Board games for quantum computers
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. RESEARCH PAPER .
February 2021, Vol. 64 122501:1–122501:16 https://doi.org/10.1007/s11432-020-3038-x
Board games for quantum computers Biao WU1,2,3* , Hanbo CHEN1 & Zhikang LUO4 1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China; 3 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; 4 College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
2
Received 27 April 2020/Revised 16 June 2020/Accepted 10 August 2020/Published online 9 November 2020
Abstract Scalable board games, including Five in a Row (or Gomoku) and Weiqi (or Go), are generalized so that they can be played on or by quantum computers. We adopt three principles for the generalization: the first two are to ensure that the games are compatible with quantum computer and the third is to ensure that the standard classical games are the special cases. We demonstrate how to construct basic quantum moves and use them to set up quantum games. There are three different schemes to play the quantized games: one quantum computer with another quantum computer (QwQ), two classical computer playing with each other on one quantum computer (CQC), and one classical computer with another classical computer (CwC). We illustrate these results with the games of Five in a Row and Weiqi. Keywords
quantum Weiqi, quantum Go, Weiqi, Five in a Row, board games
Citation Wu B, Chen H B, Luo Z K. Board games for quantum computers. Sci China Inf Sci, 2021, 64(2): 122501, https://doi.org/10.1007/s11432-020-3038-x
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Introduction
There are many interesting board games. Chess, Weiqi (or Go as usually called in English), and Five in a Row (FIR) (or Gomoku) are among the most popular. In particular, both Weiqi and FIR are played on scalable square boards (see Figure 1), where two players take turn to place black and white stones on the board. Following the convention of quantum information, we call the two players Alice and Bob who play, respectively, white stones and black stones. In this work, we focus our attention on these scalable board games and discuss how to generalize them so that they can be played by or on quantum computers with intrinsic quantum moves. One can benefit from either studying or playing these quantum board games in at least two aspects. (1) People have always tried to understand how mind or intelligence emerges from matter. Although most of physicists think that the neural network of our brain is classical [1], there are still physicists think with good reasons that quantum physics is essential to understand our brain, that is, our brain in a certain sense is a quantum computer or bears some common features with quantum computer [2, 3]. Studying how quantum computers play board games against each other without any external observer may help us to clarify this fundamental issue (see discussion with QwQ (one quantum computer with another quan
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