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Physics-Uspekhi

Josephson solid-state qubits

Yu. A. Pashkin, O. V. Astafiev, Tsuyoshi Yamamoto, Yasunobu Nakamura, Jaw-Shen Tsai

Published Sep 30, 2004• 0 citations
Publisher

Abstract

Superconducting states and magnetic hysteresis in finite superconductors Gelii F Zharkov Theory of magnetic contacts between clean superconductors Yurii S Barash, Irina V Bobkova and T Kopp A quantum bit based on a Josephson contact between conventional and high-temperature superconductors (theory) Mikhail V Feigel'man Superconductivity and superfluidity (what was done and what was not) Vitalii L Ginzburg Realization of topologically protected quantum bits in a Josephson junction array L B Ioffe and Mikhail V Feigel'man Bloch oscillations in quantum dot superlattices Robert A Suris and Ivan A Dmitriev Axisymmetric steady flows in astrophysics Vasilii S Beskin Josephson solid-state qubits

DOI
10.1070/pu2004v047n09abeh001874

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Superconducting states and magnetic hysteresis in finite superconductors Gelii F Zharkov Theory of magnetic contacts between clean superconductors Yurii S Barash, Irina V Bobkova and T Kopp A quantum bit based on a Josephson contact between conventional and high-temperature superconductors (theory) Mikhail V Feigel'man Superconductivity and superfluidity (what was done and what was not) Vitalii L Ginzburg Realization of topologically protected quantum bits in a Josephson junction array L B Ioffe and Mikhail V Feigel'man Bloch oscillations in quantum dot superlattices Robert A Suris and Ivan A Dmitriev Axisymmetric steady flows in astrophysics Vasilii S Beskin Josephson solid-state qubits
We propose a complete quantum computation process on a topologically protected Josephson junction array system, originally proposed by Ioffe and Feigel'man [Phys. Rev. B 66, 224503 (2002)]. Logical qubits for computation are encoded in the punctured array. The number of qubits is determined by the number of holes. The topological degeneracy is lightly shifted by tuning the flux along specific paths. We show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.
A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called $\ensuremath{\pi}$ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such $\ensuremath{\pi}$ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one $\ensuremath{\pi}$ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and $\ensuremath{\pi}$ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].
Control and manipulation of quantum states by measurements and bath engineering in open quantum systems, like in a quantum computer, have emerged as new paradigms in many-body physics. Taking a prototypical example of Josephson junction arrays (JJAs), we show how monitoring through continuous weak measurements and feedback can transform an insulating steady state in JJAs to a superconductor (SC) and vice versa. We show that the quantum feedback, when not too large, is crucial to realize such a superconducting steady state by maintaining an effective temperature in a semiclassical limit. However, we show that large feedback can destroy superconductivity by enhancing quantum phase fluctuations. Thus, dissipation and phase fluctuations in the presence of monitoring have fundamental differences from those in the well-studied case of JJAs in contact with an equilibrium Ohmic bath. In general, a description in terms of only an effective temperature is not adequate for the monitored JJAs. Using a variational approximation, and by considering various limiting cases, we demonstrate that these differences can give rise to reentrant SC-insulator phase transitions leading to an unusual inverse transition from a seemingly low-effective-temperature insulating normal state to a superconducting state at intermediate temperature.