Is it possible to simulate QFT to make pretty animations?

Question

Is it possible to simulate QFT and make animations of it? For example, it is relatively straightforward to simulate something like the Schrödinger equation or the Klein–Gordon equation if you don't worry too much about accuracy and just want to look at the animations. Just discretize space and time and then integrate the equations of motion using Euler integration or some other more fancy integrator. This would give an animation like this for the 2D Klein–Gordon equation:

Now if I want to simulate QFT I run into problems. The domain of the 2D Klein–Gordon is $\mathbb R^2$ or $\mathbb C^2$ so to simulate this you need a $2\times2$ array of numbers. For QFT you are working on a Fock space and I don't even know how you would simulate this. I also don't know how you would incorporate the equations of motion. Is this even feasible because the Fock space is so large?

You might need to be more specific about what you want to animate. For context, state-of-the-art computer calculations in lattice QCD use a barbaric discretization of 3d space down to a grid of only $\sim 64^3$ points, and QCD has multiple independent field-variables for each one of those points. That means the "wavefunction" (state-vector) is a complex-valued function of millions of variables, in contrast to the two-variable animation displayed in the question. — Chiral Anomaly, Oct 25 '21 at 02:14
@KeithMcClary That was kind of what I was looking. I was hoping to be able to simulate it myself so if I understand that paper correctly it is possible but really hard. — AccidentalTaylorExpansion, Oct 25 '21 at 07:32
@ChiralAnomaly I left it vague intentionally but anything simple that could reproduce pictures similar to the Klein Gordon animation would be nice. For example a free boson/fermion. Or even QED — AccidentalTaylorExpansion, Oct 25 '21 at 07:37
Related: How do you visualize a quantized electromagnetic field? — Ruslan, Jan 07 '22 at 19:51
@Ruslan the most upvoted answer to that question is really nice! I'll have a look into that — AccidentalTaylorExpansion, Jan 07 '22 at 21:59

Is it possible to simulate QFT to make pretty animations?

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