Yu. Makhlin ^{1,2}, G. Schön ^{1,3}, and
A. Shnirman ^{1}

*
^{1}Institut für Theoretische Festkörperphysik,
Universität Karlsruhe, D-76128 Karlsruhe, Germany
^{2}Landau Institute for Theoretical Physics,
Kosygin St. 2, 117940 Moscow, Russia
^{3}Institut für Nanotechnologie, Forschungszentrum Karlsruhe,
D-76021 Karlsruhe, Germany
*

**Nanoscale superconducting quantum bits**

Physica C **350**, 161-165 (2001)

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits.

In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses.

The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a dc-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.