The Unexpected Connection Between Quantum Computing and Aperiodic Tilings

Friday - March 1 2024, 09:48 UTC - 1 year ago

Aperiodic tilings, a type of tiling set with endlessly unique patterns, have been studied by mathematicians since the 1960s. Recently, two physicists discovered a connection between aperiodic tilings and quantum error-correcting codes, a critical component of future quantum computers. This unexpected link highlights the potential for cross-disciplinary inspiration and innovation in both fields.

The simplicity of square tiles used in bathroom tiling projects may be deceiving - it turns out that from a mathematical perspective, square tilings are quite dull. Unlike aperiodic tilings, which exhibit fascinating and complex behavior, square tilings offer little new to discover as the pattern remains the same when shifted over by a fixed amount. Aperiodic tilings, on the other hand, have been captivating mathematicians for over half a century. These tilings provide infinitely many unique patterns that never repeat, no matter how the tiles are arranged.

Aperiodic tilings are a type of tiling set that exhibit non-repeating patterns. They were first studied in the 1960s, and have since inspired research in various fields, from mathematics and physics to computer science and crystallography. One of the most famous types of aperiodic tiling is the Penrose tiling, discovered by mathematician and future Nobel laureate Roger Penrose in the 1970s. It uses two diamond-shaped tiles, and no matter how they are arranged, the pattern never repeats.

While aperiodic tilings may seem disconnected from other branches of science, two physicists have recently discovered a surprising link between these tilings and quantum computing. In a paper published in November 2020, they showed how Penrose tilings and other aperiodic tilings can be transformed into quantum error-correcting codes, a critical component of future quantum computers.

Quantum computers are designed to work with quantum bits (or qubits), which can hold much more information than traditional computers. However, qubits are extremely fragile, and even the slightest error can cause them to collapse, ruining any computations in progress. Quantum error-correcting codes, first proposed by mathematician Peter Shor in 1995, help protect against these errors by encoding information in a way that is resilient to them. The researchers found that the structure of aperiodic tilings shares some key properties with quantum error-correcting code, making them a potential source of inspiration for future quantum computing advances.

The connection between aperiodic tilings and quantum computing may seem unlikely, but it's just one example of how seemingly unrelated fields can intersect and inspire new ideas and innovations. As researchers continue to explore the potential of aperiodic tilings and quantum computing, we can expect to see even more unexpected connections and advancements in both fields.