# Questions tagged [matrix-representation]

For questions about matrix representations of quantum gates.

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### I have two Choi matrix I suspect be equivalent. Can I manipulate them?

I am performing a process tomography over a protocol I suspect to be equivalent to the $CS$ gate. To compare basic operators I usually compute the Choi matrix of the target gate -- which in this case ...
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### CNOT circuit synthesis with Gauss elimination. Explanation and beyond?

This paper introduces to the synthesis of a (optimal) circuit of CNOTs only; starting from a parity map encoded into a matrix. It is based on Gaussian Elimination. This is an important result, which ...
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### Easy way to look at matrix in computational and Hadamard bases?

Given a $2^n \times 2^n$ matrix $M$ of classical data (so, just a bunch of numbers), is there any way to query that matrix in both the computational basis (basically, $M$) and the Hadamard basis, i.e. ...
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### Prove $\sum_{ij}(\mathcal{A_G})_{ij}(|\rho\rangle\!\rangle)_j|i\rangle\!\rangle={\cal A}_G|\rho\rangle\!\rangle$ in the Pauli-Liouville representation

Define the Pauli-Liouville representation of a (linear) map $\mathcal{G}$ as $\mathcal{A_G}$, which has components \begin{equation}\label{2} (\mathcal{A_G})_{ij}:=\mathrm{tr}[P_i\mathcal{G}(P_j)] \...
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### How to prove that these equations are correct for $CZ$ and $CX$?

How do I prove that the equation on the right is $CX$ and $CZ$ gate? I don't think that reaching the matrix of the CX or CZ is possible with the given equation. For (b) I keep getting $I \otimes I$ ...
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### Generic circuit for signature matrix

Consider a set $A = \{a_0,a_2,\ldots,a_{k-1}\} \subset [N] := \{0,1,\ldots,N-1\}$. Consider the diagonal matrix \begin{equation} R := I - 2 \sum_{a\in A} |a\rangle\langle a|, \end{equation} which is ...
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### Question about performing VQE with an embedded Hamiltonian

Say I have a physical Hamiltonian $\mathcal{H}$ which is $D$-dimensional and I encode it into a larger matrix $M$ which is $\Delta$-dimensional. In the cases I care about $\Delta$ is strictly greater ...
In this and other papers relating to the kicked top model, it is mentioned that spin coherent states can be expressed as: $$\left|\theta,\phi\right>=R(\theta,\phi)\left|j,j\right>$$ for given ...