Rotor code 

A rotor analogue of the Pauli string basis for qubit codes consists of rotor generalized Pauli operators. For a single rotor, its elements are products of exponentials of the rotor's angular position (\(\hat\phi\)) and angular momentum (\(\hat L\)) operators, acting on the rotor's angular position states \(|\phi\rangle\) for \(\phi\in U(1)\) as \begin{align} e^{-i\varphi\hat{L}}\left|\phi\right\rangle =\left|\phi+\varphi\right\rangle \,\,\text{ and }\,\,e^{i\ell\hat{\phi}}\left|\phi\right\rangle =e^{i\ell\phi}\left|\phi\right\rangle ~, \tag*{(1)}\end{align} where \(\varphi\in U(1)\) and \(\ell\in\mathbb{Z}\). For multiple rotors, error set elements are tensor products of elements of the single-rotor error set. For multiple rotors, error set elements are tensor products of elements of the single-rotor error set, characterized by vectors of angle and integer coefficients multiplying vectors of angular momentum (\(\hat\boldsymbol{L}\)) and angular position (\(\hat\boldsymbol{\phi}\)) operators.