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In this note I survey the extensive literature on the dynamics of large series arrays of identical current biased Josephson junctions coupled through various shared loads. The equations describing the dynamics are invariant under…

Dynamical Systems · Mathematics 2017-07-04 D. G. Aronson

We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally…

Superconductivity · Physics 2007-05-23 Marco Frasca

We study a quantum Hamiltonian that models an two--dimensional array of Josephson junctions with short range Josephson couplings, (given by the Josephson energy E_J and charging energiey E_C due to the small capacitance of the junctions. We…

Superconductivity · Physics 2009-11-10 T. K. Kopec , T. P. Polak

We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 L. B. Ioffe , M. V. Feigel'man

We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for…

Quantum Physics · Physics 2019-08-16 Waltraut Wustmann , Vitaly Shumeiko

With the goal of understanding the intricate behavior and dynamics of collections of neurons, we present superconducting circuits containing Josephson junctions that model biologically realistic neurons. These "Josephson junction neurons"…

Superconductivity · Physics 2013-05-29 Patrick Crotty , Daniel Schult , Ken Segall

Superconducting circuits comprising Josephson junctions have spurred significant research activity due to their promise to realize scalable quantum computers. Effective Hamiltonians for these systems have traditionally been derived assuming…

Quantum Physics · Physics 2025-10-02 Thomas J. Maldonado , Alejandro W. Rodriguez , Hakan E. Türeci

Operation of a Superconducting Quantum Interference Device (SQUID) made of stacked Josephson junctions is analyzed numerically for a variety of junction parameters. Due to a magnetic coupling of junctions in the stack, such a SQUID has…

Superconductivity · Physics 2009-11-07 V. M. Krasnov

Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions,…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Yuriy Makhlin , Gerd Schoen , Alexander Shnirman

The properties of vortices in Josephson junction arrays are investigated in the quantum regime near the superconductor-insulator transition. We derive and study an effective action for vortex dynamics that is valid in the region where the…

Condensed Matter · Physics 2009-10-22 Anne van Otterlo , Rosario Fazio

Already in the first edition of this book (Barone and Paterno, "Fundamentals and Physics and Applications of the Josephson Effect", Wiley 1982), a great number of interesting and important applications for Josephson junctions were…

Quantum Physics · Physics 2019-08-27 Anton Frisk Kockum , Franco Nori

This paper illustrates a unified approach, classical circuit and control theories, to study a nonlinear LC circuit with a current dependent inductance as model of the Josephson junction, the mathematical analysis is complemented with…

Signal Processing · Electrical Eng. & Systems 2019-02-11 Alberto Delgado

Josephson junction parametric amplifiers are playing a crucial role in the readout chain in superconducting quantum information experiments. However, their integration with current 3D cavity implementations poses the problem of…

Quantum Physics · Physics 2014-07-23 A. Narla , K. M. Sliwa , M. Hatridge , S. Shankar , L. Frunzio , R. J. Schoelkopf , M. H. Devoret

An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the…

Quantum Physics · Physics 2007-05-23 K. Ch. Chatzisavvas , C. Daskaloyannis , C. P. Panos

The coherence of superconductivity and its suppression near a quantum phase transition is governed by the interplay between local pairing and macroscopic phase coherence. Using scanning SQUID, we image the local susceptibility in a hybrid…

Scaling superconducting quantum processors to large qubit counts faces challenges in control signal delivery, thermal management, and hardware complexity, particularly in achieving microwave signal multiplexing and long-distance quantum…

Quantum Physics · Physics 2025-09-30 Mustafa Bakr

In a Josephson phase qubit the coherent manipulations of the computational states are achieved by modulating an applied ac current, typically in the microwave range. In this work we show that it is possible to find optimal modulations of…

Mesoscale and Nanoscale Physics · Physics 2010-09-08 Shabnam Safaei , Simone Montangero , Fabio Taddei , Rosario Fazio

Even in the absence of Coulomb interactions phase fluctuations induced by quantum size effects become increasingly important in superconducting nano-structures as the mean level spacing becomes comparable with the bulk superconducting gap.…

Superconductivity · Physics 2014-03-05 Pedro Ribeiro , Antonio M. García-García

We discuss a charge qubit consisting of a circular array of Josephson junctions. The two-level system we consider couples the two charge states through a higher order tunneling process thus making it possible to achieve a long relaxation…

Mesoscale and Nanoscale Physics · Physics 2013-05-29 Joachim Sjostrand , Anders Karlhede

Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum…

Quantum Physics · Physics 2022-06-13 Timo Hillmann , Fernando Quijandría