RESUMO
We introduce a framework to decompose a bosonic mode into two virtual subsystems-a logical qubit and a gauge mode. This framework allows the entire toolkit of qubit-based quantum information to be applied in the continuous-variable setting. We give a detailed example based on a modular decomposition of the position basis and apply it in two situations. First, we decompose Gottesman-Kitaev-Preskill grid states and find that the encoded logical state can be damaged due to entanglement with the gauge mode. Second, we identify and disentangle qubit cluster states hidden inside of Gaussian continuous-variable cluster states.
RESUMO
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum computing with error correction. We show that applying GKP error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional non-Gaussian elements. Fault tolerance is possible with sufficient squeezing and low enough external noise. Thus, Gaussian operations are sufficient for fault-tolerant, universal quantum computing given a supply of GKP-encoded Pauli eigenstates.
