Analog surface code[1]

Cousins

• Modular-qudit surface code— The tiger surface code can be thought of as a realization of the \(q\to\infty\) \(\mathbb{R}\) oscillator limit [4] of the qudit surface code as a bosonic stabilizer code.
• Abelian topological code— The analog surface code realizes a straightforward extension of the modular-qudit surface code to infinite local dimension, \(q\to\infty\) [4]. The code realizes a phase of 2D \(\mathbb{R}\) gauge theory. There are two types of anyons, \(e\) and \(m\), with each type being valued in a continuous domain as opposed to \(\mathbb{Z}_q\) for the qudit surface code.
• Compactified \(\mathbb{R}\) gauge theory code— The compactified \(\mathbb{R}\) gauge theory code can be obtained from the analog surface code by condensing certain anyons [5]. This results in a pinning of each mode to the space of periodic functions, which make up a physical rotor, and can be thought of as compactification of the 2D \(\mathbb{R}\) gauge theory phase realized by the analog surface code.
• \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code— The \(U(1)_{2n} \times U(1)_{-2m}\) Chern-Simons GKP code can be obtained from the analog surface code by condensing certain anyons [5].
• GKP-surface code— The GKP-surface code can be obtained from the analog surface code by condensing certain anyons [5].