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.
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.
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.
In building a quantum-information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent testbed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low-dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This paper summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.
In the last 20 years, there have been lots of novel developments and remarkable achievements in quantum information processing theoretically and experimentally. Among them, the 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, NMR platform has many 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. There are also many outstanding researches in the recent several years. So we focus on the recent researches in this review article. First, we introduce the basic principle of the liquid-state NMR quantum computing and two new methods reported in the pseudo-pure state preparation which has more advantages than the traditional methods. The quantum noise-injection methods and the quantum tomography technology in liquid-state NMR are also mentioned. Then we overview Horrow-Hassidim-Lioyd algorithm, quantum support vector machine algorithm, duality quantum computing and their implementations in liquid-state NMR system. Also, we report recent researches about quantum simulations, including quantum tunneling, high-energy physics and topological sequences. Then we display the quantum cloud platform of our group. In order to let more people, either amateurs or professionals, embrace and more importantly participate in the tidal wave of quantum science, we launch our NMR quantum cloud computing (NMRCloudQ) service. Through NMRCloudQ, we offer a direct access to a real, physical spectrometer in our laboratory and encourage users to explore quantum phenomena and demonstrate quantum algorithms. Finally, we discuss the development prospects and development bottlenecks of NMR, and point out the prospects for the future development direction.
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.
Solid-state nuclear magnetic resonance (NMR) has emerged as an important technique for material characterization, finding extensive applications across a diverse range of disciplines including physics, materials science, chemistry, and biology. Its utility stems from the ability to probe the local atomic environments and molecular dynamics within solid materials, which provides information on the composition of the material. In recent years, the scope of solid-state NMR has expanded into the realm of quantum information science and technology, where its abundant many-body interactions pulse control methodologies make it have significant research value and application potential. This paper offers a comprehensive overview of the research objects and theoretical underpinnings of solid-state NMR, delving into the critical nuclear spin interaction mechanisms and their corresponding Hamiltonian forms. These interactions, which include dipolar coupling, chemical shift anisotropy, and quadrupolar interactions, are fundamental to the interpretation of NMR spectra and the understanding of material properties at the atomic level. Moreover, the paper introduces typical dynamical control methods employed in the manipulation of solid-state nuclear spins. Techniques such as dynamical decoupling, which mitigates the effects of spin-spin interactions to extend coherence times, and magic-angle spinning, which averages out anisotropic interactions to yield high-resolution spectra. These methods are essential for enhancing the sensitivity and resolution of NMR experiments, enabling the extraction of detailed structural and dynamic information from complex materials. Then we introduce some recent advancements in quantum control based on solid-state NMR, such as nuclear spin polarization enhancement techniques, which include dynamic nuclear polarization (DNP) and cross polarization (CP), significantly boost the sensitivity of NMR measurements. Additionally, the control techniques of Floquet average Hamiltonians are mentioned, showcasing their role in the precise manipulation of quantum states and the realization of quantum dynamics. Finally, the paper presents a series of seminal research works that illustrate the application of solid-state NMR quantum control technologies in the field of quantum simulation. These studies demonstrate how solid-state NMR can be leveraged to simulate and investigate quantum many-body systems, providing valuable insights into quantum phase transitions, entanglement dynamics, and other phenomena relevant to quantum information science. By bridging the gap between fundamental research and practical applications, solid-state NMR continues to play a crucial role in advancing our understanding of quantum materials and technologies.
An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.