## AbstractMaximum a Posteriori (MAP) inference in graphical models is a fundamental task but is generally NP-hard. We present a quantum computing algorithm to speed up this task. The algorithm uses only small, local operators, and is based on a physical analogy of striking the nodes in a net with superposed ‘coolants’. It may be viewed as a quantum version of the Gibbs sampler, making use of entanglement and superposition to represent the entire joint over N variables using only N physical nodes in 2N states of superposition, and exploring all MCMC trajectories simultaneously. It requires information to be carried away by the coolants, so making essential use of decoherence – which is often thought of as a hindrance rather than a beneﬁt to quantum computation. The algorithm creates a superposition whose amplitudes represent model probabilities, then cools it to leave a sharp peak at the MAP solution. As quantum observation probabilities are the squares of these amplitudes, the probability of observing the MAP and near-MAP solutions is ampliﬁed quadratically over the classical case. Proof-of-concept simulations are presented.
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