Matthew D. Grace

Robust control of quantum gates via sequential convex programming

Resource trade-offs can often be established by solving an appropriate robust optimization problem for a variety of scenarios involving constraints on optimization variables and uncertainties. Using an approach based on sequential convex programming, we demonstrate that quantum gate transformations can be made substantially robust against uncertainties while simultaneously using limited resources of control amplitude and bandwidth. Achieving such a high degree of robustness requires a quantitative model that specifies the range and character of the uncertainties. Using a model of a controlled one-qubit system for illustrative simulations, we identify robust control fields for a universal gate set and explore the trade-off between the worst-case gate fidelity and the field fluence. Our results demonstrate that, even for this simple model, there exists a rich variety of control design possibilities. In addition, we study the effect of noise represented by a stochastic uncertainty model.

Advances in sediment transport modelling

A detailed description of how recently-developed sediment dynamics formulations are incorporated into the United States Environmental Protection Agencys Environmental Fluid Dynamics Code is presented. The new approach is an extension of previous models and accounts for multiple sediment size classes, has a unified treatment of suspended load and bedload, and appropriately replicates bed armouring. The resulting flow, transport, and sediment dynamics model is an improvement to previous models because it may directly incorporate site-specific data, while maintaining a physically consistent, unified treatment of bedload and suspended load. Experimental data from a noncohesive sediment erosion experiment in a straight channel help validate the numerical model. In this simulation, unknown parameters representing the active layer thickness and the erosion rates of the two largest sediment size classes when they are newly deposited are identified from the available data.

Environment-invariant measure of distance between evolutions of an open quantum system

The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite quantum system that consists of a sub-system of interest (e.g. a quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite system, when the effect on only the sub-system of interest is considered. The invariance to the environments transformation makes it possible to quantitatively compare the evolution of an open quantum system and its closed counterpart. The distance measure also determines the fidelity bounds of a general quantum channel (a completely positive and trace-preserving map acting on the sub-system of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the system and straightforward to numerically calculate. As an example, the measure is used in numerical

Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations

Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the trade-off between the competitive objectives of maximizing the gate fidelity

Sandia National Laboratories environmental fluid dynamics code : sediment transport user manual.

\mathcal{F}

Encoding a qubit into multilevel subspaces

and minimizing the control time

Recent Advances in Sediment Transport Modeling

T

Characterization of control noise effects in optimal quantum unitary dynamics

. In order to identify the critical time

Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments

T^{\ast}

Optimized pulses for the control of uncertain qubits.

, below which the target transformation is not reachable, as well as to determine the associated Pareto front, we introduce a numerical method of Pareto front tracking (PFT). We consider closed two- and multi-qubit systems with constant inter-qubit coupling strengths and each individual qubit controlled by a separate time-dependent external field. Our analysis demonstrates that unit fidelity (to a desired numerical accuracy) can be achieved at any