  We extend the Krylov-subspace based time-dependent numerical simulation
technique for a qubit interacting with photons in a waveguide to the multiple
qubit case. We analyze photon scattering from two qubits analytically and
derive expressions for the bound states in the continuum (BIC). We show how the
BIC can be excited. We use the BIC in a recent Pauli-Z gate proposal involving
decoherence free subspaces and obtain the gate fidelity as a function of the
gate parameters. The techniques presented in the paper are useful for
investigating the time evolution of quantum gates and other many-body systems
with multiple quenches in the Hamiltonian.
