On the Complexity of Solving Subtraction Games

Quantum-over-classical Advantage in Solving Multiplayer Games

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction games became the first explicitly defined class of zero-sum combinatorial games with provable separation between quantum and classical complexity of solving them. For a narrower subset of Subtraction games, an exact quantum sublinear algorithm is known that surpasses all deterministic algorithms for finding solutions with probability $1$. Typically, both Nim …

Solving diner's dilemma game, circuit implementation, and verification on IBMQ simulator

Diners dilemma is one of the most interesting problems in both economic and game theories. Here, we solve this problem for n (number of players) =4 with quantum rules and we are able to remove the dilemma of diners between the Pareto optimal and Nash equilibrium points of the game. We find the quantum strategy that gives maximum payoff for each diner without affecting the payoff and strategy of others. We use the quantum principles of superposition and entanglement that gives supremacy over any classical strategies. We present the circuit implementation for the game, design it on the IBM quant…

一个基于博弈论的量子算法用于解决魔方阵

A Game-Theoretic Quantum Algorithm for Solving Magic Squares

本文提出一个变分框架用于解决魔方阵游戏，通过构造价值哈密顿量和优化量子电路，强调代数结构和可解释性，通过数值实验验证方法并扩展到更大规模的游戏。

(Of course) algorithms beat gamers at solving quantum control problems

Dries Sels and Allan Grønlund have demonstrated numerical algorithms that outperform the players of our Quantum Moves game and they call the conclusions of our article Exploring the Quantum Speed Limit with Computer Games, Nature, 532, 210 (2016)] 'untenable'. Sels and Grønlund ignore that our article already emphasizes that the players do not solve the quantum optimization challenge to any desired accuracy. Our key finding is that player solutions can be employed either as seeds for numerical optimization algorithms or as guidance towards low-dimensional representations of the solutions.