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If suitable quantum optical interactions were available, transforming opticalfield mode operators in a nonlinear fashion, the all-photonics platform couldbe one of the strongest contenders for realizing a quantum computer. Unlikeother, matter-based (solid-state or atomic) platforms, photonic qubits can beoperated at room temperature and high clock rates (GHz or, in principle, evenTHz). In addition, recent continuous-variable time-domain approaches areextremely well scalable. Moreover, while single-photon qubits may be processeddirectly, "brighter" logical qubits may be embedded in individual oscillatormodes, using so-called bosonic codes, for an in-principle fault-tolerantprocessing. In this work, we show how elements of all-optical, universal, andfault-tolerant quantum computation can be implemented using only beam splitterstogether with single-mode cubic phase gates in reasonable numbers, and possiblyoffline squeezed-state or single-photon resources. Our approach is based on anovel decomposition technique combining exact gate decompositions andapproximate trotterization. This allows for efficient decompositions of certainnonlinear continuous-variable multi-mode gates into the elementary gates, wherethe few cubic gates needed may even be weak or all identical, thus facilitatingpotential experiments. The final gate operations include two-mode controlledphase rotation and three-mode Rabi-type Hamiltonian gates, which are shown tobe employable for realizing high-fidelity single-photon two-qubit entanglinggates or, as a bosonic-code example, creating high-qualityGottesman-Kitaev-Preskill states. We expect our method of general use withvarious applications, including those that rely on quartic Kerr-typeinteractions.

All-optical quantum computing using cubic phase gates