Teacher leadership: a survey analysis of KwaZulu-Natal teachers’ perceptions

The notion of teacher leadership is implicit in official documentation in the South African education system post 1994, which emphasises a move towards a more shared and participatory approach to the practice of leadership and management in schools. The concept of teacher leadership is embedded in a distributed leadership theoretical framing which emphasises that leadership need not be located only in the position of the principal but can be stretched over a range of people who work at different levels in a school. We report on a study in which the perceptions of teachers’ on their understanding and experiences of teacher leadership were explored. The study adopted a survey approach and utilised closed questionnaires to gather data from 1,055 post level-one teachers across a range of schools of diverse contexts in KwaZulu-Natal. We found that while teachers supported the notion of shared leadership and believed they were equipped to lead, their leadership was largely restricted to their classrooms. There was some evidence of teacher leadership amongst teacher colleagues in certain curricular and extra-curricular activities. However, teacher leadership in relation to school-wide and community issues was almost non-existent. We signal two problematics regarding the leadership of school teachers and consider the implication of these for the distribution of leadership, and therefore change, in schools.Keywords: distributed leadership; education leadership; power; schoolmanagement teams; teacher leadership; teacher

Quantum Simulations on a Quantum Computer

We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.Comment: 4 pages, 2 figures (\documentstyle[prl,aps,epsfig,amscd]{revtex}); to appear in Phys. Rev. Let

Quantum gates and quantum algorithms with Clifford algebra technique

We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum algorithms needed in quantum computers in an elegant way. We identify $n$-qubits with spinor representations of the group SO(1,3) for a system of $n$ spinors. Representations are expressed in terms of products of projectors and nilpotents. An algorithm for extracting a particular information out of a general superposition of $2^n$ qubit states is presented. It reproduces for a particular choice of the initial state the Grover's algorithm.Comment: 9 pages, revte

Simulating Physical Phenomena by Quantum Networks

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by means of the algebra generated by the usual fermionic creation and annihilation operators, or by using the algebra of Pauli (spin-1/2) operators. The correspondence between the two algebras is given by the Jordan-Wigner isomorphism. As we previously noted similar one-to-one mappings enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental concept in quantum information processing to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g, spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian $H$.Comment: 44 pages, 15 psfigur

Clifford algebras and universal sets of quantum gates

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR

Experimental Implementation of the Quantum Baker's Map

This paper reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance (NMR) quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backwards to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to applied perturbations. These experiments are used to investigate previous predicted properties of quantum chaotic dynamics.Comment: submitted to PR

A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy

Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics.Comment: 33 pages plus 6 figures, LaTeX article class with amsmath & graphicx package