Shift-resistant quantum codes for Josephson-junction devices

•Mateusz Cholascinski1,2, Yuriy Makhlin1,3 und Gerd Schön1,4
2Nonlinear Optics Division, University of Poznan, Umultowska85, 61614 Poznan, Poland
3Landau Institute for Theoretical Physics, Kosygin St. 2, 117940, Moscow, Russia
4Forschungszentrum Karlsruhe, Institut für Nanotechnologie, D-76021 Karlsruhe
1Institut für Theoretische Festkörperphysik, Universität Karlsruhe

We describe properties of an rf-SQUID in terms of quantum information theory, bringing together the ideas of three different fields; namely quantum error correction, the use of Josephson-junction technology to realize qubits, and the analysis of decoherence in these systems. Since the system is characterized by two conjugate variables, the flux through the loop, and the charge on the leads of the junction, we may cleverly encode a qubit in the wave function using shift-resistant quantum codes (developed and described for quantum-optical implementation by Gottesman et al. 2001) so that quantum error correction is feasible. We show that this new approach to quantum error correction is applicable to solid state implementation. We discuss how to prepare the initial state of quantum register, implement a universal set of quantum gates and perform error-recovery in this system. We also analyze the sources of decoherence in the system leading to amplitude damping and dephasing in terms of model errors. Finally we discuss the sources of possible imperfections.