  We present a systematic quantum algorithm, which integrates both the hadronic
state preparation and the evaluation of real-time light-front correlators, to
study parton distribution functions (PDFs). As a proof of concept, we
demonstrate the first direct simulation of the PDFs in the 1+1 dimensional
Nambu-Jona-Lasinio model. We show the results obtained by exact diagonalization
and by quantum computation using classical hardware. The agreement between
these two distinct methods and the qualitative consistency with QCD PDFs
validate the proposed quantum algorithm. Our work suggests the encouraging
prospects of calculating QCD PDFs on current and near-term quantum devices. The
presented quantum algorithm is expected to have many applications in high
energy particle and nuclear physics.
