Parton physics on a quantum computer

Parton distribution functions and hadronic tensors may be computed on a universal quantum computer without many of the complexities that apply to Euclidean lattice calculations. We detail algorithms for computing predictions of parton distribution functions and the hadronic tensor in the Thirring model. Their generalization to QCD is discussed with the conclusion that the parton distribution function is best obtained by fitting the hadronic tensor rather than direct calculation. As a side effect of this method, we find that lepton-hadron cross sections may be computed relatively cheaply. Finally, we estimate the computational cost of performing such a calculation on a digital quantum computer, including the cost of state preparation for physically relevant parameters.

Figure 1

The quark distribution function of the lowest-lying fermion in the Thirring model, computed on a ten-site lattice. The Fourier transform of Eq. (9) is taken with $\epsilon =3$.