Modular bosonic subsystem codes

Bosonic codes[1] introduce a notion of a qubit in the context of infinite-dimensional Hilbert spaces. Namely, the Gottesman-Kitaev-Preskill (GKP) bosonic code[2] has several desirable properties[1] and has seen a sharp increase in interest over the past few years.

A problem with bosonic subspace encodings is that the code subspace is vanishingly small compared to the full CV Hilbert space. Another problem is that, for the GKP code, the codewords are unphysical. Further, their physical versions can have little overlap, yet represent the same logical information.

I introduce a formalism where a mode is divided into two virtual subsystems: a qubit and a mode. I show how, from this perspective, every continuous-variable state encodes qubits. I then give several demonstrations of how, with the subsystem approach, the tools from standard quantum computing are readily available to CV schemes. Finally, I apply the modular subsystem formalism to a real-world scheme for CV quantum computation-CV cluster states.

References
[1] Albert, Victor V., et al. - Physical Review A 97.3 (2018): 032346.
[2] Gottesman, Daniel, Alexei Kitaev, and John Preskill. - Physical Review A 64.1 (2001): 012310.