Multiple silicon dangling-bond charge qubits for quantum computing: a Hilbert-space analysis of the Hamiltonian

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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.