### Quantum Josephson Junction Circuits

A superconductor can be characterized by the absolute value (number of the quasiparticles) and the phase f of the macroscopic wavefunction, representing the order parameter. As for any quantum system, both of them cannot be determined simultaneously. If a Josephson junction is formed by the two massive superconductors they are insensitive to the fluctuations of the quasiparticle number and the junction evolution can be described by the classical equations for the relative phase of the contacting superconductors. Small superconductors, however, have small capacitance ; if the charging energy exceeds the Josephson energy , then the charge fluctuations are suppressed, and the circuit demonstrates essentially quantum behavior. It has been demonstrated that in this case it is possible to create a quantum superposition of the two different charge states of the superconductor, thus, forming a qubit. This is possible by biasing the additional gate contact [31] or applying a microwave radiation [32]. As a result, the Bloch oscillations of frequency between the two charge states are inspired. Addressing of the qubit can be accomplished by the control of the duration of the gate voltage pulse, while the two-qubit operation can be organized by coupling of the different circuits. The obvious advantage of this scheme is that it exploits a quantum behavior of a macroscopic system that promises relatively easy control of the qubit. On the other hand, this concept is not free of some drawbacks. In particular, to inspire the Bloch oscillations, the applied voltage pulse must be sharp on the time scale . Although the Josephson energy can be controlled by external magnetic flux, to avoid decoherence during the computation, it should be kept at the level about 50 meV, as the London length and the coherence length of the Cooper which corresponds to about 10 GHz in the frequency domain. Obviously, it is a great challenge to achieve reliable operation at such high frequencies of massive circuits containing a large number of qubits. In addition, there are some restrictions in the possible miniaturization of the Josephson-junction circuits. Currently, the experiments accomplished where done with the superconductor having dimensions of the order of a micron that corresponds to the charging energy about 0.1 meV. Scaling down the junction dimensions increases the charging energy. As a result, a more precise adjustment of the gate voltage required for the resonance condition is necessary. What is more fundamental, the scaling of the junction dimensions is restricted by such scales pairs.