2003/10/31 by Alec Maassen van den Brink · 1 citation
Computer Science · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum Information and Cryptography #Quantum and electron transport phenomena #cond-mat.mes-hall #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.71.064503
published as Phys. Rev. B_71_, 064503 (2005) · REVTeX4, 16pp., one figure. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. Informal note. v2: completely rewritten; correction of final result and major expansion. v3: added numerical verification plus a discussion of Ref. [2]
arxiv created 2003/12/12 · openalex publication_date 2005/02/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary ``free'' 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a ``fast variable,'' which can be eliminated adiabatically. However, the commonly used junction phases are not appropriate ``slow variables,'' and instead one introduces degrees of freedom that are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L\ensuremath→0. While their effect thus formally dominates over the classical self-flux, it merely renormalizes the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.