The Penrose Tiling is a Quantum Error-Correcting Code
- URL: http://arxiv.org/abs/2311.13040v2
- Date: Thu, 25 Jan 2024 15:48:10 GMT
- Title: The Penrose Tiling is a Quantum Error-Correcting Code
- Authors: Zhi Li, Latham Boyle
- Abstract summary: A quantum error-correcting code (QECC) is a clever way of protecting quantum information from noise, by encoding the information with a sophisticated type of redundancy.
In this paper we point out that PTs give rise to (or, in a sense, are) a remarkable new type of QECC.
In this code, quantum information is encoded through quantum geometry, and any local errors or erasures in any finite region, no matter how large, may be diagnosed and corrected.
- Score: 3.7536679189225373
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Penrose tiling (PT) is an intrinsically non-periodic way of tiling the
plane, with many remarkable properties. A quantum error-correcting code (QECC)
is a clever way of protecting quantum information from noise, by encoding the
information with a sophisticated type of redundancy. Although PTs and QECCs
might seem completely unrelated, in this paper we point out that PTs give rise
to (or, in a sense, are) a remarkable new type of QECC. In this code, quantum
information is encoded through quantum geometry, and any local errors or
erasures in any finite region, no matter how large, may be diagnosed and
corrected. We also construct variants of this code (based on the Ammann-Beenker
and Fibonacci tilings) that can live on finite spatial tori, in discrete spin
systems, or in an arbitrary number of spatial dimensions. We discuss
connections to quantum computing, condensed matter physics, and quantum
gravity.
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