Abstract
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 [Sandbo Changet al., Phys. Rev. X10, 011011 (2020)],to a cubic phase state. The first protocol is deterministic and it involves active (in-line) 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 in-line 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.
Highlights
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
In this work we focus on the cubic phase state as a resource state, and we provide explicit protocols to convert a non-Gaussian state that has recently been generated within microwave circuits—namely the trisqueezed state [51]—into a cubic phase state, with simple Gaussian operations that are readily available in the laboratory, in both the optical and the microwave regimes
In order to characterize conversion protocols that map the trisqueezed state onto the cubic phase state or aim at approximating the latter as well as possible, we need to define a measure of the distance between the target state and the transformed input state
Summary
Continuous-variable (CV) systems [1] are promising candidates to implement quantum computation in a variety of physical settings where quantum systems cannot be described within a finite-dimensional Hilbert space, including optical [2] and microwave radiation [3,4,5], trapped ions [6,7], optomechanical systems [8,9,10], atomic ensembles [11,12,13,14], and hybrid systems [15]. The second route is instead based on the so-called cubic phase state [22] that, by enabling the implementation of a nonlinear gate [33], can in principle unlock universality regardless of the use of a specific encoding [28]—including, for example, the generation of GKP states via the probabilistic protocol introduced in Ref. In Appendix B we provide an extensive discussion of the numerical methods used for our optimizations, while other technical details are provided in the remaining appendixes
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