Quantum behavior of the dc SQUID phase qubit

We analyze the behavior of a dc Superconducting Quantum Interference Device
(SQUID) phase qubit in which one junction acts as a phase qubit and the rest of
the device provides isolation from dissipation and noise in the bias leads.
Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and
use numerical methods and a cubic approximation to solve Schrodinger's equation
for the eigenstates, energy levels, tunneling rates, and expectation value of
the currents in the junctions. Using these results, we investigate how well
this design provides isolation while preserving the characteristics of a phase
qubit. In addition, we show that the expectation value of current flowing
through the isolation junction depends on the state of the qubit and can be
used for non-destructive read out of the qubit state.