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Understanding the definition of quantum neural network of Abbas et al. 2020
My Question based on this Paper https://arxiv.org/pdf/2011.00027.pdf "Power of Quantum Neural Networks" - Section 2.
So I know that there are different ways to implement Neural Networks into QNNs. In that paper, they used the QNN as a subclass from…
Jeff24
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6
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How to compute the average value $\langle X_1 Z_2\rangle$ for a two-qubit system?
Show that the average value of the observable $X_1Z_2$ in a two-qubit system measured in the state $(|00\rangle + |11\rangle)/\sqrt{2}$ is zero.
How would we approach this question? I understand that $X_1$ means $\sigma_1$ acting on the first…
Alk
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6
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Quantum Algorithm SAT structure
"Quantum magic won't be enough" (Bennett et al. 1997)
If you throw away the problem structure, and just consider the space of $2^n$ possible solutions, then even a quantum computer needs about $\sqrt{2^n}$ steps to find the correct one (using…
Didix
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6
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Quantum Circuit for $e^{iAt}$ Hamiltonian Simulation in HHL algorithm
In HHL algorithm, there is a step in Quantum Phase Estimation where we have to apply powers of $e^{iAt}$ to the register (see pic). I am not able to understand how to find the quantum circuit corresponding to this unitary transformation i.e. if I…
quankid
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6
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VQE - How to get from expectation value to eigenvalue?
In VQE, for a single-qubit Hamiltonian, I can use a standard ansatz to make a state $\psi$ and use two products to compute the expectation value $\langle\psi|{\cal H}|\psi\rangle$. As I vary the parameters to the ansatz I get very close to the…
rhundt
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6
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How is a promise gap related to a spectral gap?
In linear algebra one often concerns oneself with the spectral gap of a given matrix, which may be defined as the difference between the smallest and second-smallest eigenvalue (or, depending on convention and context, between the largest and…
Mark Spinelli
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6
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2 answers
How to reason about absorbing Pauli Product rotations into measurements?
In this image, the orange box refers to the operator $\exp(-i P \frac{\pi}{4})$ and the blue box refers to the Pauli Measurement $P'$. The idea behind these rules is to show how all the Pauli Product $\frac{\pi}{4}$ rotations at the end of the…
shashvat
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6
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Can I simultaneously plot 2 vectors on a single Bloch sphere and rotate the angle of visualization?
I'm trying to plot 2 vectors on the same Bloch sphere. From the qiskit documentation here, we can find plot_bloch_vector(bloch, title='', ax=None, figsize=None, coord_type='cartesian'). So I'm not quite sure if we could plot 2 vectors (say [0,0,1]…
ZR-
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Is there a way to use titles on circuit drawing?
As you may know, one can use barriers in Qiskit to seperate gates on a circuit in a proper way. So, I was wondering is there a way to give a title to these "sections" seperated by barriers?
I provide an example in Figure below. Titles does not need…
Saba
- 63
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6
votes
2 answers
Exponentiating Pauli matrices using trapped ion native gates (single-qubit rotations + XX, YY, ZZ)
I'm wondering what are the known/good/standard ways of exponentiating Pauli terms (i.e. constructing circuits, which implement $\exp(i\alpha XIIZYI...)$) using gates supported by trapped ion quantum computers — single-qubit rotations and…
mavzolej
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6
votes
1 answer
Claimed "potential revenue" from machine learning in 2023?
In this plot:
taken from here, IonQ is claiming to have a potential application in machine learning by 2023. What applications could they have in mind?
From what I understand, modern error correction prevents obtaining speedup from any quadratic…
Steven Sagona
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What are examples of zero capacity quantum channels with Choi rank less than $d$?
All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given channel:
A channel is said to be PPT if its Choi…
mathwizard
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6
votes
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How to prove that a naive quantum random walk is non-unitary
A 2000 paper by Nayak and Vishwanath provides an analysis of the dynamics of quantum random walks. In this paper, they mention a "naive" approach to defining a walk. I include the quote as follows:
In direct analogy, one may naively try to define…
Shadow43375
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6
votes
2 answers
In Stinespring dilation, can we always use a mixed state as the ancilla?
The Stinespring dilation theorem states that any CPTP map $\Lambda$ on a system with Hilbert space $\mathcal{H}$ can be represented as $$\Lambda[\rho]=tr_\mathcal{A}(U^\dagger (\rho\otimes |\phi\rangle\langle \phi|)U)$$ where $\mathcal{A}$ is an…
Jacob Drori
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6
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2 answers
How do I decompose the given $4\times 4$ matrix in terms of Pauli matrices?
I have been working on a question where I have to decompose this matrix in terms of Pauli Matrices:
\begin{bmatrix}1&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&1\end{bmatrix}
I already have a solution but I don't understand the solution I've been given, this is…
Sire
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