Mark S. Byrd

Aging and Cognitive Deficits

The general belief that cognitive abilities decline with age has been somewhat qualified in recent years. Many age-related effects previously demonstrated in studies using cross-sectional designs have been shown to be artifacts of sampling or of the different social and economic conditions experienced by different age cohorts (Schaie, 1973). In addition, older people tested in laboratory studies are usually further removed in time from formal education, and have not had so much recent practice at cognitive skills as their younger counterparts. Older experimental subjects may be less motivated to perform well on artificial laboratory tasks, they may have had less formal schooling and may be less healthy. As Avorn (Chapter 17) points out, these factors and others make interpretation of apparent age losses difficult and ought to induce substantial caution before observed deficits are attributed unequivocally to the aging process as such. On the other hand, it does not seem unreasonable to propose that genuine age-related deficits in cognitive functioning do occur. Physical strength, agility, and endurance clearly decline with age, and the various physiological systems of the body (respiratory, circulatory, digestive, excretory) also decline in efficiency as a person grows older (Finch & Hayflick, 1977). It would be rather extraordinary if the nervous system and its associated psychological functions were found to be immune to these otherwise widespread changes.

Polynomial-time simulation of pairing models on a quantum computer.

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between the ground and the first excited states and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.

Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing.

Proposals for scalable quantum computing devices suffer not only from decoherence due to the interaction with their environment, but also from severe engineering constraints. Here we introduce a practical solution to these major concerns, addressing solid-state proposals in particular. Decoherence is first reduced by encoding a logical qubit into two qubits, then completely eliminated by an efficient set of decoupling pulse sequences. The same encoding removes the need for single-qubit operations, which pose a difficult design constraint. We further show how the dominant decoherence processes can be identified empirically, in order to optimize the decoupling pulses.

Differential geometry on SU(3) with applications to three state systems

The left and right invariant vector fields are calculated in an “Euler angle”-type parametrization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This enables the calculation of the invariant volume element or Haar measure. These are then used to describe the density matrix of a pure state and geometric phases for three state systems.

Age differences in the ability to recall and summarize textual information

In order to examine age differences in the ability to manipulate textual information, young and old adults were asked to recall and summarize prose passages. It was found that while older adults showed a moderate age-related decline in the amount of information recalled, they had considerable difficulties in summarizing the same material. It was thought that this deficiency was due to the inability of the older adults to simultaneously comprehend textual information and organize an effective summary of the information. These results, which suggest that older adults manifest an age-related decrement in effortful linguistic processes, were discussed in terms of Kintsch and van Dijks [1978] model of discourse processing.

Overview of quantum error prevention and leakage elimination

Abstract Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally, we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as ‘leakage elimination operations’ or ‘LEOs’.

The geometry of SU(3)

The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.

Bures measures over the spaces of two- and three-dimensional density matrices

Abstract Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of more fundamental importance than (as several people have remarked to us) “just another parameterization of the density matrix”. There are several uses to which this methodology can be put. One that has received particular attention is in the construction of certain distinguished (Bures) measures on the ( n 2 −1)-dimensional convex sets of n × n density matrices.

Bang–Bang Operations from a Geometric Perspective

AbstractStrong, fast pulses, called “bang–bang” controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, provide a geometric picture for evaluating errors due to imperfect bang–bang controls and give conditions for the compatibility of BB operations with other controlling operations. This will provide additional support for the usefulness of such controls as a means for providing more reliable quantum information processing. PACS: 0.365.Yz, 03.67.Lx, 03.67-a

Nonperturbative leakage elimination operators and control of a three-level system.

Dynamical decoupling operations have been shown to reduce errors in quantum information processing. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEOs) were introduced. Here we provide an analysis of nonideal pulses, rather than the well-understood idealization or bang-bang controls. Under realistic conditions, we show that these controls will provide the same protection from errors as idealized controls. Our work indicates that the effectiveness of LEOs depends on the integral of the pulse sequence in the time domain, which has been missing because of the idealization of pulse sequences. Our results are applied to a three-level system for the nitrogen-vacancy centers under an external magnetic field and are illustrated by the fidelity dynamics of LEO sequences, ranging from regular rectangular pulses, random pulses, and even disordered (noisy) pulses.