The x+y Floquet code: A simple example for topological quantum computation in the path integral approach

• URL: http://arxiv.org/abs/2408.07265v2
• Date: Mon, 17 Mar 2025 02:06:09 GMT
• Title: The x+y Floquet code: A simple example for topological quantum computation in the path integral approach
• Authors: Andreas Bauer,
• Abstract summary: We construct a new fault-tolerant circuit for the toric-code phase by traversing its path integral on a $(x,y,z)$ cubic lattice in the $x+y$ direction.<n>We show how to incorporate boundaries and corners into the fault-tolerant circuit and how to perform topologically protected logic gates.
• Score: 0.7873629568804646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example: We construct a new fault-tolerant circuit for the toric-code phase by traversing its path integral on a $(x,y,z)$ cubic lattice in the $x+y$ direction. The circuit acts on qubits on a square lattice, and alternates between horizontal nearest-neighbor $CX$ gates and vertical nearest-neighbor $ZZ$ and $XX$ measurements. We show how to incorporate boundaries and corners into the fault-tolerant circuit and how to perform topologically protected logic gates. As a specific example, we consider performing a fault-tolerant logical $ZZ$ measurement via lattice surgery of two spatial rectangular blocks of our fault-tolerant circuit.

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