What is Quantum Minigolf ?

A quantum ball (right, colored) propagating towards the hole (left, yellow). The obstacle shown is the infamous "double slit". Move the mouse over the image to see a nice shot.

The idea

The game quantum minigolf is nearly the same as the game minigolf - except that the ball obeys the laws of quantum mechanics.
Such a ball can be at several places at once. It can diffract around obstacles and interfere with itself. Apart from that, the rules are the same: You can play on various tracks involving various obstacles. You hit the ball with a club and try to kick it into a hole on the other side of the track.

The software

To play quantum minigolf, download the game in the download section. It is a GPLed C++ program, which has been tested under Windows and Linux. It features a simple user interface. You can add your own tracks by editing them in any image editing software and saving them in bmp format.

The hardware

Photo courtesy of Y. Colombe

There also exists a (virtually) real version of quantum minigolf. It permits to play with a real club and a ball which is projected onto the track by a video projector mounted on a 2m (6ft) high tripod. The club is marked by an infrared LED, and detected by a webcam next to the video projector. An image recognition algorithm in the quantum minigolf software computes the club position and feeds back hits into the simulation.

The rules of the game

What you see in the game - Visualization scheme

On the left of each track, you see a yellow ring. This is the hole. When the ball is inside this region at the end of the game, you win. Otherwise you lose.

The obstacles are white. Their "whiteness" shows their height. A white spot is thus a pillar standing out of the playing field. A white area is a block standing out. A grey area is a block standing out, but not as high as a white area.

The quantum ball appears as a blob colored in all rainbow colors. Quantum mechanics tells us that the ball is everywhere inside the blob at once. But it is a bit more where the blob is very intense than where it is barely visible.
For the experts: The ball is visualized by mapping the complex wavefunction to the color circle. The modulus of the wavefunction is thus intensity-coded, the phase is color-coded. See e.g. the books Visual quantum mechanics for a more thorough analysis.

The Hit - Initializing the wavepacket

At the beginning of each quantum minigolf game, the ball rests at the drive position (on the right). When you hit it with the club, it will start to move.
For the experts: Hitting the ball, you define an initial momentum. The ball is then initialized as a Gaussian wavepacket of hard-coded width, centered around the driving position in position space and around the initial momentum in momentum space.

Crossing the obstacle course - Propagation

Once it moves, the ball will cross the track nearly like a classical ball. However you will note peculiar things, such that it tends to spread itself everywhere and that it can flow around obstacles, which shows its quantum-mechanical nature.

Getting into the hole - The Position measurement

Since a quantum mechanical ball is most of the time at several places at once, it is impossible to say, whether it is in the hole or not. It is just "at once inside and outside" the hole. However, there is a trick: Quantum mechanics allows to make a "position measurement" which will let the ball collapse at a certain position. Think of this as taking a photo of the ball. A quantum particle can be at several places at once - but on a photo it will always appear on one and only one positon.
At the end of each game you take thus a virtual photo of the track. If the ball appears in the hole, you win. Otherwise you lose.