Homological Quantum Rotor Codes - Logical Qubits from Torsion

Explore a comprehensive lecture on homological quantum rotor codes and their applications in quantum computing. Delve into the formal definition of these codes, which utilize multiple quantum rotors to encode logical information. Understand how they generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes. Discover the unique ability of these codes to encode both logical rotors and logical qudits within the same code block, depending on the homology of the underlying chain complex. Examine specific examples, such as codes based on tessellations of the real projective plane or Möbius strip, which can encode a qubit. Investigate the distance scaling for these codes, considering the concept of logical operator spreading by continuous stabilizer phase-shifts. Learn about various constructions of homological quantum rotor codes based on 2D and 3D manifolds and products of chain complexes. Explore potential hardware implementations using superconducting devices, including the 0-π-qubit and Kitaev's current-mirror qubit (Möbius strip qubit). Gain insights into possible extensions and future developments in this field of quantum coding theory.