If you have good references about the CV model that are understandable from a computer science background, that would be great. If they include numerical examples, that would even be better.


One of the best places to learn about the continuous-variable (CV) model is the documentation of the Strawberry Fields software for photonic quantum computing. It also includes several numerical examples. You can also read the white paper here, which contains a dedicated section to explaining the CV model.

Additionally, this review paper by Braunstein and van Loock contains a short section on quantum computing with continuous variables. If you're also interested in physical implementations, this paper by Gu et al. has a nice description of the cluster-state model of photonic quantum computing.

To get you started, the fundamental difference between the CV model and the traditional qubit model is that in the CV model, we formally apply operations on infinite-dimensional instead of two-dimensional systems. Of course, in practice, each system can be effectively described by a large but finite-dimensional Hilbert space, but it is more mathematically convenient to describe operators and states on the full infinite-dimensional space. The result is simply that in the CV model, we end up with a different set of canonical states and gates, as summarized for example in the table below (taken from the Strawberry Fields white paper):

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