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### Can arbitrary matrices be decomposed using the Pauli basis? [duplicate]

Is it possible to decompose a hermitian and unitrary matrix $A$ into the sum of the Pauli matrix Kronecker products? For example, I have a matrix 16x16 and want it to be decomposed into something ...
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### Quantum circuit to implement matrix exponential

I want to build a circuit which will implement $e^{iAt}$, where $A= \begin{pmatrix} 1.5 & 0.5\\ 0.5 & 1.5\\ \end{pmatrix}$ and $t= \pi/2$. We see that $A$ can be written as, $A=1.5I+0.5X$. ...
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### Representation of rotation operators $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ about arbitrary axis for $3$ qubits

I was wondering in how to interpret and represent the operator $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ for a 3 qubit system in a circuit using qiskit. I was thinking I could just perform an ...
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### How to decompose a multi-target controlled gate?

I'm trying to replicate with qiskit the results of this paper in which basically they implement a quantum version of the Principal Component Analysis applying Quantum Phase Estimation algorithm in ...
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### How to perform a time evolution of a quantum state with Qiskit Aqua?

How can we perform a time evolution of a quantum state for a given Hamiltonian with qiskit Aqua operator flow? I'm interested in it due to its higher efficiency.
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### Is there a tool to get the quantum circuit corresponding to a sparse matrix?

If I know a sparse matrix, is there any tool that allows me to get the corresponding quantum circuit directly? If not what should I do? For example，I want to try hamilton simulation and I have the ...
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### How do I find the matrix and circuit equivalent to this transformation?

First I would like to find the matrix corresponding to the transformation and then implement it with rotational gates. How can I do it?