Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation

The use of spin echoes to refocus one spin interactions (chemical shifts) and two spin interactions (spin-spin couplings) plays a central role in both conventional NMR experiments and NMR quantum computation. Here we describe schemes for efficient refocussing of such interactions in both fully and partially coupled spin systems.Comment: 4 pages, RevTeX, including 4 LaTeX figure

Quantum Logic Gates and Nuclear Magnetic Resonance Pulse Sequences

We demonstrate how NMR can in principle be used to implement all the elements required to build quantum computers, and briefly discuss the potential applications of insights from quantum logic to the development of novel pulse sequences with applications in more conventional NMR experiments.Comment: Sixteen pages, no figures. Submitted to Journal of Magnetic Resonance. Primarily pedagogical rather than a description of novel research result

Doctor of Philosophy

dissertationIn connectomics the goal is to generate a full 3D reconstruction of neurons within the brain. This reconstruction will help neuroscientists better understand how the brain functions and also how it fails in the case of dementia and other neurodegenerative diseases. Attempts for this reconstruction are ongoing at varying levels of resolution from the millimeter scale of magnetic resonance imaging (MRI) to the nanometer scale of electron microscopy. In this dissertation, we develop tools that improve the ability of researchers to trace neurons through a volume in vitro at a resolution sufficient for the identification of synapses. The first toolset will speed up the process for generating training datasets in newly acquired volumes to be used in supervised learning methods. Current methods of training dataset generation require dense labeling by a trained research scientist over hundreds of hours. This toolset will reduce the time required for training data generation by using sparse sampling and reduce the cost of that time by using a priori knowledge of the structure to allow for less specialized researchers to assist in the process. The second toolset is targeted at speeding up the correction of errors introduced in automatic neuron segmentation methods. Often referred to as proofreading, current methods require significant user input and fail to fully incorporate the information generated by the automatic segmentation method. I will use novel 2D and 3D visualization techniques to take advantage of the information generated during automatic segmentation into the proofreading process. This toolset will consist of two different applications, with one process targeting 2D proofreading with 3D linking and the other process targeting direct 3D proofreading

NMR Quantum Logic Gates for Homonuclear Spin Systems

If NMR systems are to be used as practical quantum computers, the number of coupled spins will need to be so large that it is not feasible to rely on purely heteronuclear spin systems. The implementation of a quantum logic gate imposes certain constraints on the motion of those spins not directly involved in that gate, the so-called "spectator" spins; they must be returned to their initial states at the end of the sequence. As a result, a homonuclear spin system where there is appreciable coupling between every pair of spins would seem to require a refocusing scheme that doubles in complexity and duration for every additional spectator spin. Fortunately, for the more realistic practical case where long-range spin-spin couplings can be neglected, simpler refocusing schemes can be devised where the overall duration of the sequence remains constant and the number of soft pulses increases only linearly with the number of spectator spins. These ideas are tested experimentally on a six qubit system: the six coupled protons of inosine.Comment: 11 pages LaTeX plus 6 fig

Pulse Sequences for NMR Quantum Computers: How to Manipulate Nuclear Spins While Freezing the Motion of Coupled Neighbours

We show how to divide a coupled multi-spin system into a small subset of ``active'' spins that evolve under chemical shift or scalar coupling operators, and a larger subset of ``spectator'' spins which are returned to their initial states, as if their motion had been temporarily frozen. This allows us to implement basic one-qubit and two-qubit operations from which general operations on $N$-qubits can be constructed, suitable for quantum computation. The principles are illustrated by experiments on the three coupled protons of 2,3-dibromopropanoic acid, but the method is applicable to any spin-1/2 nuclei and to systems containing arbitrary numbers of coupled spins.Comment: 11 pages, 5 fig

Chumash Heritage National Marine Sanctuary Sacred Waters Film

The debate to designate a National Marine Sanctuary off the Central Coast of California has been alive for nearly 30 years. With a recent move by the National Oceanic and Atmospheric Administration (NOAA) to nominate the stretch of water as a sanctuary the issue has become one of great concern to local stakeholders. With concern for additional bureaucracy and regulation that could negatively impact the local economy people choose to stand in opposition. Yet many that are concerned for the future of the region\u27s waters want the protections from offshore oil drilling and other harmful practices that a Sanctuary would provide and therefore are supportive of designation. The film aims to tell the stories and share perspectives of the main stakeholders to give the region at large an understanding of the issue so they can take a stance rooted in their own values. The project covers strategy for social media promotion, crowdfunding, and final distribution of Sacred Waters Film

Geometric quantum computation with NMR

The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that depends on the quantum state of another subsystem. In particular, the subsystem may acquire a conditional phase shift. Here we consider a novel scenario in which this phase is of geometric rather than dynamical origin. As the conditional geometric (Berry) phase depends only on the geometry of the path executed it is resilient to certain types of errors, and offers the potential of an intrinsically fault-tolerant way of performing quantum gates. Nuclear Magnetic Resonance (NMR) has already been used to demonstrate both simple quantum information processing and Berry's phase. Here we report an NMR experiment which implements a conditional Berry phase, and thus a controlled phase shift gate. This constitutes the first elementary geometric quantum computation.Comment: Minor additions at request of referees. 4 pages revtex including 2 figures (1 eps). Nature in pres

Experimental realization of a highly structured search algorithm

The highly structured search algorithm proposed by Hogg[Phys.Rev.Lett. 80,2473(1998)] is implemented experimentally for the 1-SAT problem in a single search step by using nuclear magnetic resonance technique with two-qubit sample. It is the first demonstration of the Hogg's algorithm, and can be readily extended to solving 1-SAT problem for more qubits in one step if the appropriate samples possessing more qubits are experimentally feasible.Comment: RevTex, 11 pages + 3 pages of figure

Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy

An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations. Gradient-diffusion experiments are also described for several more complex forms of decoherence, including the well-known collective isotropic model. Finally, it is shown that the Hadamard formalism gives a concise representation of decoherence with arbitrary correlations among the fluctuating fields at the different spins involved, and that this can be applied to both decoherence (T2) as well as nonadiabatic relaxation (T1) processes.Comment: RevTeX, 11 page single-spaced preprint, no figures. Version two has new title, abstract, introduction & conclusions, while the main body of the text remains substantially the sam

NMR analogues of the quantum Zeno effect

We describe Nuclear Magnetic Resonance (NMR) demonstrations of the quantum Zeno effect, and discuss briefly how these are related to similar phenomena in more conventional NMR experiments.Comment: 8 pages including 4 figures; intended as a possible answer to Malcolm Levitt's question at the 2005 Magnetic Resonanace GRC: "What is the NMR analogue of the quantum Zeno effect?". In press at Physics Letters