Planar Floquet Codes

Abstract

A protocol called the "honeycomb code", or generically a "Floquet code", was introduced by Hastings and Haah in \cite{hastings_dynamically_2021}. The honeycomb code is a subsystem code based on the honeycomb lattice with zero logical qubits but such that there exists a schedule for measuring two-body gauge checks leaving enough room at all times for two protected logical qubits. In this work we show a way to introduce boundaries to the system which curiously presents a rotating dynamics but has constant distance and is therefore not fault-tolerant.