Latham Boyle (University of Edinburgh)

Date: Tue. April 23rd, 2024, 11:30 am-12:30 pm

The Penrose tiling is a quantum error correcting code

Abstract: I will begin by introducing Penrose tilings (“PTs”) and quantum error correcting codes (“QECCs”).  A PT is a remarkable, intrinsically non-periodic way of tiling the plane whose many beautiful and unexpected properties have fascinated physicists, mathematicians, and geometry lovers of all sorts, ever since its discovery in the 1970s.  A QECC is a fundamental way of protecting quantum information from noise, by encoding the information with a sophisticated type of redundancy.  Such codes play an increasingly important role in physics: in quantum computing (where they protect the delicate quantum state of the computer); in condensed matter physics (where they underpin the notion of topologically-ordered phases); and even in quantum gravity (where the “holographic” or “gauge/gravity” duality may be understood as such a code).

Although PTs and QECCs might seem unrelated, I will explain how PTs gives rise to (or, in a sense, *are*) a new type of QECC in which any local errors or erasures in any finite region of the code space, no matter how large, may be diagnosed and corrected.  Variants of this code (based on the cousins of the Penrose tiling, called the Ammann-Beenker and Fibonacci tilings) can live in a finite space, in discrete spin systems, and in an arbitrary number of spatial dimensions.

Host: Fernando Cornet Gomez