Picoputt

Taking the concept of miniature golf to its logical extreme, in picoputt your golf ball is a quantum particle.

Currently, it is not so much an actual game as it is an interactive simulation/toy, and I'm still working on porting some key features from my Python prototype (also not a complete game) to C/GLSL.

Currently, picoputt has the following features:

• Fast, GPU-accelerated simulation of the Schrödinger equation. On my laptop's integrated GPU, it's ~60x faster than the equivalent Python/numpy implementation from my prototype.
• Putting: hit the quantum golf-ball around using a golf club "putt-wave" with adjustable radius.
• Measurement of position (though it's currently not implemented as a proper partial measurement).
• Visualization with fancy pseudo-3D graphics:

demo.mp4

Build instructions

Picoputt depends on SDL2 and GLEW. I install them with vcpkg: vcpkg install sdl2 glew.

Build with CMake and run:

$ cmake .  # If using vcpkg, add -DCMAKE_TOOLCHAIN_FILE=...
$ cmake --build .
$ ./picoputt

By default, picoputt looks for resources in its parent directory. If you want to use a different build directory, since these files are not copied over to the build directory, you may want to override the base directory using the $PICOPUTT_BASE_PATH environment variable:

$ cmake --build builddir
$ PICOPUTT_BASE_PATH=. ./builddir/picoputt

You can also create a zip package with all necessary components using cmake --build builddir -- package

How to play

Click and drag to putt.

Scroll up and down (or use [ and ]) to adjust the radius of the putt-wave.

The de Broglie wavelength of the putt-wave is shortest (and is approximately a plane wave) inside this radius, so that is where you will have the biggest and most uniform effect on the momentum of the particle. Outside of this radius, the effect on local momentum is small, but the distortion of the putt-wave can be useful to compress, disperse, or otherwise manipulate the shape of a wavepacket.

Press space to measure position. Although it's intended to resemble a partial measurement, currently the post-measurement state always has $\langle{}p\rangle = 0$ which isn't very realistic.

Here's an example of pulling apart some quantum taffy and measuring its position:

measurement.mp4

Goals

Contrary to the source material, I don't want picoputt to be too much of a game of chance -- god might play dice, but we're trying to play golf. Although there will be (partial) position measurement, it won't be a matter of measuring the golf ball's position until you get lucky enough for it to end up in the hole, measurement will just be a tool to re-localize the golf ball that adds to your score, just like putting will.

The object of the game will be to reach some probability threshold in a particular energy eigenstate of the golf course, specifically the local minimum energy state at the hole. Since it will be based on energy state rather than position, simply getting probability into the hole won't be sufficient -- the ball needs to come to rest there. For this to work, we'll need a dissipative effect. The plan is to use an effect I call phase drag, which acts as a linear drag force on the phase gradient. The local minimum energy state at the hole of the total golf-course Hamiltonian $H_g = H_0 + V_{hole}$ will be approximated by simply using the ground state of the hole Hamiltonian.

I've yet to implement this phase-drag effect in picoputt, but I have implemented it in my prototype by using skimage's unwrap_phase to do a 2D phase unwrapping, which I then scale down and reapply to the wavefunction's magnitude to decrease the phase gradient everywhere each timestep. Although it's a bit mathematically sketchy, qualitatively it works quite well as a drag force and has some interesting effects like decreasing the tendency of a wavepacket to spread out (making it "more classical").