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http://hdl.handle.net/2005/6
2017-05-22T00:02:29ZOptimization Of NMR Experiments Using Genetic Algorithm : Applications In Quantum Infomation Processing, Design Of Composite Operators And Quantitative Experiments
http://hdl.handle.net/2005/2616
Title: Optimization Of NMR Experiments Using Genetic Algorithm : Applications In Quantum Infomation Processing, Design Of Composite Operators And Quantitative Experiments
Authors: Manu, V S
Abstract: Genetic algorithms (GA) are stochastic global search methods based on the
mechanics of natural biological evolution, proposed by John Holland in 1975. Here
in this thesis, we have exploited possible utilities of Genetic Algorithm optimization
in Nuclear Magnetic Resonance (NMR) experiments. We have performed
(i ) Pulse sequence generation and optimization for NMR Quantum Information
Processing, (ii ) efficient creation of NOON states, (iii ) Composite operator design
and (iv ) delay optimization for refocused quantitative INEPT. We have generated
time optimal as well as robust pulse sequences for popular quantum gates. A
Matlab package is developed for basic Target unitary operator to pulse sequence
optimization and is explained with an example.
Chapter 1 contains a brief introduction to NMR, Quantum computation and Genetic
algorithm optimization. Experimental unitary operator decomposition using
Genetic Algorithm is explained in Chapter 2. Starting from a two spin homonu-
clear system (5-Bromofuroic acid), we have generated hard pulse sequences for
performing (i ) single qubit rotation, (ii ) controlled NOT gates and (iii ) pseudo
pure state creation, which demonstrates universal quantum computation in such
systems. The total length of the pulse sequence for the single qubit rotation of an
angle π/2 is less than 500µs, whereas the conventional method (using a selective
soft pulse) would need a 2ms shaped pulse. This substantial shortening in time
can lead to a significant advantage in quantum circuits. We also demonstrate the
creation of Long Lived Singlet State and other Bell states, directly from thermal
equilibrium state, with the shortest known pulse sequence. All the pulse sequences
generated here are generic i.e., independent of the system and the spectrometer.
We further generalized this unitary operator decomposition technique for a variable
operators termed as Fidelity Profile Optimization (FPO) (Chapter 3) and
performed quantum simulations of Hamiltonian such as Heisenberg XY interaction
and Dzyaloshinskii-Moriya interaction. Exact phase (φ) dependent experimental
unitary decompositions of Controlled-φ and Controlled Controlled-φ are solved
using ﬁrst order FPO. Unitary operator decomposition for experimental quantum
simulation of Dzyaloshinskii-Moriya interaction in the presence of Heisenberg XY
interaction is solved using second order FPO for any relative strengths of interactions
(γ) and evolution time (τ ). Experimental gate time for this decomposition
is invariant under γ or τ , which can be used for relaxation independent studies of
the system dynamics. Using these decompositions, we have experimentally verified
the entanglement preservation mechanism suggested by Hou et al. [Annals of
Physics, 327 292 (2012)].
NOON state or Schrodinger cat state is a maximally entangled N qubit state
with superposition of all individual qubits being at |0 and being at |1 . NOON
states have received much attention recently for their high precession phase
measurements, which enables the design of high sensitivity sensors in optical interfer-
ometry and NMR [Jones et al. Science, 324 1166(2009)]. We have used Genetic
algorithm optimization for efficient creation of NOON states in NMR (Chapter 4).
The decompositions are, (i ) a minimal in terms of required experimental resources
– radio frequency pulses and delays – and have (ii ) good experimental fidelity.
A composite pulse is a cluster of nearly connected rf pulses which emulate the
effect of a simple spin operator with robust response over common experimental
imperfections. Composite pulses are mainly used for improving broadband de-
coupling, population inversion, coherence transfer and in nuclear overhauser effect
experiments. Composite operator is a generalized idea where a basic operator
(such as rotation or evolution of zz coupling) is made robust against common
experimental errors (such as inhomogeneity / miscalibration of rf power or errror
in evaluation of zz coupling strength) by using a sequence of basic operators
available for the system. Using Genetic Algorithm optimization, we have designed
and experimentally verified following composite operators, (i ) broadband rotation
pulses, (ii ) rf inhomogeneity compensated rotation pulses and (iii ) zz evolution
operator with robust response over a range of zz coupling strengths (Chapter 5).
We also performed rf inhomogeneity compensated Controlled NOT gate.
Extending Genetic Algorithm optimization in classical NMR applications, we have
improved the quantitative refocused constant-time INEPT experiment (Q-INEPT-
CT) of M¨kel¨ et al. [JMR 204(2010) 124-130] with various optimization constraints
. The improved ‘average polarization transfer’ and ‘min-max difference’
of new delay sets effectively reduces the experimental time by a factor of two
(compared with Q-INEPT-CT, M¨kel¨ et al.) without compromising on accuracy
(Chapter 6). We also introduced a quantitative spectral editing technique based
on average polarization transfer. These optimized quantitative experiments are
also described in Chapter 6.
Time optimal pulse sequences for popular quantum gates such as, (i ) Controlled
Hadamard (C-H) gate, (ii ) Controlled-Controlled-NOT (CCNOT) Gate and (iii )
Controlled SWAP (C-S) gate are optimized using Genetic Algorithm (Appendix.
A). We also generated optimal sequences for Quantum Counter circuits, Quantum
Probability Splitter circuits and efficient creation of three spin W state. We
have developed a Matlab package based on GA optimization for three spin target
operator to pulse sequence generator. The package is named as UOD (Unitary
Operator Decomposition) is explained with an example of Controlled SWAP gate
in Appendix. B.
An algorithm based on quantum phase estimation, which discriminates quantum
states non-destructively within a set of arbitrary orthogonal states, is described
and experimentally verified by a NMR quantum information processor (Appendix.
C). The procedure is scalable and can be applied to any set of orthogonal states.
Scalability is demonstrated through Matlab simulation.2017-05-20T18:30:00ZStructure, Dynamics And Thermodynamics Of Confined Water Molecules
http://hdl.handle.net/2005/2618
Title: Structure, Dynamics And Thermodynamics Of Confined Water Molecules
Authors: Kumar, Hemant
Abstract: This thesis deals with several aspects of the structure and dynamics of water molecules confined in nanoscopic pores. Water molecules confined in hydrophobic nanocavities exhibit unusual structural and dynamic properties. Confining walls of single-wall carbon nanotubes (SWCNTs) promote strong inter-water hydrogen bonding which in turn leads to several novel structural, dynamic and thermodynamic features not found in bulk water. Confined water molecules form ordered hydrogen-bonded networks, exhibit exceptionally high flow rates as compared to conventional flow in pipes, allow fast proton conduction and exhibit various other anomalous properties. Proteins are known to exploit some of the properties of confined water to perform certain physiological functions. Various properties of confined water can also be exploited in the design of nanofludic devices such as those for desalination and flow sensors. In addition, water molecules confined in SWCNTs and near graphene sheets serve as model systems to study various effects of confinement on the properties of liquids. In this thesis, we present the results of detailed molecular dynamics simulation studies of confined water molecules.
In chapter 1, we summarize the findings of existing simulations and experimental studies of bulk and confined water molecules. We also highlight the significance of studying the structure and dynamics of confined water molecules in biological and biotechnological applications. Chapter 2 provides a brief ac-count of the methods and techniques used to perform the simulations described in subsequent chapters of the thesis. We also present a brief overview of the methods used to extract physical properties of water molecules from simulation data, with emphasis on the Two Phase Thermodynamics (2PT) method which we have used to compute the entropy of confined and bulk water molecules.
In chapter 3, we discuss the thermodynamics of water entry in SWCNTs of various diameters. Experiments and computer simulations demonstrate that water spontaneously fills the interior of a carbon nanotube. Given the hydrophobic nature of the interior of carbon nanotubes and the strong confinement produced by narrow nanotubes, the spontaneous entry of water molecules in the pores of such nanotubes is surprising. To gain a quantitative thermodynamic understanding of this phenomenon, we use the recently developed Two Phase Thermodynamics (2PT) method to compute translational and rotational entropies of water molecules confined in SWCNTs and show that the increase in energy of a water molecule inside the nanotube is compensated by the gain in its rotational entropy. The confined water is in equilibrium with the bulk water and the Helmholtz free energy per water molecule of confined water is the same as that in the bulk within the accuracy of the simulation results. A comparison of translational and rotational spectra of water molecules confined in carbon nanotubes with those of bulk water shows significant shifts in the positions of spectral peaks that are directly related to the tube radius. These peaks are experimentally accessible and can be used to characterize water dynamics from spectroscopy experiments. We have also computed the free-energy transfer when a bulk water molecule enters a SWCNT for various temperatures and carbon-water interactions. We show that for reduced carbon-oxygen interaction, the free energy transfer is unfavourable and the SWCNT remains unoccupied for significant periods of time. As the temperature is increased, the free energy of confined water becomes unfavourable and reduced occupancy of water is observed.
Bulk water exhibits many anomalous properties. No single water model is able to reproduce all properties of bulk water. Different empirical water models have been developed to reproduce different properties of water. In chapter 4, a comparative study of the structure, dynamics and thermodynamic proper-ties of water molecules confined in narrow SWCNTs, obtained from simulations using several water models including polarizable ones, is presented. We show that the inclusion of polarizability quantitatively affects the nature of hydro-gen bonding which governs different properties of water molecules. The SPC/E water model is shown to reproduce results in close agreement with those from polarizable water models with much less computational cost.
In chapter 5, we report results obtained from simulations of the properties of water confined in the space between two planar surfaces. We consider three cases: two graphene surfaces, two Boron Nitride (BN) surfaces and one graphene and one BN surface. This is the ﬁrst detailed study of the behaviour of water near extended BN surfaces. We show that the hydrophilic nature of the BN surface leads to several interesting effects on the dynamics of water molecules near it. We have observed a change in the activation energy, extracted from the temperature dependence of the translational and rotational dynamics, near 280K. This change in activation energy coincides with a change in the structure of the confined sheet of water, indicated by a sudden change in energy. We have also found signatures of glassy dynamics at low temperatures for all three cases, the glassy effects being the strongest for water molecules confined between two BN sheets. These results are similar to those of earlier studies in which novel phases of water have been found for water molecules conﬁned between other surfaces at high pressure.
In chapter 6, we have described our observation of a novel phenomenon exhibited by water molecules flowing through a SWCNT under a pressure gradient. We have shown that the flow induces changes in the orientation of the water molecules flowing through the nanotube. In particular, the dipole moments of the water molecules inside the nanotube get aligned along the axis of the nanotube under the effect of the flow. With increasing flow velocities, the net dipole moment ﬁrst increases and eventually saturates to a constant value. This behaviour is similar to the Langevin theory of paramagnetism with the flow velocity acting as an effective aligning field. Preferential entry of water molecules with dipole moments pointing inward is shown to be the main cause of this effect. This observation provides a way to control the dipolar alignment of water molecules inside nano-channels, with possible applications in nanofluidic devices. Chapter 7 contains a summary of our main results and a few concluding re-marks.2017-05-20T18:30:00ZElectrical Transport And Low Frequency Noise In Graphene And Molybdenum Disulphide
http://hdl.handle.net/2005/2617
Title: Electrical Transport And Low Frequency Noise In Graphene And Molybdenum Disulphide
Authors: Ghatak, Subhamoy
Abstract: This thesis work contains electrical transport and low frequency (1/f) noise measurements in ultrathin graphene and Molybdenum disulphide (MoS2) field effect transistors (FET). From the measurements, We mainly focus on the origin of disorder in both the materials.
To address the orgin of disorder in graphene, we study single and bilayer graphene-FET devices on SiO2 substrate. We observe that both conductivity and mobility are mainly determined by substrate induced long range, short range, and polar phonon scattering. For further confirmation, we fabricate suspended graphene devices which show extremely high mobility. We find that, in contrast to substrate-supported graphene, conductivity and mobility in suspended graphene are governed by the longitudinal acoustic phonon scattering at high temperature and the devices reach a ballistic limit at low temperature. We also conduct low frequency 1/f noise measurements, known to be sensitive to disorder dynamics, to extract more information on the nature of disorder. The measurements are carried out both in substrate-supported and suspended graphene devices. We find that 1/f noise in substarted graphene is mainly determined by the trap charges in the SiO2 substrate. On the other hand, noise behaviour in suspended graphene devices can not be explained with trap charge dominated noise model. More-over, suspended devices exhibit one order of magnitude less noise compared to graphene on SiO2 substrate. We believe noise in suspended graphene devices probably originate from metal-graphene contact regions.
In the second part of our work, We present low temperature electrical transport in ultrathin MoS2 fields effect devices, mechanically exfoliated onto Si/SiO2 substrate. Our experiments reveal that the electronic states in MoS2 are localized well up to the room temperature over the experimentally accessible range of gate voltage. This manifests in two dimensional (2D) variable range hopping (VRH) at high temperatures, while below ~ 30 K the conductivity displays oscillatory structures in gate voltage arising from resonant tunneling at the localized sites. From the correlation energy (T0) of VRH and gate voltage dependence of conductivity, we suggest that the charged impurities are the dominant source of disorder in MoS2. To explore the origin of the disorder, we perform temperature dependent I - V measurements at high source-drain bias. These measurements indicate presence of an exponentially distributed trap states in MoS2 which originate from the structural inhomogeneity. For more detailed investigation, we employ 1/f noise which further confirms possible presence of structural disorder in the system. The origin of the localized states is also investigated by spectroscopic studies, which indicate a possible presence of metallic 1T-patches inside semiconducting 2H phase. From all these evidences, we suggest that the disorder is internal, and achieving high mobility in MoS2 FET requires a greater level of crystalline homogeneity.2017-05-20T18:30:00ZDevelopment Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography
http://hdl.handle.net/2005/2608
Title: Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography
Authors: Gupta, Saurabh
Abstract: Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation, namely, diffuse optical tomography (DOT) and one of its variations, ultrasound-modulated optical tomography (UMOT). Since in both these imaging modalities the system matrices are ill-conditioned owing to insufficient and noisy data, the emphasis in this work is to develop robust stochastic filtering algorithms which can handle measurement noise and also account for inaccuracies in forward models through an appropriate assignment of a process noise.
However, we start with demonstration of speeding of a Gauss-Newton (GN) algorithm for DOT so that a video-rate reconstruction from data recorded on a CCD camera is rendered feasible. Towards this, a computationally efficient linear iterative scheme is proposed to invert the normal equation of a Gauss-Newton scheme in the context of recovery of absorption coefficient distribution from DOT data, which involved the singular value decomposition (SVD) of the Jacobian matrix appearing in the update equation. This has sufficiently speeded up the inversion that a video rate recovery of time evolving absorption coefficient distribution is demonstrated from experimental data. The SVD-based algorithm has made the number of operations in image reconstruction to be rather than. 2()ONN3()ONN
The rest of the algorithms are based on different forms of stochastic filtering wherein we arrive at a mean-square estimate of the parameters through computing their joint probability
distributions conditioned on the measurement up to the current instant. Under this, the first algorithm developed uses a Bootstrap particle filter which also uses a quasi-Newton direction within. Since keeping track of the Newton direction necessitates repetitive computation of the Jacobian, for all particle locations and for all time steps, to make the recovery computationally feasible, we devised a faster update of the Jacobian. It is demonstrated, through analytical reasoning and numerical simulations, that the proposed scheme, not only accelerates convergence but also yields substantially reduced sample variance in the estimates vis-à-vis the conventional BS filter. Both accelerated convergence and reduced sample variance in the estimates are demonstrated in DOT optical parameter recovery using simulated and experimental data.
In the next demonstration a derivative free variant of the pseudo-dynamic ensemble Kalman filter (PD-EnKF) is developed for DOT wherein the size of the unknown parameter is reduced by representing of the inhomogeneities through simple geometrical shapes. Also the optical parameter fields within the inhomogeneities are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions). The EnKF is then used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the Pseudo-Dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ‘measurement’ equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. In our numerical simulations we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes ( such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as = 0.01 mm-1 and = 1.0 mm-1respectively. We also assume=0.02 mm-1 within the inhomogeneity (for the single inhomogeneity case) and=0.02 and 0.03 mm-1 (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one.
The superiority of a modified version of the PD-EnKF, which uses an ensemble square root filter, is also demonstrated in the context of UMOT by recovering the distribution of mean-squared amplitude of vibration, related to the Young’s modulus, in the ultrasound focal volume. Since the ability of a coherent light probe to pick-up the overall optical path-length change is limited to modulo an optical wavelength, the individual displacements suffered owing to the US forcing should be very small, say within a few angstroms. The sensitivity of modulation depth to changes in these small displacements could be very small, especially when the ROI is far removed from the source and detector. The contrast recovery of the unknown distribution in such cases could be seriously impaired whilst using a quasi-Newton scheme (e.g. the GN scheme) which crucially makes use of the derivative information. The derivative-free gain-based Monte Carlo filter not only remedies this deficiency, but also provides a regularization insensitive and computationally competitive alternative to the GN scheme. The inherent ability of a stochastic filter in accommodating the model error owing to a diffusion approximation of the correlation transport may be cited as an added advantage in the context of the UMOT inverse problem.
Finally to speed up forward solve of the partial differential equation (PDE) modeling photon transport in the context of UMOT for which the PDE has time as a parameter, a spectral decomposition of the PDE operator is demonstrated. This allows the computation of the time dependent forward solution in terms of the eigen functions of the PDE operator which has speeded up the forward solution, which in turn has rendered the UMOT parameter recovery computationally efficient.2017-04-26T18:30:00Z