The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform

T. Zhang - One of the best experts on this subject based on the ideXlab platform.

Metin Demiralp - One of the best experts on this subject based on the ideXlab platform.

  • topology of optimally controlled quantum mechanical Transition Probability landscapes
    Physical Review A, 2006
    Co-Authors: Herschel Rabitz, Taksan Ho, Michael Hsieh, Robert L Kosut, Metin Demiralp
    Abstract:

    An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical Transition Probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the Transition Probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce Transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a Transition Probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the Transition Probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a Transition Probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a Transition Probability of unit value is shown to have an extensive null space and only a finite number of negativemore » eigenvalues. Collectively, these findings show that (a) the Transition Probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.« less

Herschel Rabitz - One of the best experts on this subject based on the ideXlab platform.

  • Bounds on the curvature at the top and bottom of the Transition Probability landscape
    Journal of Physics B, 2011
    Co-Authors: Vincent Beltrani, Taksan Ho, Jason Dominy, Herschel Rabitz
    Abstract:

    The Transition Probability between the states of a controlled quantum system is a basic physical observable, and the associated control landscape is specified by the Transition Probability as a function of the applied field. An initial control likely will produce a Transition Probability near the bottom of the landscape, while the final goal is to find a field that results in a high Transition Probability value at the top. For controls producing either of the latter extreme landscape values, the Hessian of the Transition Probability with respect to the control field characterizes the curvature of the landscape and the ease of leaving either limit. Prior work showed that the Hessian spectrum possesses an upper bound on the number of non-zero eigenvalues as well as an infinite number of zero eigenvalues. The associated eigenfunctions accordingly specify the coordinated control field changes that either maximally or minimally influence the Transition Probability. We show in this paper that there exists a lower bound on the number of non-zero Hessian eigenvalues at either the top or bottom of the landscape. In particular, there is at least one non-zero eigenvalue at the top and generally one at the bottom. Under special circumstances, the Hessian may be identically zero at the bottom (i.e. it possesses no non-zero eigenvalues). These results dictate the curvature of the top and bottom of the landscape, which has important physical significance for seeking optimal control fields. At the top, a field that produces a single non-zero Hessian eigenvalue of small magnitude will generally exhibit a high degree of robustness to field noise. In contrast, at the bottom, working with a field producing the maximum number of non-zero eigenvalues will generally assure the most rapid climb towards a high Transition Probability.

  • topology of optimally controlled quantum mechanical Transition Probability landscapes
    Physical Review A, 2006
    Co-Authors: Herschel Rabitz, Taksan Ho, Michael Hsieh, Robert L Kosut, Metin Demiralp
    Abstract:

    An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical Transition Probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the Transition Probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce Transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a Transition Probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the Transition Probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a Transition Probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a Transition Probability of unit value is shown to have an extensive null space and only a finite number of negativemore » eigenvalues. Collectively, these findings show that (a) the Transition Probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.« less

Kungching Chang - One of the best experts on this subject based on the ideXlab platform.

Yun He - One of the best experts on this subject based on the ideXlab platform.

  • Trigger Identification Using Difference-Amplified Controllability and Dynamic Transition Probability for Hardware Trojan Detection
    IEEE Transactions on Information Forensics and Security, 2020
    Co-Authors: Kai Huang, Yun He
    Abstract:

    To remain dormant in the validation and manufacturing test, Trojans tend to have at least one trigger signal at the gate-level netlist with a very low Transition Probability. Our paper exploits this stealthy nature of trigger signals to detect Trojans using static and dynamic Transition probabilities. The proposed trigger identification is a reference-free scheme, and no prior knowledge of a Trojan-free design is required. First, we reveal the relation between combinational 0/1-controllability and 0/1-Probability and propose a static Transition Probability analysis based on our proposed difference-amplified controllability, which can be easily obtained by the Sandia Controllability/Observability Analysis Program. The k-means clustering method is adopted for potential trigger classification to extend the scalability and adaptability to different circuit sizes. Second, we propose to utilize the Transition Probability of a dynamic simulation for correction of the results. Experiments show that the proposed detection scheme can obtain a 0% false negative rate and a maximum 11.7% false positive rate on Trust-HUB benchmarks.