Clifford Operations and Homological Codes for Rotors and Oscillators

Explore a 23-minute conference talk from the 19th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2024) that delves into quantum information processing fundamentals for planar rotors. Learn how rotor wavefunctions can be interpreted as periodically identified wavefunctions of harmonic oscillators, leading to the development of the n-rotor Clifford group. Discover the classification of homological rotor error-correcting codes and various rotor states based on Clifford operation equivalence. Understand the mapping of homological rotor codes and Clifford operations back to oscillators, revealing new multimode homological bosonic codes that protect against dephasing and occupation number changes. Examine techniques for non-destructive oscillator phase measurement using conditional occupation-number addition and post-selection, along with various implementations of GKP-stabilizer codes for both rotors and oscillators. Presented by researchers Yijia Xu, Yixu Wang, and Victor V. Albert at OIST, Japan, this theoretical quantum information science presentation advances understanding of quantum error correction and information processing primitives.