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1500 questions
6
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1 answer
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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6
votes
2 answers
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
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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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6
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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
1 answer
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
votes
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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6
votes
1 answer
What is the general method for creating real gate sequences from mathematical algorithms?
Background
I have been doing research on quantum computing on my own for over a year now and I feel like I may have missed a fundamental step. I have no idea how to take a mathematical algorithm and create an equivalent gate sequence for an actual…
Jadon Erwin
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6
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0 answers
What is quantum tomography useful for?
First time poster and just started with quantum computing for my master thesis, so I'm sorry if the question seems obvious.
I understand that the tomography is used to reconstruct the state and/or process of a quantum circuit, without directly…
Oliver Müller
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6
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2 answers
How can I find a Clifford+T approximation of an arbitrary one qubit gate in Qiskit?
I know the Solovay-Kitaev algorithm can achieve this. Is there an implementation of this or any other algorithm for the same task in Qiskit? Or perhaps some other library that interfaces well with Qiskit?
shashvat
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