Quantum complexity

• We find that the behavior of a drifting resonant quantum system is closely related to that of its classical counterpart. The quantized Harper model which is similar to the pendulum but confined to phase space of a torus, is remarkably simple when written in terms of generalized Pauli operators, but the distance between its neighboring energy levels can span many orders of magnitude. If the system drifts, then non-adiabatic behavior such as transitions in to a superposition state, cannot be entirely supressed. Notions of Adiabatic Drift in the Quantized Harper model Will be posted soon!
• In classical systems, the width of a chaotic region can be estimated from the integral of a perturbation along the separatrix orbit. We derive an analogous relation for a discrete quantum system by taking the average of the perturbation in the interaction picture and using an eigenstate state with energy near that of the separatrix. Quantum chaos on the separatrix of the periodically perturbed Harper model (on arxiv) , In AVS Quantum Science

Classical orbits on the left. Husimi functions showing phase space of Floquet states of the associated quantum system on the right.
• Bridging between quantum and classical phenomena on a quantum computer Generating quantum channels from functions on discrete sets (on arxiv) , in Quantum Information processing