玩量子井字游戏的战略见解
Strategic Insights From Playing the Quantum Tic-Tac-Toe
摘要：
在本文中，我们执行一个最小的量化井字游戏的经典，通过允许叠加的经典动作。为了使量子博弈正确地还原为经典博弈，我们要求合法的量子移动与之前的所有移动正交。我们也承认干扰效应，通过对玩家所有移动的振幅之和进行平方来计算他或她在给定地点的占领水平。当我们在$3 \times 3$网格中画出的八条直线上的职业之和大于三时，玩家获胜。我们先随机玩量子井字棋，然后确定性地玩，以探索不同的开局、残局以及不同的进攻和防守策略组合对游戏结果的影响。与经典的井字游戏不同，确定性量子游戏并不总是以平局告终。与大多数经典的没有机会的两人游戏相反，参与人2有可能获胜。更有趣的是，我们发现参与人1在以量子移动开始时享有压倒性的量子优势，但在以经典移动开始时失去了这种优势。我们还发现，量子阻挡移动，其中包括一个加权叠加的移动，对手可以用来赢得比赛，是非常有效的否认对手他或她的胜利。然后，我们推测这些结果可能对量子信息转移和投资组合优化有什么影响。
英文摘要：
In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit interference effects, by squaring the sum of amplitudes over all moves by a player to compute his or her occupation level of a given site. A player wins when the sums of occupations along any of the eight straight lines we can draw in the $3 \times 3$ grid is greater than three. We play the quantum tic-tac-toe first randomly, and then deterministically, to explore the impact different opening moves, end games, and different combinations of offensive and defensive strategies have on the outcome of the game. In contrast to the classical tic-tac-toe, the deterministic quantum game does not always end in a draw. In contrast also to most classical two-player games of no chance, it is possible for Player 2 to win. More interestingly, we find that Player 1 enjoys an overwhelming quantum advantage when he opens with a quantum move, but loses this advantage when he opens with a classical move. We also find the quantum blocking move, which consists of a weighted superposition of moves that the opponent could use to win the game, to be very effective in denying the opponent his or her victory. We then speculate what implications these results might have on quantum information transfer and portfolio optimization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
