  Silicon-based dangling-bond charge qubit is one of the auspicious models for
universal fault-tolerant solid-state quantum computing. In universal quantum
computing, it is crucial to evaluate and characterize the computational Hilbert
space and reduce the complexity and size of the computational space. Here, we
recognize this problem to understand the complexity and characteristics of the
Hilbert space in our dangling-bond qubit model. The size of the desired Hilbert
space can prominently be reduced by considering assumptions regarding the qubit
loss. Moreover, the dimension of the desired subsets in the space shrinks by a
factor of two due to the spin preservation property. Finally, the required
classical memory for storage of the qubit information, Hamiltonian and Hilbert
space is analysed when the number of qubits grows.
