  A model master equation suitable for quantum computing dynamics is presented.
In an ideal quantum computer (QC), a system of qubits evolves in time unitarily
and, by virtue of their entanglement, interfere quantum mechanically to solve
otherwise intractable problems. In the real situation, a QC is subject to
decoherence and attenuation effects due to interaction with an environment and
with possible short-term random disturbances and gate deficiencies. The
stability of a QC under such attacks is a key issue for the development of
realistic devices. We assume that the influence of the environment can be
incorporated by a master equation that includes unitary evolution with gates,
supplemented by a Lindblad term. Lindblad operators of various types are
explored; namely, steady, pulsed, gate friction, and measurement operators. In
the master equation, we use the Lindblad term to describe short time intrusions
by random Lindblad pulses. The phenomenological master equation is then
extended to include a nonlinear Beretta term that describes the evolution of a
closed system with increasing entropy, plus a Bath environment term stipulated
by a fixed temperature. Here we explore the case of a simple one-qubit system
in preparation for generalization to multi-qubit, qutrit and hybrid
qubit-qutrit systems. This model master equation can be used to test the
stability of memory and the efficacy of quantum gates. The properties of such
hybrid master equations are explored, with emphasis on the role of thermal
equilibrium and entropy constraints.
