  A quantum algorithm of SU(N) Yang-Mills theory is formulated in terms of
quantum circuits. It can nonperturbatively calculate the Dyson series and
scattering amplitudes with polynomial complexity. The gauge fields in the
interaction picture are discretized on the same footing with the lattice
fermions in momentum space to avoid the fermion doubling and the gauge symmetry
breaking problems. Applying the algorithm to the quantum simulation of quantum
chromodynamics, the quark and gluon's wave functions evolved from the initial
states by the interactions can be observed and the information from wave
functions can be extracted at any discrete time. This may help us understand
the natures of the hadronization which has been an outstanding question of
significant implication on high energy phenomenological studies.
