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Example game boards for (a) Tchoukaillon (a solitaire type of protractor) and its direct quantitative counterpart ManQala in (b). Here, we show both panels with N = 3 stones and M = 3 grid sites, and represent the seeding with arrows (which become unitary operators in the protractor site). Sequential unit procedures1 And you2 In the figure represents the deterministic quantum analogue of the first two motions of a chokelon via permutations between location and population. The final move of Tchoukaillon has no uniform hyperbolic realization in the quantum version of the game. Hence, Yu3 Leads the case in which the probability of observing the winning board is maximized. Upon observation (projective measurement), the target state is achieved, | 3,0,0⟩ with probability 4/9, and another case that is deterministic action away from the target case, | 0,3,0⟩ is achieved with a probability of 2/9 (6/9 in total). With a probability of 3/9, the board returns to the configuration before U3, which is | 1,2,0⟩ and the last step is repeated until it succeeds. credit: AVS Quantum Science (2023). doi: 10.1116/5.0148240
Protractor game It probably originated as early as 6000 BC in Jordan It is 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 objective of the game is to get all the stones into the last hole at the end of the board.
In a new study published in AVS Quantum ScienceResearchers at Tulane University have applied a modified solitaire version of the protractor, which they call ManQala, to quantum state geometry, the field of quantum physics that deals with putting quantum systems into specific states.
The central problem that quantum state engineering is trying to solve, said Ryan Glaser, assistant professor of physics in the College of Science and Engineering, is, “What do I need to do to get my quantum system into the state I want?” Essentially, researchers need to figure out how to make particles stay in certain places or have certain energies in order to study them and use quantum computers.
This is more difficult with quantum particles than it is with, say, stones on a protractor plate. “Quantum things, in general, are very sensitive and difficult to control,” Glaser said. “The system can quickly break down and cause you to lose any quantitative advantage you have or would like to have.”
Quantum physicists already have some ways to solve these problems, but the simulations conducted by the researchers in this study showed that ManQala is more efficient, even on simpler systems. “We’re already seeing advantages, even in these simplified three-and-three-hole systems,” Glaser said.
The study is one of many in the field of quantum games, Glaser said, which “effectively takes ordinary games like Sudoku, checkers or tic-tac-toe and applies the rules of quantum physics to them and sees interesting things that might happen.” When dealing with quantum particles rather than physical stones, there is a chance for the particles to interfere with each other when they are in adjacent “pits”. This means there are more moves available, and for Mancala, at least, “you can win the game if you use the quantitative rules where you wouldn’t be able to if you used the classical rules,” Glaser said.
Although this study focused on simulations, Glaser is optimistic about future applications of the protractor. “It’s in the realm of theory right now, but I think it’s definitely feasible experimentally,” Glaser said. He hopes to apply ManQala to an IBM Quantum cloud computer, which he has used for research in the past, along with fellow researchers Thomas Searles of the University of Illinois at Chicago and Brian Kirby, assistant professor of physics at Tulane.
more information:
Onur Danaci et al, ManQala: Game-inspired strategies for quantum state engineering, AVS Quantum Science (2023). doi: 10.1116/5.0148240
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