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(a) Example game board for Tchoukaillon (the solitaire version of Mancala) and its direct quantum analog ManQala (b). Here we show both boards with N = 3 stones and M = 3 lattice sites, with arrows representing seeding (which in ManQala would be a single operator with 2 sites). continuous single motion U1 and U2 in the figure represent deterministic quantum analogues of the first two Tchoukaillon transfers with site population permutations. The final step of the Tchoukaillon game has no deterministic unitary realization in the quantum version of the game. Therefore, U3 Drives a state in which the probability of observing a winning board is maximized. Observing (projective measurement), the goal state |3,0,0⟩ is achieved with probability 4/9, and another state |0,3,0⟩, which is a deterministic move away from the goal state, is Achieved with a 2/9 (6/9 total) chance. There is a 3/9 chance that the board will revert to the U previous configuration.3This is |1,2,0⟩ and the last step is repeated until success. credit: AVS Quantum Science (2023). DOIs: 10.1116/5.0148240
game mancala It may have originated in Jordan in 6000 BC And it is still played all over the world to this day. It consists of stones that players move between a series of small holes on a wooden game board. The point of the game is to get all the stones into the last hole at the edge of the board.
In a new study published in AVS Quantum ScienceResearchers at Tulane University have applied a modified solitaire version of Mancala, called ManQala, to quantum state engineering, the branch of quantum physics that deals with placing quantum systems into specific states.
Ryan Glasser, an associate professor of physics in the Faculty of Science and Engineering, said the central problem quantum state engineering is trying to solve is “what do I need to do to put a quantum system in the state I want it to be?” . Fundamentally, researchers need to know how to place particles in specific locations or have specific energies in order to study them and use quantum computers.
This is more difficult for quantum particles than, for example, stones on the Mancala plate. “Quantum stuff in general is very delicate and difficult to control,” Glasser said. “The system could quickly collapse and you could lose any quantum advantage you have or hope to have.”
Quantum physicists already have some ways to solve these problems, but the simulations the researchers performed in this study show that ManQala is more effective, even for simpler systems. it was done. “Even with a simplified system of three stones and three pits, we are already seeing benefits,” Glasser said.
This work, one of many in the field of quantum games, “effectively takes regular games such as Sudoku, checkers, or tic-tac-toe, and applies the rules of quantum physics to them to determine which We’re looking to see if something interesting like that happens,” Glasser said. When dealing with quantum particles rather than physical stones, particles can interfere with each other if they are in adjacent “pits”. This means that more hands are available, and at least for Mancala, “a game that would be unwinnable using classical rules could be won using quantum rules.” We can do that,” Glasser said.
Although the research is focused on simulation, Glasser is optimistic about ManQala’s future applications. “It’s in the realm of theory at this point, but I think it’s definitely viable experimentally,” Glasser said. He, along with fellow researchers at the University of Illinois at Chicago, Thomas Searles, and adjunct professor of physics at Tulane University, Brian Kirby, would like to apply ManQala to the IBM Quantum cloud computers they’ve used in past research. ing.
For more information:
Onur Danaci et al., ManQala: A Game-Inspired Quantum State Engineering Strategy, AVS Quantum Science (2023). DOIs: 10.1116/5.0148240