Physicists Create Quantum Rubik’s Cube and Discover the Best Way to Solve It
Quantum physics is already a puzzle in itself — and now, researchers have taken that quite literally. A team of mathematicians from the University of Colorado Boulder has developed a quantum version of the Rubik’s Cube, featuring infinite possible configurations and strange new moves that make the challenge even more complex.
The Classic Cube and the Permutation Space
The traditional Rubik’s Cube is a classic example of a permutation puzzle, where the goal is to rearrange a series of pieces until they form a specific pattern — in this case, six uniformly colored faces. There are about 43 quintillion possible configurations for the standard cube.
However, when quantum concepts such as superposition are introduced — where a piece can be both moved and not moved at the same time — the number of possible states becomes infinite.
“With superpositions, the number of unique allowed states in the puzzle becomes infinite, unlike the classic permutation puzzles sold in toy stores,” the researchers explain in the paper.
To explore this concept, the scientists began with a simplified puzzle: a 2×2 grid with only green and blue tiles. The goal was to place the green tiles above the blue ones. In the classical version, this setup allows for only six possible permutations. But by treating the colors as quantum particles — indistinguishable from each other — they begin to behave in a way similar to quantum entanglement.
Three types of simulated “players” were tested in solving 2,000 randomly scrambled versions of the puzzle: a classical solver (who could only swap adjacent tiles), a quantum solver (who could use superpositions), and a hybrid solver (who could do both).
Results: Quantum Advantage
As expected, the hybrid solver performed best, solving the puzzle in an average of 4.77 moves. The quantum solver took about 5.32 moves on average, and the classical solver lagged behind at 5.88 moves.
Interestingly, while the classical solver occasionally solved the puzzle in fewer than five moves, it often took twice as long in other cases — unlike the quantum solver, which almost always finished within eight moves. The researchers believe that this quantum advantage would become even more evident with more complex puzzles.
After each attempt, a “referee” checks whether the puzzle was solved. The measurement collapses the quantum superposition into a single defined state — which may or may not be the correct one. If not, the puzzle is scrambled again and the solver tries again.
Even the classical solver can beat a quantum puzzle — especially if it gets lucky and starts with one of the six classical possibilities. Otherwise, it needs to maneuver close to the solution and hope that measurement collapses it into the correct configuration.
Although quantum actions have an edge, they also have a drawback: performing a classical swap takes two quantum moves. That’s why classical solvers sometimes have an early advantage — but ultimately, the hybrid solver consistently performs better.
Expanding to Three Dimensions
The team also created a 3D version of the quantum puzzle, shaped as a 2x2x1 block. Like the 2D version, it allows for infinite states and can be solved using similar strategies.
In practice, such quantum permutation puzzles could potentially be built using ultracold atoms arranged in optical lattices. For now, however, the idea remains a theoretical experiment for math and quantum science enthusiasts.
The research has been accepted for publication in the journal Physical Review A and is currently available on the preprint server arXiv.
Read the original article on: Science Alert
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