New Opportunities for Control: Quantum Internal Model Principle and Decoherence Control

Abstract

Decoherence, which is caused due to the interaction of a quantum system with its environment plagues all quantum systems and leads to the loss of quantum properties that are vital for quantum computation and quantum information processing. Superficially, this problem appears to be the disturbance decoupling problem in classical control theory. In this talk first we briefly review recent advances in Quantum Control. Then we propose a novel strategy using techniques from geometric systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment, is presented. This literally corresponds to the Internal Model Principle for Quantum Mechanical Systems which is quite different from the classical theory due to the quantum nature of the system. Almost all the earlier work on decoherence control employ density matrix and stochastic master equations to analyze the problem. Our approach to decoherence control involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. This approach yields interesting results on open loop decouplability and Decoherence Free Subspaces (DFS). The results are also shown to be superior to the ones obtained via master equations. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems performing decoherence free Quantum Computing. Open problems and future directions in quantum control also will be discussed.