Skip to main content

Arindam Ghosh

NISER, Chemistry, Faculty Member

Followers

79

Following

3

Public Views

Arindam Ghosh is Reader - F in the department of Chemistry at the National Institute of Science Education and Research (NISER), Bhubaneswar, India

He was a postdoctoral associate in the department of Chemistry in State University of New York at Buffalo from 2006 to 2010. He received his Ph.D. in Physics from Indian Institute of Science, Bangalore, India in the year of 2006.
Supervisors: Prof. Anil Kumar, Dept of Physics, IISc, Bangalore
Address: FC102, National Institute of Science Education and Research (NISER)
Institute of Physics Campus, Sachivalaya Marg, Bhubaneswar 751005

less

InterestsView All (8)

Uploads

Papers by Arindam Ghosh

Curriculum Vitae

2006-2010 Postdoctoral Associate, SUNY UB, Buffalo, NY, USA 2001-2006 Doctoral studies at Indian ... more

Theory of mirrored time domain sampling for NMR spectroscopy

A generalized theory is presented for novel mirrored hypercomplex time domain sampling (MHS) of N... more A generalized theory is presented for novel mirrored hypercomplex time domain sampling (MHS) of NMR spectra. It is the salient new feature of MHS that two interferograms are acquired with different directionality of time evolution, that is, one is sampled forward from time t = 0 to the maximal evolution time tmax, while the second is sampled backward from t = 0 to −tmax. The sampling can be accomplished in a (semi) constant time or non constant-time manner. Subsequently, the two interferograms are linearly combined to yield a complex time domain signal. The manifold of MHS schemes considered here is defined by arbitrary settings of sampling phases (‘primary phase shifts’) and amplitudes of the two interferograms. It is shown that, for any two given primary phase shifts, the addition theorems of trigonometric functions yield the unique linear combination required to form the complex signal. In the framework of clean absorption mode (CAM) acquisition of NMR spectra being devoid of residual dispersive signal components, ‘secondary phase shifts’ represent time domain phase errors which are to be eliminated. In contrast, such secondary phase shifts may be introduced by experimental design in order to encode additional NMR parameters, a new class of NMR experiments proposed here.

2009/2012_US20090230959A1_Patent

The present invention relates to a method of conducting an N-dimensional nuclear magnetic resonan... more The present invention relates to a method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by the use of forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure time domain amplitudes and secondary phase shifts. The present invention also relates to methods of conducting an N-dimensional NMR experiment in a phase-sensitive manner by the use of dual forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image signal components arising in the frequency domain from secondary phase shifts.

Clean Absorption-Mode NMR Data Acquisition

Based on phase-shifted mirrored sampling (PMS) of indirect evolution periods of multi-dimensional... more Based on phase-shifted mirrored sampling (PMS) of indirect evolution periods of multi-dimensional experiments, new acquisition schemes eliminate, without application of a phase correction, dispersive signal components that exacerbate peak identification and shift peak maxima. The resulting enhanced resolution is of particular value for systems with high chemical shift degeneracy.

Clean absorption mode NMR data acquisition based on time-proportional phase incrementation

Clean absorption mode NMR data acquisition is presented based on mirrored time domain sampling an... more Clean absorption mode NMR data acquisition is presented based on mirrored time domain sampling and widely used time-proportional phase incrementation (TPPI) for quadrature detection. The resulting NMR spectra are devoid of dispersive frequency domain peak components. Those peak components exacerbate peak identification and shift peak maxima, and thus impede automated spectral analysis. The new approach is also of unique value for obtaining clean absorption mode reduced-dimensionality projection NMR spectra, which can rapidly provide high-dimensional spectral information for high-throughput NMR structure determination.

Z-matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra

Due to the limited sensitivity of many nuclear magnetic resonance (NMR) applications, careful con... more Due to the limited sensitivity of many nuclear magnetic resonance (NMR) applications, careful consideration must be given to the effect of NMR data processing on spectral noise. This work presents analytical relationships as well as simulated and experimental results characterizing the propagation of noise by unsymmetric covariance NMR processing, which concatenates two NMR spectra along a common dimension, resulting in a new spectrum showing spin correlations as cross peaks that are not directly measured in either of the two input spectra. It is shown how the unsymmetric covariance spectrum possesses an inhomogeneous noise distribution across the spectrum with the least amount of noise in regions whose rows and columns do not contain any cross or diagonal peaks and with the largest amount of noise on top of signal peaks. Therefore, methods of noise estimation commonly used in Fourier transform spectroscopy underestimate the amount of uncertainty in unsymmetric covariance spectra. Different data processing procedures, including the Z-matrix formalism, thresholding, and maxima ratio scaling, are described to assess noise contributions and to reduce noise inhomogeneity. In particular, determination of a Z score, which measures the difference in standard deviations of a statistic from its mean, for each spectral point yields a Z matrix, which indicates whether a given peak intensity above a threshold arises from the covariance of signals in the input spectra or whether it is likely to be caused by noise. Application to an unsymmetric covariance spectrum, obtained by concatenating two 2D 13C–1H heteronuclear, single quantum coherence (HSQC) and 13C–1H heteronuclear, multiple bond correlation (HMBC) spectra of a metabolite mixture along their common proton dimension, reveals that for sufficiently sensitive input spectra the reduction in sensitivity due to covariance processing is modest.

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant... more Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant quantum computations. However, since decoherence plays a crucial role in such studies, understanding of mixed state geometric phase has become important. While mixed state geometric phase was first introduced mathematically by Uhlmann, recently Sjöqvist et al. [Phys. Rev. Lett. 85 (14) (2000) 2845] have described the mixed state geometric phase in the context of quantum interference and shown theoretically that the visibility as well as the shift of the interference pattern are functions of geometric phase and the purity of the mixed state. Here we report the first experimental study of the dependence of interference visibility and shift of the interference pattern on the mixed state geometric phase by nuclear magnetic resonance.

Relaxation of pseudo pure states: the role of cross-correlations

In quantum information processing by NMR one of the major challenges is relaxation or decoherence... more In quantum information processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like quantum error correction codes or noiseless subsystems. Here we study the relaxation behavior of various pseudo pure states and analyze the role of cross-terms between different relaxation processes, known as cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground ... more Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover’s search algorithm and Deutsch–Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover’s search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch–Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh’s algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order View the MathML source (where N = 2n and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

Quantum Information Processing by NMR using strongly coupled spins

The enormous theoretical potential of quantum information processing (QIP) is driving the pursuit... more The enormous theoretical potential of quantum information
processing (QIP) is driving the pursuit for its
practical realization by various physical techniques.
Currently, nuclear magnetic resonance (NMR) has
been the forerunner by demonstrating a majority of
quantum algorithms. In NMR, spin-systems consisting
of coupled nuclear spins are utilized as qubits. In
order to carry out QIP, a spin-system has to meet two
major requirements: (i) qubit addressability and (ii)
mutual coupling among the qubits. It has been demonstrated
that the magnitude of the mutual coupling
among qubits can be increased by orienting the spinsystems
in a liquid crystal matrix and utilizing the residual
dipolar couplings. While utilizing residual dipolar
couplings may be useful to increase the number
of qubits, nuclei of the same species (homonuclei)
might become strongly coupled. In strongly coupled
spin-systems, spins lose their individual identity of
being qubits. We propose that even such strongly coupled
spin-systems can be used for QIP and the qubitmanipulation
can be achieved by transition-selective
pulses. We demonstrate experimental preparation of
pseudopure states, creation of maximally entangled
states, implementation of logic gates and implementation
of Deutsch–Jozsa (DJ) algorithm in strongly coupled
2, 3 and 4 spin-systems. The energy levels of the
strongly coupled 3 and 4 spin-systems were obtained
using a Z-COSY experiment.

Quantum Information Processing by NMR: Relaxation of Pseudo Pure States, Geometric Phases and Algorithms

Curriculum Vitae

2006-2010 Postdoctoral Associate, SUNY UB, Buffalo, NY, USA 2001-2006 Doctoral studies at Indian ... more

Theory of mirrored time domain sampling for NMR spectroscopy

A generalized theory is presented for novel mirrored hypercomplex time domain sampling (MHS) of N... more A generalized theory is presented for novel mirrored hypercomplex time domain sampling (MHS) of NMR spectra. It is the salient new feature of MHS that two interferograms are acquired with different directionality of time evolution, that is, one is sampled forward from time t = 0 to the maximal evolution time tmax, while the second is sampled backward from t = 0 to −tmax. The sampling can be accomplished in a (semi) constant time or non constant-time manner. Subsequently, the two interferograms are linearly combined to yield a complex time domain signal. The manifold of MHS schemes considered here is defined by arbitrary settings of sampling phases (‘primary phase shifts’) and amplitudes of the two interferograms. It is shown that, for any two given primary phase shifts, the addition theorems of trigonometric functions yield the unique linear combination required to form the complex signal. In the framework of clean absorption mode (CAM) acquisition of NMR spectra being devoid of residual dispersive signal components, ‘secondary phase shifts’ represent time domain phase errors which are to be eliminated. In contrast, such secondary phase shifts may be introduced by experimental design in order to encode additional NMR parameters, a new class of NMR experiments proposed here.

2009/2012_US20090230959A1_Patent

The present invention relates to a method of conducting an N-dimensional nuclear magnetic resonan... more The present invention relates to a method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by the use of forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure time domain amplitudes and secondary phase shifts. The present invention also relates to methods of conducting an N-dimensional NMR experiment in a phase-sensitive manner by the use of dual forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image signal components arising in the frequency domain from secondary phase shifts.

Clean Absorption-Mode NMR Data Acquisition

Based on phase-shifted mirrored sampling (PMS) of indirect evolution periods of multi-dimensional... more Based on phase-shifted mirrored sampling (PMS) of indirect evolution periods of multi-dimensional experiments, new acquisition schemes eliminate, without application of a phase correction, dispersive signal components that exacerbate peak identification and shift peak maxima. The resulting enhanced resolution is of particular value for systems with high chemical shift degeneracy.

Clean absorption mode NMR data acquisition based on time-proportional phase incrementation

Clean absorption mode NMR data acquisition is presented based on mirrored time domain sampling an... more Clean absorption mode NMR data acquisition is presented based on mirrored time domain sampling and widely used time-proportional phase incrementation (TPPI) for quadrature detection. The resulting NMR spectra are devoid of dispersive frequency domain peak components. Those peak components exacerbate peak identification and shift peak maxima, and thus impede automated spectral analysis. The new approach is also of unique value for obtaining clean absorption mode reduced-dimensionality projection NMR spectra, which can rapidly provide high-dimensional spectral information for high-throughput NMR structure determination.

Z-matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra

Due to the limited sensitivity of many nuclear magnetic resonance (NMR) applications, careful con... more Due to the limited sensitivity of many nuclear magnetic resonance (NMR) applications, careful consideration must be given to the effect of NMR data processing on spectral noise. This work presents analytical relationships as well as simulated and experimental results characterizing the propagation of noise by unsymmetric covariance NMR processing, which concatenates two NMR spectra along a common dimension, resulting in a new spectrum showing spin correlations as cross peaks that are not directly measured in either of the two input spectra. It is shown how the unsymmetric covariance spectrum possesses an inhomogeneous noise distribution across the spectrum with the least amount of noise in regions whose rows and columns do not contain any cross or diagonal peaks and with the largest amount of noise on top of signal peaks. Therefore, methods of noise estimation commonly used in Fourier transform spectroscopy underestimate the amount of uncertainty in unsymmetric covariance spectra. Different data processing procedures, including the Z-matrix formalism, thresholding, and maxima ratio scaling, are described to assess noise contributions and to reduce noise inhomogeneity. In particular, determination of a Z score, which measures the difference in standard deviations of a statistic from its mean, for each spectral point yields a Z matrix, which indicates whether a given peak intensity above a threshold arises from the covariance of signals in the input spectra or whether it is likely to be caused by noise. Application to an unsymmetric covariance spectrum, obtained by concatenating two 2D 13C–1H heteronuclear, single quantum coherence (HSQC) and 13C–1H heteronuclear, multiple bond correlation (HMBC) spectra of a metabolite mixture along their common proton dimension, reveals that for sufficiently sensitive input spectra the reduction in sensitivity due to covariance processing is modest.

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant... more Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant quantum computations. However, since decoherence plays a crucial role in such studies, understanding of mixed state geometric phase has become important. While mixed state geometric phase was first introduced mathematically by Uhlmann, recently Sjöqvist et al. [Phys. Rev. Lett. 85 (14) (2000) 2845] have described the mixed state geometric phase in the context of quantum interference and shown theoretically that the visibility as well as the shift of the interference pattern are functions of geometric phase and the purity of the mixed state. Here we report the first experimental study of the dependence of interference visibility and shift of the interference pattern on the mixed state geometric phase by nuclear magnetic resonance.

Relaxation of pseudo pure states: the role of cross-correlations

In quantum information processing by NMR one of the major challenges is relaxation or decoherence... more In quantum information processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like quantum error correction codes or noiseless subsystems. Here we study the relaxation behavior of various pseudo pure states and analyze the role of cross-terms between different relaxation processes, known as cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground ... more Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover’s search algorithm and Deutsch–Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover’s search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch–Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh’s algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order View the MathML source (where N = 2n and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

Quantum Information Processing by NMR using strongly coupled spins

The enormous theoretical potential of quantum information processing (QIP) is driving the pursuit... more The enormous theoretical potential of quantum information
processing (QIP) is driving the pursuit for its
practical realization by various physical techniques.
Currently, nuclear magnetic resonance (NMR) has
been the forerunner by demonstrating a majority of
quantum algorithms. In NMR, spin-systems consisting
of coupled nuclear spins are utilized as qubits. In
order to carry out QIP, a spin-system has to meet two
major requirements: (i) qubit addressability and (ii)
mutual coupling among the qubits. It has been demonstrated
that the magnitude of the mutual coupling
among qubits can be increased by orienting the spinsystems
in a liquid crystal matrix and utilizing the residual
dipolar couplings. While utilizing residual dipolar
couplings may be useful to increase the number
of qubits, nuclei of the same species (homonuclei)
might become strongly coupled. In strongly coupled
spin-systems, spins lose their individual identity of
being qubits. We propose that even such strongly coupled
spin-systems can be used for QIP and the qubitmanipulation
can be achieved by transition-selective
pulses. We demonstrate experimental preparation of
pseudopure states, creation of maximally entangled
states, implementation of logic gates and implementation
of Deutsch–Jozsa (DJ) algorithm in strongly coupled
2, 3 and 4 spin-systems. The energy levels of the
strongly coupled 3 and 4 spin-systems were obtained
using a Z-COSY experiment.

Quantum Information Processing by NMR: Relaxation of Pseudo Pure States, Geometric Phases and Algorithms