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

Multiple Silicon Dangling-Bond Charge qubits for quantum computing: A Hilbert-Space Analysis of the Hamiltonian