Quantum systems are inherently infinite dimensional. In particular quantum computers will use quantum systems as gates to store and manipulate information. But such systems suffer from decoherence which is caused by the quantum gate becoming entangled with its environment and losing information into that quantum environment. Feedback control has the promise of reducing this decoherence, but the feedback must be adaptive in the sense that it can perform its control tasks with very little information about the details of the quantum system itself. This paper is concerned with providing a framework for adaptive control of infinite dimensional quantum systems. The quantum system is describe as a linear continuous-time infinite-dimensional plant on a complex Hilbert space with persistent disturbances of known waveform but unknown amplitude and phase caused by fluctuations in the external quantum environment. We show here that there is a stabilizing direct model reference adaptive control law with disturbance rejection and robustness properties. The plant is described by a closed, densely defined linear operator, which is the Hamiltonian of the quantum system that generates a continuous semigroup of bounded operators on the complex Hilbert space of states. There is no state or disturbance estimation used in this adaptive approach. This will provide a framework for understanding adaptive feedback control in quantum systems.
展开▼
