Optimal control for generating quantum gates in open dissipative systems

Overview & Synopsis

Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control fully exploiting known relaxation parameters against time-optimal control (the alternative for unknown relaxation parameters) is explored and exemplied in numerical and in algebraic terms: for instance, relaxation-based optimal control is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalising ideal decoherence-free subspaces to more realistic scenarios, opengrape-derived controls realise a cnot with delities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benet their control elds are orders of magnitude lower in power than bang-bang decouplings.