Stabilizing coherence and arbitrary target properties with Hamiltonian control - Part 1: Theory

To harness the full potential of quantum computers, it is crucial to maintain specific properties of quantum systems, such as coherence or fidelity. In this talk, we present a theory identifying which target properties of a quantum system can be perfectly preserved using purely Hamiltonian control. The theory also provides us with a constructive way to design the corresponding Hamiltonians. This applies for both Markovian and time-local non-Markovian environments. We provide concrete examples of such control Hamiltonians for preserving coherence or fidelity for a qubit system. Additionally, we identify the presence of 'stable points'—states where the desired property remains intact indefinitely. We also identify 'breakdown times,' which indicate the duration for which the Hamiltonian control method effectively maintains the property, after which the Hamiltonian diverges and maintaining the target property becomes impossible. Both stable points and the phenomenon of control breakdown depend on the particular target property and the type of environment. Our theory applies to arbitrary-dimensional quantum systems. This talk is part 1 or 2; the second talk describes our experimental realization of the theory.