A qubit unitary lattice algorithm is developed for the evolution of five coupled Gross–Pitaesvkii equations that govern the dynamics of a spin-2 Bose–Einstein Condensate. On introducing 2 qubits/scalar component of the order parameter, 10 qubits/lattice node are required. The interleaved sequence of unitary collide-stream operators relies on their non-commutivity in order that their be non-trivial evolution equations. This collisional entanglement followed by streaming of this entanglement throughout the lattice is a hallmark of the algorithm. The qubit algorithm for spin-2 is summarized and new Pade initial conditions are determined. Being unitary, the algorithm can be directly encoded onto a quantum-gate computer.