Error Estimates for Space-Time Discretization of Parabolic Time-Optimal Control Problems with Bang-Bang Controls
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The technical objectives of the program were to develop an integrated, fully automated command and data interface between the TXM-Wizard developed at SLAC and the Xradia control software that is used on the Xradia Nano-TXM x-ray microscope with the goal of allowing non-experts including industry users to routinely access the advanced imaging modes that employ collection of images with spectroscopic information. The major accomplishment associated with this goal was the development of a plan to convert the TXM-Wizard software from MatLab to Python and the hiring of an expert Python programmer under contract to perform the conversion.
The technical objectives of the program were to develop an integrated, fully automated command and data interface between the TXM-Wizard developed at SLAC and the Xradia control software that is used on the Xradia Nano-TXM x-ray microscope with the goal of allowing non-experts including industry users to routinely access the advanced imaging modes that employ collection of images with spectroscopic information. The major accomplishment associated with this goal was the development of a plan to convert the TXM-Wizard software from MatLab to Python and the hiring of an expert Python programmer under contract to perform the conversion.
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The evolution of the state of a quantum computer is governed by Schrödinger's equation. We introduce compositional methods, a way to increase the order of symmetric methods by replacing one timestep by multiple timesteps. We perform several numerical experiments, including a simulation of a two qubit CNOT gate, using compositional variants of Störmer-Verlet and the implicit midpoint rule. We observe that the compositional methods demonstrate greater computational efficiency than the base methods when the desired error tolerance is less than ~ 10 -4 to 10 -5 . We discuss the trade-offs of using each compositional method, as well as differences between using Störmer-Verlet or the implicit midpoint rule as the base integrator of the compositional methods.
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