A quantum Rubik’s cube would be infinitely more complex than the traditional puzzle, but mathematical modelling shows it wouldn’t be unsolvable.
In the summer of 2022, and at the University of Colorado Boulder and their colleagues made a bet: how many possible states would a quantum Rubik’s cube have? To even make their guesses, they first had to define what a quantum Rubik’s cube would entail.
An ordinary Rubik’s cube has six sides divided into a grid of nine squares, each of which is one of six colours, resulting in more than a billion trillion possible configurations. In the quantum version, the researchers replaced each coloured square with a different type of particle. Their puzzle wasn’t quite a cube: it was two particles tall and wide and one particle deep. To solve either puzzle, similar squares – those of the same colour or particle type – must end up together on a face of the cube.
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These particles are moved around in the quantum puzzle similar to how the coloured squares are moved to different sides of the cube in the traditional game, but the researchers also added a fundamentally quantum move. Here, two particles can be put into a superposition – simultaneously left in place and having their positions swapped.
With these basic rules in place, it was time to bet. Each team member gave the highest number of configurations they thought would be possible. At one point, the largest was 20,922,789,888,000, but Trank-Greene upped the ante. She guessed that the possibilities were infinite and the team found that the addition of superpositions made her right.
But Lordi says that this didn’t make the quantum Rubik’s cube unsolvable. Borrowing methods from mathematics and quantum computing, the team determined that a specific sequence of moves for solving the quantum puzzle does exist. However, while the record for solving a traditional Rubik’s cube is just over 3 seconds, Lordi says that the quantum version may take a finite but still unimaginably large amount of time.
“If I give you a scrambled puzzle, it could take you arbitrarily many moves to solve. I could give you a scramble that takes 20 million moves to solve,” he says.
The way out of this problem is to add another fundamentally quantum move. The researchers calculated what would happen if the player were allowed to perform a measurement, which changes the quantum state of the puzzle. This process is probabilistic, so playing a measurement move won’t always result in the Rubik’s cube being solved and will sometimes mean that the puzzle needs to be re-scrambled. But over many games, a player could learn to employ it in such a way that they solve the puzzle most of the time. In this sense, a classical Rubik’s cube champion and a quantum Rubik’s cube champion would have to develop very different game strategies, says Lordi.
Playing the quantum Rubik’s cube can also be viewed as a quantum computing problem with digital quantum bits, which is a more complex approach to quantum computing than most that are used today. at the University of Milan in Italy says that this could make it useful for developing quantum simulations. “We may expect quantum puzzles to be available on quantum computers not only to play, but also to explore chemistry, phase transitions and mesoscopic [physics] systems,” he says.
arXiv
