  In this paper we discuss solid-state nanoelectronic realizations of Josephson
flux qubits with large tunneling amplitude between the two macroscopic states.
The latter can be controlled via the height and wells form of the potential
barrier, which is determined by quantum-state engineering of the flux qubit
circuit. The simplest circuit of the flux qubit is a superconducting loop
interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude
between two macroscopically different states can be essentially increased, by
engineering of the qubit circuit, if tunnel junction is replaced by a ScS
contact. However, only Josephson tunnel junctions are particularly suitable for
large-scale integration circuits and quantum detectors with preset-day
technology. To overcome this difficulty we consider here the flux qubit with
high-level energy separation between "ground" and "excited" states, which
consists of a superconducting loop with two low-capacitance Josephson tunnel
junctions in series. We demonstrate that for real parameters of resonant
superposition between the two macroscopic states the tunneling amplitude can
reach values greater than 1K. Analytical results for the tunneling amplitude
obtained within semiclassical approximation by instanton technique show good
correlation with a numerical solution.
