Hamiltonian for coupled flux qubits

Details Hamiltonian for coupled flux qubits Hamiltonian for coupled flux qubits

2003-10-17

arxiv.org/abs/cond-mat/0310425v3

Phys. Rev. B_71_, 064503 (2005)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

REVTeX4, 16pp., one figure. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. Informal note. v2: completel

Scientific paper

10.1103/PhysRevB.71.064503

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 which 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->0. Fortunately, they merely renormalize 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.

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