Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces

Abstract

In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.

Figures (4)

• Figure 1: (a) Process of clipping derivation of the $\{p,q\}$ tessellation. In the figure on the left, the original tessellation, in the figure on the right, in solid lines, the semi-regular $[2p,2p,q]$ tessellation, and in dashed lines the dual tessellation of $[2p,2p,q]$. (b) Incenter derivation process of the $\{p,q\}$ tessellation. In the figure on the left, there is the original tessellation; in the figure on the right, in solid lines, there is the semi-regular tessellation $[2p,2q,4]$; and in dashed lines, there is the dual tessellation of $[2p,2q,4]$.
• Figure 2: An example of a regular three colorable tessellation.
• Figure 3: The check measurements in the rounds.
• Figure 4: The logical operators of the two logical qubits of the Floquet code.

Theorems & Definitions (9)

• Theorem 2.1
• Proposition 1
• Proposition 2
• Corollary 1
• Proposition 3
• Definition 1
• Proposition 4
• Theorem 4.1
• proof