Reduced control Hamiltonian of the silent phase qubit has been found and dependence of the Hamiltonian matrix elements on applied magnetic field has been analyzed. The obtained results yield in concept of qubit logic operations accomplished by means of magnetic field application. One can propose a set of the qubits, each designed for specific logic operation. The qubit logic specialization may be fixed by both the junction current-phase relation and the characteristic Josephson-to-Coulomb energy ratio s. As current-phase relation is assigned, the qubit specialization can be tuned by the ratio s which varies with Josephson junction area. Examples of some logic operations are considered. Estimation of both the decoherence time and the quality factor Q has been obtained for such a qubit based on high-T_c superconductors, which could provide the required current-phase relation.
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