Continuous-variable fault-tolerant quantum computation under general noise

Quantum error-correcting code in continuous-variable (CV) systems attracts much attention due to its flexibility and high resistance against specific noise. However, the theory of fault tolerance in CV systems is premature and lacks a general strategy to translate noise in CV systems into noise in logical qubits, leading to severe restrictions on correctable noise models. In this paper, we show that Markovian-type noise in CV systems is translated into Markovian-type noise in the logical qubits through the Gottesman-Kitaev-Preskill code. We analyze an upper bound on the resulting noise strength in terms of our newly introduced noise parameterization. Combined with the established threshold theorem of concatenated codes against Markovian-type noise, we show that CV quantum computation has a fault-tolerant threshold against general Markovian-type noise, closing the existing crucial gap in CV quantum computation. We also give a new insight into the fact that careful management of the energy of a state is required to achieve fault tolerance in CV systems.