?
I have heard multiple times the claim that three rounds of syndrome measurement required for fault-tolerance in the surface code. I'm not sure what situation would require this, as I think less would suffice. Unfortunately, all these mentions were…
James Wootton
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6
votes
1 answer
How does $x^{\frac{r}{2}} \equiv -1 \pmod {p_i^{a_i}}$ follow from "if all these powers of $2$ agree"?
From Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer (Shor, 1995) (arXiv), p. 15:
To find a factor of an odd number $n$, given a method for computing the order $r$ of $x$, choose a random $x \pmod…
Sanchayan Dutta
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6
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1 answer
The meaning of measurements in different bases
There are other similar questions. But I don't understand the answers.
Suppose I express $a|0⟩+b|1⟩$ in the form $\frac{c}{\sqrt2}(|0⟩+|1⟩)+\frac{d}{\sqrt 2}(|0⟩−|1⟩)$ where $a,b,c,d∈\mathbb C$. Then in my new basis the vector $|0⟩$ is represented…
bilanush
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6
votes
1 answer
Using parametrised values and 'Symbols' in Cirq
I'm just wondering how one should go about using parametrised values and the Symbol object that gets resolved at runtime?
For example, if I would like to implement the gate
$R_x(\theta) = e^{-i\theta/2}$, but would like to leave $\theta$ as a Symbol…
QC90
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6
votes
1 answer
If $|\psi\rangle, U|\psi\rangle$ are known, how many pairs of such qubits are required to find the operator $U$?
Assume that we know a quantum state and the result of applying an unknown unitary $U$ on it. For example, if the quantum states are pure qubits, we know $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ and…
raycosine
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