Quantum State Engineering with a Mancala Game on a Real Quantum Board

Quantum games can serve as research tools to simulate physical phenomena with near-term intermediate-scale quantum computers. Here, we propose ManQala as a quantum version of the sowing game Mancala. In ManQala, seeds, pits, and sowing are replaced by bosons, bosonic modes, and two-site hopping as encountered in the Bose-Hubbard model. We implement the game using IBM Qiskit by representing bosonic modes truncated to d=4 dimensional Hilbert space. And, represent these modes using standard binary encoding of qubits to simulate unitary moves through Trotter decomposition of the time-evolution. We find ManQala breaks the unidirectional gameplay of Mancala and introduces Mott-insulator like stalemate configurations that can only be broken through the introduction of probabilistic measurements. Further, ManQala corresponds to a quantum state engineering strategy that emulates the winnability conditions of the solitaire Mancala game on a quantum board by minimizing the number of projective measurements in a fixed unitary evolution and measurements (FUMES) type strategy. This way it steers an initial state to a target state more deterministically.