Our studies of atomic collisions have enabled us to identify a new knob for controlling the two-body interaction between trapped atoms: Trap-induced resonances. I will show how these surprising new resonances can be used to implement two-qubit operations. I apply this to a realistic atomic species and describe our model of neutral atom quantum computing in addressable optical lattice systems. I will also discuss our generalized pseudopotential method that not only allows an accurate description of interactions in the system in question, but is widely applicable to atomic many-body systems.