It seems to be a widely held belief within the scientific community that it is possible to do "universal, fault-tolerant" quantum computation using optical means by following what is called "linear optical quantum computing (LOQC)" pioneered by KLM (Knill, Laflamme, Milburn). However, LOQC uses only modes of light that contain either zero or one photon, not more.
Continuous modes of light contain, by definition, much more than one photon. The paper Probabilistic Fault-Tolerant Universal Quantum Computation and Sampling Problems in Continuous Variables Douce et al. (2018) [quant-ph arXiv:1806.06618v1] claims "probabilistic universal fault-tolerant" quantum computation can also be done using continuous modes of squeezed light. The paper goes even further and claims it is possible to demonstrate quantum supremacy using continuous modes. In fact, the paper's abstract says:
Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses.
A quantum computing startup called Xanadu that has some credibility because it has written several papers with Seth Lloyd, seems to be claiming that they too will ultimately be able to do quantum computation with continuous modes of light, and perform some tasks better than a classical computer.
And yet, what they are doing seems to me to be analog computing (is fault tolerant error correction possible for analog computing?). Also, they use squeezing and displacement operations. Such operations do not conserve energy (squeezing or displacing a mode can change its energy), so such operations seem to require exchanges of macroscopic amounts (not quantized amounts) of energy with an external environment, which probably can introduce a lot of noise into the qc. Furthermore, squeezing has only been achieved in the lab for limited small values, and a claim of universality might require arbitrary large squeezing as a resource.
So, my question is, are these people being too optimistic or not? What kind of computing can be done realistically in the lab with continuous modes of light?