  Unconventional superconductors exhibit an order parameter symmetry lower than
the symmetry of the underlying crystal lattice. Recent phase sensitive
experiments on YBCO single crystals have established the d-wave nature of the
cuprate materials, thus identifying unambiguously the first unconventional
superconductor. The sign change in the order parameter can be exploited to
construct a new type of s-wave - d-wave - s-wave Josephson junction exhibiting
a degenerate ground state and a double-periodic current-phase characteristic.
Here we discuss how to make use of these special junction characteristics in
the construction of a quantum computer. Combining such junctions together with
a usual s-wave link into a SQUID loop we obtain what we call a `quiet' qubit
--- a solid state implementation of a quantum bit which remains optimally
isolated from its environment.
