  Here, we present the quantum version of a very famous statistical decision
problem, whose classical version is counter-intuitive to many. The Monty Hall
game can be phrased as a two person game between Alice and Bob. In their
pioneering work, Flitney and Abbott [Phys. Rev. A 65, 062318 (2002)] showed
that by using a maximally entangled system for Alice and Bob's choices, and
using quantum strategies, Bob and Alice can win or lose depending on the
strategy chosen by either of the players. Here we develop a new quantum
algorithm with quantum circuits for playing the quantum Monty Hall game by a
user. Our quantum algorithm uses the quantum principles of superposition and
entanglement so that it can be efficiently played on a quantum computer. We
present two schemes, one calculating the probability of winning or loss and the
other determining whether a player (say Alice) wins or not.
