Gaussian Conversion Protocols for Cubic Phase State Generation

Universal quantum computing with continuous variables requires non-Gaussian resources, in addition to a Gaussian set of operations. A known resource enabling universal quantum computation is the cubic phase state, a non-Gaussian state whose experimental implementation has so far remained elusive. In this paper, we introduce two Gaussian conversion protocols that allow for the conversion of a non-Gaussian state that has been achieved experimentally, namely the trisqueezed state [Chang et al., Phys. Rev. X 10, 011011 (2020)], to a cubic phase state. The first protocol is deterministic and it involves active (inline) squeezing, achieving large fidelities that saturate the bound for deterministic Gaussian protocols. The second protocol is probabilistic and it involves an auxiliary squeezed state, thus removing the necessity of inline squeezing but still maintaining significant success probabilities and fidelities even larger than for the deterministic case. The success of these protocols provides strong evidence for using trisqueezed states as resources for universal quantum computation.

Automated summary

This paper introduces two Gaussian conversion protocols for converting experimentally achieved non-Gaussian states, specifically trisqueezed states, into cubic phase states. One protocol is deterministic involving active squeezing, while the other is probabilistic involving an auxiliary squeezed state. Both protocols demonstrate high success probabilities and fidelities, supporting the use of trisqueezed states as resources for universal quantum computation.