Modular Bosonic Subsystem Codes

Abstract

We introduce a formalism for encoding a qubit into a bosonic mode as a discrete subsystem. Using a modular decomposition of the position operator, we divide the bosonic mode into two subsystems: a logical qubit and a gauge mode. This formalism enables the analysis of continuousvariable quantum information using standard qubit-based quantum information tools. We apply the formalism to approximate Gottesman-Kitaev-Preskill (GKP) states and show that the logical qubit experiences decoherence due to entanglement with the gauge mode. We also identify and disentangle a qubit cluster state hidden inside of a Gaussian continuous-variable cluster state.

Quantum Computing with Rotation-Symmetric Bosonic Codes

“…VII. The first is that for large average excitation number in the code, the performance (as measured 22 Recently it was shown that GKP codes can be decomposed into two subsystems-a logical qubit and gauge mode-according to their discrete translation symmetry [92], and a similar decomposition for rotation codes based on discrete rotation symmetry is likely. Note that the translation symmetry of any GKP code also implies two-fold rotation symmetry (see Appendix C).…”

Equivalence of approximate Gottesman-Kitaev-Preskill codes

“…In order to analyze the relation among the three approximations, we derive the position and momentum representations, q q|j and p p|j , of the approximate code states. Note that the position and momentum representations of Approximation 1 have already appeared in the past literature [7,9,23,35,37,38,40,42,44,45], but we rewrite them for the completeness. For that, we first define the following functions.…”