Quantum Computing Implemented via Optimal Control: Application to Spin and Pseudospin Systems
Thomas Schulte‐Herbrüggen, Andreas K. Spörl, Raimund Marx, Navin Khaneja, John M. Myers, Amr Fahmy, Samuel J. Lomonaco, Louis Hirsch Kauffman, Steffen J. Glaser · 2016
This chapter discusses algorithmic and experimental aspects of quantum control of spin and pseudospin systems in view of realizing quantum algorithms or quantum simulations at minimal cost, in particular in a minimum amount of time. Geometric and optimal quantum control are most powerful tools for optimizing experimental implementations of quantum computing, whenever the quantum degrees of freedom can be described in closed Lie-algebraic form. It is highly desirable to strive for time-optimal implementations of quantum algorithms or their modules in order to avoid unnecessary decoherence. Apart from low temperatures, hyperpolarization techniques, or in situ reactions with para-hydrogen, even thermal ensemble states may be used for nuclear magnetic resonance (NMR) implementations of quantum algorithms, which are in principle scalable. NMR quantum processors are examples of expectation-value quantum computers (EVQC), where the outcome of a given quantum algorithm can be extracted from the resulting NMR spectra.