  We theoretically consider possible errors in solid state quantum computation
due to the interplay of the complex solid state environment and gate
imperfections. In particular, we study two examples of gate operations in the
opposite ends of the gate speed spectrum, an adiabatic gate operation in
electron-spin-based quantum dot quantum computation and a sudden gate operation
in Cooper pair box superconducting quantum computation. We evaluate
quantitatively the non-adiabatic operation of a two-qubit gate in a
two-electron double quantum dot. We also analyze the non-sudden pulse gate in a
Cooper-pair-box-based quantum computer model. In both cases our numerical
results show strong influences of the higher excited states of the system on
the gate operation, clearly demonstrating the importance of a detailed
understanding of the relevant Hilbert space structure on the quantum computer
operations.
