The X-Cube Floquet Code

• URL: http://arxiv.org/abs/2211.05784v1
• Date: Thu, 10 Nov 2022 18:59:55 GMT
• Title: The X-Cube Floquet Code
• Authors: Zhehao Zhang, David Aasen, Sagar Vijay
• Abstract summary: We introduce the X-Cube Floquet code, a dynamical quantum error-correcting code where the number of encoded logical qubits grows with system size. Within a single Floquet cycle, the codespace between that of the X-Cube switches fracton order and layers of entangled, two-dimensional toric codes. The encoded logical qubits' dynamics are analyzed, and we argue that the new code has a non-zero error threshold.
• Score: 2.191505742658975
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inspired by the coupled-layer construction of the X-Cube model, we introduce the X-Cube Floquet code, a dynamical quantum error-correcting code where the number of encoded logical qubits grows with system size. The X-Cube Floquet code is defined on a three-dimensional lattice, built from intersecting two-dimensional layers in the $xy$, $yz$, and $xz$ directions, and consists of a periodic sequence of two-qubit measurements which couple the layers together. Within a single Floquet cycle, the codespace switches between that of the X-Cube fracton order and layers of entangled, two-dimensional toric codes. The encoded logical qubits' dynamics are analyzed, and we argue that the new code has a non-zero error threshold. We provide a new Hamiltonian realization of the X-Cube model and, more generally, explore the phase diagram related to the sequence of measurements that define the X-Cube Floquet code.

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