Josephson Junctions
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The device that is the workhorse of most superconducting computers is the Josephson Junction, which consists of two superconducting regions separated by a non-superconducting layer—usually an insulator. In this chapter, the authors begin with a basic discussion of tunneling. They use a phenomenological approach to model the coupling between the superconductors in a Josephson junction resulting from the tunneling of Cooper pairs. A qubit can also be formed by placing two Josephson junctions in parallel. This configuration is referred to as a Superconducting Quantum Interference Device, or SQUID. By biasing the Josephson junction with different currents, it can also be used to realize a time-varying inductance that is used in low noise parametric amplifiers. Finally, when two junctions are placed in parallel, the effective inductance can be varied by the application of a magnetic field. This makes it possible to realize tunable qubits.Keywords:
Superconducting tunnel junction
Kinetic inductance
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the “ground” and “excited” states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution.
Flux qubit
Charge qubit
Superconducting tunnel junction
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Superconducting tunnel junction
Flux qubit
Charge qubit
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We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.
Flux qubit
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Superconducting tunnel junction
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We report development and microwave characterization of rf SQUID (Superconducting QUantum Interference Device) qubits, consisting of an aluminium-based Josephson junction embedded in a superconducting loop patterned from a thin film of TiN with high kinetic inductance. Here we demonstrate that the systems can offer small physical size, high anharmonicity, and small scatter of device parameters. The hybrid devices can be utilized as tools to shed further light onto the origin of film dissipation and decoherence in phase-slip nanowire qubits, patterned entirely from disordered superconducting films.
Kinetic inductance
Superconducting tunnel junction
Flux qubit
Coplanar waveguide
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We report development and microwave characterization of rf SQUID (Superconducting QUantum Interference Device) qubits, consisting of an aluminium-based Josephson junction embedded in a superconducting loop patterned from a thin film of TiN with high kinetic inductance. Here we demonstrate that the systems can offer small physical size, high anharmonicity, and small scatter of device parameters. The work constitutes a non-tunable prototype realization of an rf SQUID qubit built on the kinetic inductance of a superconducting nanowire, proposed in Phys. Rev. Lett. 104, 027002 (2010). The hybrid devices can be utilized as tools to shed further light onto the origin of film dissipation and decoherence in phase-slip nanowire qubits, patterned entirely from disordered superconducting films.
Kinetic inductance
Flux qubit
Superconducting tunnel junction
Coplanar waveguide
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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)].
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Superconducting tunnel junction
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Charge qubit
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The superconducting phase qubit combines Josephson junctions into superconducting loops and defines one of the promising solid state device implementations for quantum computing. While conventional designs are based on magnetically frustrated superconducting loops, here we discuss the advantages offered by $π$-junctions in obtaining naturally degenerate two-level systems. Starting from a basic five-junction loop, we show how to construct degenerate two-level junctions and superconducting phase switches. These elements are then effectively engineered 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 analogue of the `quiet' s-wave-d-wave-s-wave Josephson junction qubits introduced by Ioffe {\it et al.} [Nature {\bf 398}, 679 (1999)].
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Superconducting tunnel junction
Charge qubit
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We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.
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Superconducting tunnel junction
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