Elucidating the Physical and Mathematical Properties of the Prouhet-Thue-Morse Sequence in Quantum Computing

TL;DR

This paper investigates the Prouhet-Thue-Morse sequence's mathematical properties and its applications in quantum computing, including error correction, quantum memories, and connections to number theory, highlighting its significance for advancing quantum technologies.

Contribution

It reveals the PTM sequence's role in quantum error correction, noise-resistant memories, and its mathematical connections, offering new insights into quantum system structures.

Findings

PTM sequence aids in quantum error correction

PTM sequence appears in Ising systems for quantum memory

Links between PTM sequence and number theory established

Abstract

This study explores the applications of the Prouhet-Thue-Morse (PTM) sequence in quantum computing, highlighting its mathematical elegance and practical relevance. We demonstrate the critical role of the PTM sequence in quantum error correction, in noise-resistant quantum memories, and in providing insights into quantum chaos. Notably, we demonstrate how the PTM sequence naturally appears in Ising X-X interacting systems, leading to a proposed robust encoding of quantum memories in such systems. Furthermore, connections to number theory, including the Riemann zeta function, bridge quantum computing with pure mathematics. Our findings emphasize the PTM sequence's importance in understanding the mathematical structure of quantum computing systems and the development of the full potential of quantum technologies and invite further interdisciplinary research.