Bosonic (And Other) Codes With Interesting Logical Gate Sets
summary
A constructive recipe builds encodings by averaging a chosen logical state and a chosen physical state over a compact group representation, using elementary representation theory and SDPs to optimize performance; it recovers GKP and cat families and produces multimode cat codes where Gaussian unitaries implement all single-qubit Cliffords, yields a 24-state 2T-qutrit competitive at low loss (fidelity vs pure-loss γ plotted), and links five- and seven-qubit examples via the Schur transform (Knill–Laflamme nearly satisfied: 90/105 conditions in one search).
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chapters (8)
- 0:00Introduction and motivation
- 3:05Bosonic code development
- 5:59Formalism for code design
- 12:28Mathematical foundation
- 20:27General construction recipe
- 27:39Applications in bosonic codes
- 37:13Cubit and arbitrary codes
- 47:01Discussion and Q&A
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