  Macroscopic quantum tunneling of the phase is a fundamental phenomenon in the
quantum dynamics of superconducting nanocircuits. The tunneling rate can be
controlled in such circuits, where the potential landscape for the phase can be
tuned with different external bias parameters. Precise theoretical knowledge of
the macroscopic quantum tunneling rate is required in order to simulate and
understand the experiments. We present a derivation, based on the instanton
technique, of an analytical expression of the escape rate in general quartic
and symmetric sextic potentials comprising two escape paths. These new
potentials were recently realized when creating a noise-insensitive phase qubit
in the camel-back potential of a dc SQUID.
