Floquetifying the Colour Code
arXiv:2307.11136 · doi:10.4204/EPTCS.384.14
Abstract
Floquet codes are a recently discovered type of quantum error correction code. They can be thought of as generalising stabilizer codes and subsystem codes, by allowing the logical Pauli operators of the code to vary dynamically over time. In this work, we use the ZX-calculus to create new Floquet codes that are in a definable sense equivalent to known stabilizer codes. In particular, we find a Floquet code that is equivalent to the colour code, but has the advantage that all measurements required to implement it are of weight one or two. Notably, the qubits can even be laid out on a square lattice. This circumvents current difficulties with implementing the colour code fault-tolerantly, while preserving its advantages over other well-studied codes, and could furthermore allow one to benefit from extra features exclusive to Floquet codes. On a higher level, as in arXiv:2303.08829, this work shines a light on the relationship between 'static' stabilizer and subsystem codes and 'dynamic' Floquet codes; at first glance the latter seems a significant generalisation of the former, but in the case of the codes that we find here, the difference is essentially just a few basic ZX-diagram deformations.
arXiv commentIn Proceedings QPL 2023, arXiv:2308.15489
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- Perturbative stability and error correction thresholds of quantum codes
- Dynamical Logical Qubits in the Bacon-Shor Code
- XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
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- Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
- High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
- ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
- Contextuality of Quantum Error-Correcting Codes
- String Diagrams for Defect-Based Surface Code Computing
- Competing automorphisms and disordered Floquet codes
- A dataflow programming framework for linear optical distributed quantum computing
- Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
- A dynamic circuit for the honeycomb Floquet code
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