  In this paper, a quantum algorithm based on gaussian process regression model
is proposed. The proposed quantum algorithm consists of three sub-algorithms.
One is the first quantum subalgorithm to efficiently generate mean predictor.
The improved HHL algorithm is proposed to obtain the sign of outcomes.
Therefore, the terrible situation that results is ambiguous in terms of
original HHL algorithm is avoided, which makes whole algorithm more clear and
exact. The other is to product covariance predictor with same method. Thirdly,
the squared exponential covariance matrices are prepared that annihilation
operator and generation operator are simulated by the unitary linear
decomposition Hamiltonian simulation and kernel function vectors is generated
with blocking coding techniques on covariance matrices. In addition, it is
shown that the proposed quantum gaussian process regression algorithm can
achieve quadratic faster over the classical counterpart.
