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Quantum Simulations by NMR : Applications to Small Spin Chains and Ising Spin Systems

‎K‎. ‎R‎. ‎K‎. ‎Rao

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital…

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Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems.
The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain.
In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations.
Chapter 4 contains a digital…
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were used as qubits to implement the three-qubit Deutsch-Josza algorithm using high-resolution NMR. A classification of the Deutsch-Josza functions according to the operator representation of the corresponding oracle transformations was given. Different classes of functions may produce full, partial or no entanglement in the output states of the algorithm. This entanglement content is not immediately evident from the output states themselves. A procedure was given for mapping of the output states onto Bell- or GHZ-states by means of local transformations which preserve the entanglement content. A method for the visualization of single-spin unitary transformations was also presented. This visual representation can facilitate analysis and design of shaped rf pulses. For the purpose of quantum computing, it can be useful to suppress couplings between qubits during the application of finite-length single-qubit gates. The feasibility of this idea was demonstrated using small molecules in a liquid crystal matrix. In a series of proof-of-principle experiments, it was shown that the magic-echo sequence can be used to suppress the dipole-dipole coupling between spins and simultaneously selectively address a single spin by a soft rf pulse. The S-bus concept for spin-quantum computing holds some scalability promise and provides a testbed for studies of large, strongly coupled quantum registers. Single-crystal CaF2 weakly doped with Ce was used to implement the concept. The nine 19F nuclear spins adjacent to the paramagnetic Ce-ion serve as qubits while the electron spin plays the role of a quantum bus. The S-bus theory was tested experimentally. Procedures were given for the measurement of parameters characterizing the quantum state of the nuclear spins. An exact numeric treatment of this ten-spin system was done to aid in understanding the experimental findings. For a pair of nuclear spins with negligible direct dipolar coupling, the CNOT operation was implemented. The spin-spin coupling mediated by the bus spin was utilized for that purpose. The four Bell-states of these two distant spins were created. An experiment was performed who's signature allows those four entangled states to be distinguished. The paramagnetic cluster in CaF2:Ce is embedded in an extended network of 19F nuclear spins. This network is a powerful source of decoherence. A number of existing and a newly designed pulse sequence were tested with respect to their ability to suppress decoherence and their aptitude for use in quantum computing.
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 spin-systems 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 same species (homonuclei) might become strongly coupled. In strongly coupled spin-systems, spins loose their individual identity of being qubits. We propose that even such strongly coupled spin-systems can be used for QIP and the qubit-manipulation can be achieved by transition-selective pulses. We demonstrate experimental preparation of pseudopure states, creation of maximally entangled states, implementation 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 by using a Z-COSY experiment.
Rapid developments in quantum information processing have been made, and remarkable achievements have been obtained in recent years, both in theory and experiments. Coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance (NMR) system, especially in liquid-state NMR. Compared with other quantum information processing systems, the NMR platform has the advantages such as the long coherence time, the precise manipulation, and well-developed quantum control techniques, which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing, and quantum simulation have been thoroughly studied over half a century. This article introduces the general principles of NMR quantum information processing, and reviews the new-developed techniques. The review will also include the recent achievements of the experimental realization of quantum algorithms for machine learning, quantum simulations for high energy physics, and topological order in NMR. We also discuss the limitation and prospect of liquid-state NMR spectroscopy and the solid-state NMR systems as quantum computing in the article.
The ability to manipulate individual quantum systems in a precise way has led to a new era of quantum technologies, including quantum computation and quantum simulation. In this thesis we present several new implementations of these quantum technologies. We first aim at addressing current experimental challenges for quantum dot based quantum computing. We propose a systematic way to study the dynamics of nuclear spin, which is responsible for the short electron spin coherence time. Our calculation is based on diffusion model and is consistent with experiments. We also invent a novel protocol to realize high-fidelity ultrafast universal quantum gate in recently-developed quantum dot molecule system. Experimental realization of our protocol requires only a simple time engineering of optical pulses. We then propose a new quantum state transfer scheme for Nitrogen-Vacancy center based quantum computer, which is applicable at room temperature. Our method accomplishes high fidelity robust quantum state transfer through uncontrolled thermal nitrogen spin chain between two remote NV registers. Our next study helps building a hybrid quantum computer by entangling disparate systems using photonic links. The photons emitted from two types of system need to be matched in both frequency and pulse shape. We propose a simple method to match the emitted pulse shape from two qubit systems with different transition linewidths. We then focus on quantum simulation with trapped ions. We show the possibility of observing a novel type of temperature driven structural phase transition in trapped ion chain, which originates from anharmonic interaction between different vibrational modes. Afterward, an experimental protocol to simulate a conceptually new state of matter, called time crystal, is proposed based on ions trapped in a ring trap. Finally, we propose two new applications based on the recently developed trapped ion quantum simulator of spin models: (1) simulation of Haldane-Shastry model, which opens the way of experimental study to a remarkable theoretical model involving spin liquid ground state and fractional excitations (2) observation of prethermalization and dynamical phase transition, which are poorly understood non-equilibrium phenomena in closed quantum many-body system.
The three-spin chain with a Heisenberg XYXYXY interaction is simulated in a three-qubit nuclear magnetic resonance quantum computer. The evolution caused by the XYXYXY interaction is decomposed into a series of single-spin rotations and the JJJ-coupling evolutions between the neighboring spins. The perfect state transfer algorithm proposed by Christandl et al.[Phys. Rev. Lett. 92, 187902 (2004)] is realized in the XYXYXY chain.