Operation of universal gates in a solid state quantum computer based on clean Josephson junctions between d-wave superconductors

Quantum computation algorithms promise of enormous speed up in dealing with certain classes of problems [1,2] can only be realized if a quantum computing device is built on a scale of at least several thousand qubits. The inherent scalability of solid state devices and high level of expertise existing in industrial electronics and experimental mesoscopic physics make solid state-based quantum computers an attractive choice [3,4]. The problem of quantum coherence preservation in such devices, in the presence of macroscopic number of degrees of freedom, is difficult but at least theoretically solvable [3,4]. Moreover, in a recent experiment on a superconducting quantum dot (single electron transistor, SET) [5] coherent quantum beats were demonstrated in this mesoscopic system, which proves its suitability as a qubit prototype.