  The key approaches for machine learning, especially learning in unknown
probabilistic environments are new representations and computation mechanisms.
In this paper, a novel quantum reinforcement learning (QRL) method is proposed
by combining quantum theory and reinforcement learning (RL). Inspired by the
state superposition principle and quantum parallelism, a framework of value
updating algorithm is introduced. The state (action) in traditional RL is
identified as the eigen state (eigen action) in QRL. The state (action) set can
be represented with a quantum superposition state and the eigen state (eigen
action) can be obtained by randomly observing the simulated quantum state
according to the collapse postulate of quantum measurement. The probability of
the eigen action is determined by the probability amplitude, which is
parallelly updated according to rewards. Some related characteristics of QRL
such as convergence, optimality and balancing between exploration and
exploitation are also analyzed, which shows that this approach makes a good
tradeoff between exploration and exploitation using the probability amplitude
and can speed up learning through the quantum parallelism. To evaluate the
performance and practicability of QRL, several simulated experiments are given
and the results demonstrate the effectiveness and superiority of QRL algorithm
for some complex problems. The present work is also an effective exploration on
the application of quantum computation to artificial intelligence.
