Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.
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.
Nuclear magnetic resonance (NMR) is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory (see the last two authors). In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with several illustrative experiments suitable for incorporation into the undergraduate physics curriculum. These experiments are spin–spin interferometry, an implementation of the quantum Fourier transform, and the quantum simulation of a harmonic oscillator.
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.
Nuclear Magnetic Resonance (NMR) forms a natural test-bed to perform quantum information processing (QIP) and has so far proven to be one of the most successful quantum information processors. The nuclear spins in a molecule treated as quantum bits or qubits which are the basic building blocks of a quantum computer. The development of NMR over half a century puts it in a platform where we can utilize its excellent control techniques over an ensemble of spin systems and perform quantum computation in a highly controlled way. Apart from a successful quantum information processor, NMR is also a highly powerful quantum platform where many of the potentially challenging quantum mechanical experiments can be performed.
The most significant achievements of this project were: (1) Development and validation of the hardware and software needed to implement "strongly modulating pulses", by which high precision quantum gates can be obtain in realistic systems of up to 12 qubits; (2) A detailed analysis and evaluation of a 3-qubit quantum Fourier transform via full quantum process tomography; (3) An extensive set of mathematical and computational techniques to accomplish these goals, including Hadamard products, the real density matrix, and methods of fitting superoperators to experimental data; (4) Creation of a 3-qubit "noiseless subsystem", of a Bell state on two 2-qubit decoherence-free subspaces (DFS), and the invention of "partial" pseudopure states which will enable us to demonstrate robust methods for controlling multi-DFS-qubit systems by NMR; (5) Implementation of several quantum chaotic maps, and the discovery that these provide a scalable approach to determining the magnitude and kind of errors present in complex quantum computations; (6) The invention of a "spin amplifier", by which entanglement can be used to enable single spin measurement, and a small-scale demonstration by NMR; (7) Experiments demonstrating that the foregoing advances enable implementation of complex entangling unitary and decoherent operations, culminating in creation of a 12-qubit CAT state.