Homological Quantum Rotor Codes: Logical Qubits from Torsion
summary
Defines homological quantum rotor codes using integer chain complexes and homology to produce logical degrees of freedom that can be either continuous rotors or finite qudits depending on torsion; shows encodes both logical rotors and logical qudits in one block and that RP2 or a Möbius-tessellation gives a logical qubit. Uses integer stabilizer matrices, cohomology duals, hypergraph-product constructions (third-root-of-N distance scaling examples) and a statistical-physics decoder mapping to XY/solid-on-solid models; notes superconducting islands (0-π and Kitaev current-mirror/Möbius qubits) as realizations.
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chapters (23)
- 0:00Homological quantum rotor codes intro
- 1:08Why study rotor error correction
- 3:21Motivations for rotor codes
- 6:39Quantum rotors definition
- 8:07Pauli operators on rotors
- 9:52Stabilizer formalism for rotors
- 12:254-rotor code example
- 14:35Homology in rotor codes
- 16:50Torsion and logical qubits
- 18:59Distortion and encoding
- 23:00Error correction characterization
- 25:33Error weights and distances
- 27:23X distance in rotors
- 28:07Phase distance challenges
- 30:21Rotor code parameters notation
- 31:06Codes from cellular homology
- 32:35Projective plane encoding
- 36:12Mobius strip rotor codes
- 38:263D rotor code constructions
- 39:09Hypergraph product codes
- 41:58Summary and future
- 44:03Decoding strategies
- 45:48Logical operations on rotors
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