  The energy gap is calculated for the ground state quantum computer circuit,
which was recently proposed by Mizel et.al. When implementing a quantum
algorithm by Hamiltonians containing only pairwise interaction, the inverse of
energy gap $1/\Delta$ is proportional to $N^{4k}$, where $N$ is the number of
bits involved in the problem, and $N^k$ is the number of control operations
performed in a standard quantum paradigm. Besides suppressing decoherence due
to the energy gap, in polynomial time ground state quantum computer can finish
the quantum algorithms that are supposed to be implemented by standard quantum
computer in polynomial time.
