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What are the eigenstates of an operator?

An eigenstate of an operator $U$ is a state $|v\rangle$ such that $U|v\rangle = c*|v\rangle$ Given a matrix $U$, the eigenvalues of $U$ are the values $\lambda \in \mathbb{C}$ such that $U |\psi \...
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Surface Code Eigenstates as Circles

All those three cases are different quantum error correction codes. First toric code has periodic boundary condition, but second one which is surface code has boundaries. Lastly third one is rotated ...
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How to find the eigenstates of a general $2\times 2$ Hermitian matrix?

You can find this from the general expressions for eigenvalues and eigenvectors of an arbitrary $2\times2$ matrix. Let $$A\equiv\begin{pmatrix}a&b\\c&d\end{pmatrix}.$$ You can readily verify ...
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1 vote

Solving Hamiltonian eigenvalue problem

Have you ever seen a derivation of Grover's search? The approach that you want is very similar. Start by defining two states, perhaps $$ |a\rangle=|\psi_N\rangle, \qquad |b\rangle=|m\rangle-|a\rangle\...
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Solving Hamiltonian eigenvalue problem

You can solve this by referring to this question. To estimate the eigenvalues of $H\left( s \right) =\left( 1-s \right) H_0+sH_m=I-\left( 1-s \right) |\psi _N\rangle \langle \psi _N|-s|m\rangle \...
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