TY  - JOUR
AU  - Vuillot, Christophe
AU  - Ciani, Alessandro
AU  - Terhal, Barbara M.
TI  - Homological Quantum Rotor Codes: Logical Qubits from Torsion
JO  - Communications in mathematical physics
VL  - 405
IS  - 2
SN  - 0010-3616
CY  - Heidelberg
PB  - Springer
M1  - FZJ-2024-03391
SP  - 53
PY  - 2024
AB  - We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code, depending on the homology of the underlying chain complex. In particular, a code based on the chain complex obtained from tessellating the real projective plane or a Möbius strip encodes a qubit. We discuss the distance scaling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the 0- qubit as well as Kitaev’s current-mirror qubit—also known as the Möbius strip qubit—are indeed small examples of such codes and discuss possible extensions.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001165283300005
DO  - DOI:10.1007/s00220-023-04905-4
UR  - https://juser.fz-juelich.de/record/1026360
ER  -