Designing toroidal cavities for quantum computation

Toroidal microwave cavities are investigated for potential use in quantum information storage and computation. Since exact analytical results are not available for this geometry, extensive numerical simulation has been used to develop a universal phenomenological model ("spectral flow diagram"). This model is needed to guide the non-trivial design of toroidal resonators. A host of new modes that do not exist in cylindrical cavities are classified, including novel counter-intuitive ground states, and "dark nodal modes" that are decoupled from the environment in the absence of antennae. Numerical results are found to be in good agreement with experimental data. The existence of dark nodal modes in a shallow smooth cavity geometry that offers easy access for high quality surface treatment, suggests that high-Q toroidal cavities may be exploited for long-term storage of quantum information used in quantum processors.