Quantum simulation of quantum field theory in the light-front formulation*

Quantum simulation of quantum field theories offers a new way to investigate properties of the fundamental constituents of matter. We develop quantum simulation algorithms based on the light-front formulation of relativistic field theories. We analyze a simple theory in 1$+$1D and show how to compute the analogues of parton distribution functions of composite particles in this theory. Upon quantizing the system in light-cone coordinates, the Hamiltonian becomes block diagonal, each block approximating the Fock space with a certain harmonic resolution K. The lower bound on the number of qubits required is O($\surd $K), and we give a complete description of the algorithm in a mapping that requires O($\surd $K logK) qubits and O(K$^{\mathrm{6}}$ ) gates. In higher dimensions, the scaling of the number of qubits remains the same, up to logarithmic factors. This is a notable advantage of the light-front formulation.