  Parton fragmentation functions (FFs) are indispensable for understanding
processes of hadron production ubiquitously existing in high-energy collisions,
but their first principle determination has never been realized due to the
insurmountable difficulties in encoding their operator definition using
traditional lattice methodology. We propose a framework that makes a first step
for evaluating FFs utilizing quantum computing methodology. The key element is
to construct a semi-inclusive hadron operator for filtering out hadrons of
desired types in a collection of particles encoded in the quantum state. We
illustrate the framework by elaborating on the Nambu-Jona-Lasinio model with
numeral simulations. Remarkably, We show that the semi-inclusive hadron
operator can be constructed efficiently with a variational quantum algorithm.
Moreover, we develop error mitigation techniques tailed for accurately
calculating the FFs in the presence of quantum noises. Our work opens a new
avenue for investigating QCD hadronization on near-term quantum computers.
