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Continuous-variable bosonic systems stand as prominent candidates forimplementing quantum computational tasks. While various necessary criteria havebeen established to assess their resourcefulness, sufficient conditions haveremained elusive. We address this gap by focusing on promoting circuits thatare otherwise simulatable to computational universality. The class ofsimulatable, albeit non-Gaussian, circuits that we consider is composed ofGottesman-Kitaev-Preskill (GKP) states, Gaussian operations, and homodynemeasurements. Based on these circuits, we first introduce a general frameworkfor mapping a continuous-variable state into a qubit state. Subsequently, wecast existing maps into this framework, including the modular and stabilizersubsystem decompositions. By combining these findings with established resultsfor discrete-variable systems, we formulate a sufficient condition forachieving universal quantum computation. Leveraging this, we evaluate thecomputational resourcefulness of a variety of states, including Gaussianstates, finite-squeezing GKP states, and cat states. Furthermore, our frameworkreveals that both the stabilizer subsystem decomposition and the modularsubsystem decomposition (of position-symmetric states) can be constructed interms of simulatable operations. This establishes a robust resource-theoreticalfoundation for employing these techniques to evaluate the logical content of ageneric continuous-variable state, which can be of independent interest.

Sufficient condition for universal quantum computation using bosonic circuits