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 F and minimizing the control time T . In order to identify the critical time T * , 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 T ≥ T * in most cases. However, the optimization search effort rises superexponentially as T decreases and approaches T * . Furthermore, a small decrease in control time incurs a significant penalty in fidelity for T < T * , indicating that it is generally undesirable to operate below the critical time. We investigate the dependence of the critical time T * on the coupling strength between qubits and the target gate transformation. Practical consequences of these findings for laboratory implementation of quantum gates are discussed.

A new set of time-dependent deterministic sampling (TDDS) measures, based on local Shannon entropy, are presented to adaptively gauge the importance of various regions on a potential energy surface and to be employed in "on-the-fly" quantum dynamics. Shannon sampling and Shannon entropy are known constructs that have been used to analyze the information content in functions: for example, time-series data and discrete data sets such as amino acid sequences in a protein structure. Here the Shannon entropy, when combined with dynamical parameters such as the instantaneous potential, gradient and wavepacket density provides a reliable probe on active regions of a quantum mechanical potential surface. Numerical benchmarks indicate that the methods proposed are highly effective in locating regions of the potential that are both classically allowed as well as those that are classically forbidden, such as regions beyond the classical turning points which may be sampled during a quantum mechanical tunneling process. The approaches described here are utilized to improve computational efficiency in two different settings: (a) It is shown that the number of potential energy calculations required to be performed during on-the-fly quantum dynamics is fewer when the Shannon entropy based sampling functions are used. (b) Shannon entropy based TDDS functions are utilized to define a new family of grid-based electronic structure basis functions that reduce the computational complexity while maintaining accuracy. The role of both results for on-the-fly quantum/classical dynamics of electrons and nuclei is discussed.

This work develops measures for quantifying the effects of field noise upon targeted unitary transformations. Robustness to noise is assessed in the framework of the quantum control landscape, which is the mapping from the control to the unitary transformation performance measure (quantum gate fidelity). Within that framework, a new geometric interpretation of stochastic noise effects naturally arises, where more robust optimal controls are associated with regions of small overlap between landscape curvature and the noise correlation function. Numerical simulations of this overlap in the context of quantum information processing reveal distinct noise spectral regimes that better support robust control solutions. This perspective shows the dual importance of both noise statistics and the control form for robustness, thereby opening up new avenues of investigation on how to mitigate noise effects in quantum systems.

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Studies of neural dynamics in lateral orbitofrontal cortex (lOFC) have shown that subsets of neurons that encode distinct aspects of behavior, such as value, may project to common downstream targets. However, it is unclear whether reward history, which may subserve lOFC's well-documented role in learning, is represented by functional subpopulations in lOFC. We analyzed neural recordings from rats performing a value-based decision-making task, in which we previously documented trial-by-trial learning that required lOFC. We found five distinct clusters of lOFC neurons, either based on clustering of their trial-averaged peristimulus time histograms (PSTHs), or a feature space defined by their average conditional firing rates aligned to different task variables. We observed weak encoding of reward attributes, but stronger encoding of reward history, the animal's left or right choice, and reward receipt across all clusters. Only one cluster, however, encoded the animal's reward history at the time shortly preceding the choice, suggesting a possible role in integrating previous and current trial outcomes at the time of choice.