Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian for coupled flux qubits   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.

25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg