  As quantum technology is advancing, the efficient design of quantum circuits
has become an important area of research. This paper provides an introduction
to the MCT quantum circuit design problem for reversible Boolean functions
without assuming a prior background in quantum computing. While this is a
well-studied problem, optimization models that minimize the true objective have
only been explored recently. This paper introduces a new optimization model and
symmetry-breaking constraints that improve solving time by up to two orders of
magnitude compared to earlier work when a Constraint Programming solver is
used. Experiments with up to seven qubits and using up to 15 quantum gates
result in several new best-known circuits, obtained by any method, for
well-known benchmarks. Finally, an extensive comparison with other approaches
shows that optimization models may require more time but can provide superior
circuits with optimality guarantees.
