This can be applied to familiar games like Chess, Go, Tic-tac-toe, Checkers, or any combinatorial game. Using the rules of the game, a superposition of all possible game histories is created and then evaluated, giving all the nodes at the base of the game tree a value. The minmax algorithm is then applied to all the nodes in the tree, ending in a value for the top of the tree, and an associated game history.

This algorithm will return the 1st forced win deterministically. It can also be configured to pick the Nth forced win. (Part of the algorithm orders all the possible games.) Remarkably, the phase of the qubits is never used: all qubits have a positive phase the entire time.

I suspect that the complexity of the algorithm growly linearly in the (depth of the game tree) times (average branching number), which means some versions of Go allowing games with 10^40 moves will not be accessible to this algorithm unless pruning is developed.

• The circuit description is a vector representing the quantum logic units in the quantum computer. Depending on the machine architecture, each unit may be a qubit, qutrit, or qudit with d representing dimensionality. E.g.: A vector of [2,2,3] represents two qubits and one qutrit.

• Recommended: Run this program in a virtual enviorment
• Running python3.7 in a virtual environment
  • sudo apt install virtualenv
  • then virtualenv -p python3.7 env_name
  • then from the same directory, source ./env_name/bin/activate
  • you should see the environment name appear in the command line, as: (env_name) user@computer:~$
  • from here, use pip3 to install the depedencies
    • numpy
    • matplotlib
    • sympy