# Is Gaussian boson sampling (used for showing quantum advantage) a subcategory of the continuous variable approach?

I read about the photonic QC Jiŭzhāng that showed quantum advantage by Gaussian boson sampling. I read that boson sampling itself is a sub-universal technique of QC (where they use single-photon states as input states). In the paper, the scientists describe how they use squeezed states for their computation, which can be produced deterministically (making it better realisable then producing single-photon states).

I know the term "squeezed states" from continuous variables approaches (which e.g. Xanadu uses), where a squeezed state is an ellipse in phase space. So I am wondering, whether boson sampling is a special algorithm implemented within the continuous variable approach in QC? Or is it really a totally independent approach of QC?

• Related, though not entirely the same: mattermodeling.stackexchange.com/q/3919/5. Also +1 and welcome to the community! Dec 14 '20 at 17:02
• its a big deal yet scratching my head on all this, dont see indication that boson sampling is trying to do "computation". what exactly does "sub universal" mean? not (known to be?) capable of universal computation? a big rationale of Aaronson paper seems to be, look at a physics operation that is hard for a classical system to calculate & then try to prove it. for QC there is decades of research showing the operations (entanglement etc) can be harnessed for logic gates etc, but there seems to be no such indication/ analysis ("yet?") for boson sampling...?
– vzn
Dec 14 '20 at 19:04
• squeezed states arise in what is usually dubbed a "continuous variable formalism", yes. This is just one way to deal with/describe coherences between different Fock states (which you can describe in specific ways in phase-space etc). Gaussian boson sampling is described with this formalism, so in this sense, I guess the answer to the question is yes. But I'm not sure what you mean with it being "a totally independent approach of QC".
– glS
Dec 15 '20 at 9:41

@gIS's comment effectively answers the question, but to provide a bit more detail Aaronson at shtetl-optimized has a nice blog post on the Gaussian Boson Sampling approach of USTC, contrasting it with Fock state Boson Sampling, wherein the presence/absence of photons correspond to something closer to a conventional digital ($$\vert 0\rangle$$/$$\vert 1\rangle$$) perspective of quantum computation.