Working on quantum systems entail different interests, for example, working on fundamental \nunderstanding of quantum systems also lay foundation for better quantum computation \ntechniques. A test for whether a system is behaving quantum mechanically or \nclassically is devised by Leggett and Garg in form of inequalities, called Leggett-Garg Inequalities \n(LGI). Such Inequalities are violated by a system whose evolution is governed \nby quantum mechanics. A precise experiment to violate LGIs require a guarantee that the \nmeasurement does not affect the system or its future dynamics. These Inequalities were \nproposed for dichotomic systems,systems which can have two outcomes. Here we present \nan LG experiment on a three-level quantum system, which theoretically have larger quantum \nupper bound than that of a two-level quantum system. This larger violation also \nprovides a bigger buffer to taking in account of the various experimental imperfections. \nPerforming a quantum computing task requires precise level of control to initialize, \nperform and measure the quantum system. With increasing size of the quantum processor \nthe challenge is to maintain optimal control. Nuclear Magnetic Resonance (NMR) has \nalways been a very faithful test-bed for quantum processing ideas. In NMR, we perform \nRadio Frequency (RF) pulses to control and steer the system to the desired state. Most \nused method to derive the exact frequency and amplitude of these pulses for a given \ntask is based on gradient. Although systematic, one have to simulate these pulses on \na classical computer first, which makes the task very inefficient. We report a a way of \nperforming optimization with a hybrid quantum-classical scheme. This scheme helps us \nperform classically harder computational tasks on the quantum processor. We optimize \npulses which drive our system from 7-coherence state to 12-coherence state on a 12-qubit \nNMR processor. \nElectron Spin Resonance (ESR) employs the same techniques as of NMR but having \nadvantage in larger polarization compared to later. Although this does not imply better \ncontrol, cause the frequency at which pulses are required to control an ESR system fall into \nmicrowave region. Microwave frequency are harder to control electronically, thus making \nit harder for performing ESR quantum computing. The hybrid scheme used in NMR \nexperiment relies on some ideal pulses which are needed to be optimized classically. We \nalleviate this requirement by using finite difference method of calculating gradient. We \ncompare these methods with the earlier methods to show the superiority of such a scheme. \nState-to-state transfer pulses are sufficient for most of the quantum computing task, \nbut, an universal quantum information implementation requires state independent pulses. \nThe techniques used in optimizing state-to-state pulses can be modified to optimize for a \nstate independent pulse. We show that this methods scale polynomially with the number \nof qubits and is general in terms of its implementation. We further reduce the resource \nrequirement by using a NMR related implementation.
Working on quantum systems entail different interests, for example, working on fundamental \nunderstanding of quantum systems also lay foundation for better quantum computation \ntechniques. A test for whether a system is behaving quantum mechanically or \nclassically is devised by Leggett and Garg in form of inequalities, called Leggett-Garg Inequalities \n(LGI). Such Inequalities are violated by a system whose evolution is governed \nby quantum mechanics. A precise experiment to violate LGIs require a guarantee that the \nmeasurement does not affect the system or its future dynamics. These Inequalities were \nproposed for dichotomic systems,systems which can have two outcomes. Here we present \nan LG experiment on a three-level quantum system, which theoretically have larger quantum \nupper bound than that of a two-level quantum system. This larger violation also \nprovides a bigger buffer to taking in account of the various experimental imperfections. \nPerforming a quantum computing task requires precise level of control to initialize, \nperform and measure the quantum system. With increasing size of the quantum processor \nthe challenge is to maintain optimal control. Nuclear Magnetic Resonance (NMR) has \nalways been a very faithful test-bed for quantum processing ideas. In NMR, we perform \nRadio Frequency (RF) pulses to control and steer the system to the desired state. Most \nused method to derive the exact frequency and amplitude of these pulses for a given \ntask is based on gradient. Although systematic, one have to simulate these pulses on \na classical computer first, which makes the task very inefficient. We report a a way of \nperforming optimization with a hybrid quantum-classical scheme. This scheme helps us \nperform classically harder computational tasks on the quantum processor. We optimize \npulses which drive our system from 7-coherence state to 12-coherence state on a 12-qubit \nNMR processor. \nElectron Spin Resonance (ESR) employs the same techniques as of NMR but having \nadvantage in larger polarization compared to later. Although this does not imply better \ncontrol, cause the frequency at which pulses are required to control an ESR system fall into \nmicrowave region. Microwave frequency are harder to control electronically, thus making \nit harder for performing ESR quantum computing. The hybrid scheme used in NMR \nexperiment relies on some ideal pulses which are needed to be optimized classically. We \nalleviate this requirement by using finite difference method of calculating gradient. We \ncompare these methods with the earlier methods to show the superiority of such a scheme. \nState-to-state transfer pulses are sufficient for most of the quantum computing task, \nbut, an universal quantum information implementation requires state independent pulses. \nThe techniques used in optimizing state-to-state pulses can be modified to optimize for a \nstate independent pulse. We show that this methods scale polynomially with the number \nof qubits and is general in terms of its implementation. We further reduce the resource \nrequirement by using a NMR related implementation.
With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.
Quantum computing set a goal to harness the quantum laws of physics and create \ncomputers more powerful than ever imagined. Different technologies can be chosen to implement quantum bits (qubits), each with their advantages and drawbacks. The idea of combining different technologies then seems natural in order to come up with an optimal quantum computer. \n \nIn this sense, Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) seem to be the perfect marriage. Indeed, while electron spins can perform quantum gates within nanoseconds, they have to fight very fast decoherence phenomena, the nuclear spins, on the other hand, require longer electromagnetic pulses to be rotated but can be controlled longer without loss of quantum information. Using electron spins as actuators and nuclear spins as memory then appears as the optimal use of this hybrid system. Another fact accounting for this association is that the control of the system through the electron spin requires techniques very similar to the well-known NMR ones. \n \nThis work focuses on characterizing as precisely as possible the Hamiltonian of a hybrid spin system in a solid-state single crystal, especially the electron-nuclear interactions, to perform high-fidelity control in a home-built pulsed ESR spectrometer. Using this knowledge, we show that we can choose the orientation of the magnetic field with respect to our crystal to obtain optimal experimental conditions. Indeed, with a good knowledge of the Hamiltonian of the system, we want demonstrate high-fidelity quantum control. \n \nThe final aim of this work is to dynamically supply highly polarized ancilla qubits that can be used in a Quantum Error Correction (QEC) experiment by implementing heat bath algorithmic cooling using a cold electron spin bath. This is an important step towards demonstrating the viability of spin systems for building quantum computers.
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. This article surveys and summarizes a broad variety of pulse control and tomographic techniques which have been developed for, and used in, NMR quantum computation. Many of these will be useful in other quantum systems now being considered for the implementation of quantum information processing tasks.
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…
Quantum computers offer the possibility of solving some problems more efficiently than their classical counterparts. The current forerunner in the experimental demonstration of quantum algorithms is Nuclear Magnetic Resonance (NMR). Known for its implementations at liquid state, NMR quantum computing consists of computing on nuclear spins. In the liquid crystal state, dipolar couplings are available, offering an increased clock frequency and a faster recycling of algorithms. Here investigated is the cost at which this comes, namely, a more complicated internal Hamiltonian, making the system harder to characterize and harder to control. In this thesis I present new methods for characterizing the Hamiltonian of dipolar coupled spin systems, and I report experimental results of characterizing an oriented 6-spin system. I then present methods and results concerning the quantum optimal control of this same spin system. Finally, I present experiments and simulations regarding the certification of computational quantum gates implemented in that same dipolar coupled spin system.
The ability to perform quantum error correction (QEC) arbitrarily many cycles is a significant challenge for scalable quantum information processing (QIP). Key requirements for multiple-round QEC are a high degree of quantum control, the ability to efficiently characterize both intrinsic and extrinsic noise, and the ability to dynamically and efficiently extract entropy from ancilla qubits. Nuclear Magnetic Resonance (NMR) based quantum devices have demonstrated high control fidelity with up to 12 qubits, and the noise characterizations can be performed using an efficient protocol known as randomized benchmarking. One of the remaining challenges with NMR systems is that qubit initialization is normally only attainable via thermal equilibration. This results in very low polarizations in reasonable experimental conditions. Moving to electron-nuclear coupled spin systems in a single crystal is a promising solution to the ancilla qubit preparation problem. One obvious advantage of incorporating electron spins comes from higher gyromagnetic ratio of the electron which yields about three orders of magnitude larger thermal spin polarization than that of nuclear spins in the same experimental condition. In addition, fast control of nuclear spins is possible provided appropriate level of anisotropic hyperfine interaction strength. The nuclear spins can be polarized even beyond the thermal electron spin temperature using a technique Heat-Bath Algorithmic Cooling (HBAC). With theoretical ideas in hand, the next step is to develop classical instrumentations to control electron-nuclear coupled systems and accomplish high fidelity coherent control. Noise characterizations are also necessary for benchmarking the quality of control over the electron-nuclear spin system. \nI first present example applications of NMR QIP with small number of qubits: Testing a foundational question in quantum mechanics and measuring spectral density of noise in a quantum system. Then I report on our home-built X-band electron spin resonance (ESR) spectrometer and progress in achieving high fidelity coherent control of electron and nuclear spins for QIP. We focus on implementing nuclear spin manipulation via anisotropic hyperfine interaction and microwave (mw) control, but discussions also include electron nuclear double resonance (ENDOR) control techniques. We perform realistic algorithmic simulations to show that an experimental cooling of nuclear spins below electron thermal temperature is feasible, and to present the electron-nuclear spin systems as promising testbeds for scalable QIP.