Inductance effects in the persistent current qubit

Abstract

A general method is illustrated to show that the Hamiltonian for circuits of Josephson junctions can he expanded in terms of three Hamiltonians: a Hamiltonian representative of the inductance-free circuit, a Hamiltonian in the form of an harmonic oscillator for the inductance effects of the circulating currents, and a small correction term. This method is used to show that the inductive effects are a small correction to the difference in energy levels in the persistent current qubit.

Magnetic states of a rf superconducting quantum interference device containing a double-barrier Josephson junction

“…[4][5][6][7] Very recently, a double-barrier Josephson junction ͑DBJJ͒ has been shown to have a nonsinusoidal current-phase relation ͑CPR͒. 8 The properties of DBJJs had already been studied both experimentally and theoretically before.…”

A multi-Josephson junction qubit

“…(1). As the qubit just described is close to the one that has been investigated by Mooij and coworkers [5,6], we can apply the results of their investigation on coupling to the environment, coupling to SQUID detectors, and the low inductance limit [7] to the system proposed here. The main difference between the current proposed system and that of Mooij and coworkers is the spatial mapping of the qubit states (which in turn can engender different coupling terms), and the proposed coupling to a Cirac Zoller type bus [8].…”

Equivalent Single-Junction Model of Superconducting Quantum Interference Devices in the Presence of Time-Varying Fields

“…Due to the intrinsic macroscopic coherence of superconductors, r. f. SQUIDs have been proposed as basic units (qubits) in quantum computing [4]. In the realm of quantum computing, nondissipative quantum systems with small (or null) inductance parameter and finite capacitance of the Josephson junctions (JJs) are usually considered [5]. The mesoscopic nonsimply connected classical devices, on the other hand, are generally operated and studied in the overdamped limit with negligible capacitance of the JJs and small (or null) values of the inductance parameter.…”