Benchmarking the Dirac-generated unitary lattice qubit collision-stream algorithm for 1D vector Manakov soliton collisions

The unitary quantum lattice gas (QLG) algorithm is a mesoscopic unitary perturbative representation that can model the mean field Gross Pitaevskii equation for the evolution of the ground state wave function of Bose Einstein Condensates (BECs). The QLG considered here consists of an interleaved sequence of unitary collide-stream operators, with the collision operator being deduced from that for the Dirac equation, with the nonlinear potentials of the BECs being the mass term in the Dirac equation. Since the unitary collision operator is more accurate one obtains a more accurate representation of the nonlinear terms. Further benchmark QLG simulations are reported here: that for the exactly soluble 1D vector Manakov soliton collisions. It is found that this Dirac-based unitary algorithm permits simulations with vector soliton parameters (soliton amplitudes and speeds) that are considerably greater than those achieved under our previous swap QLG algorithm.