Quantum Information Protection3Ased On Nuclear-spin System

As one of the cornerstones of modern physics, quantum mechanics is undoubt-edly whipping up a storm. Quantum mechanics presents many weird phenomena which are different from the world of our immediate experience. Curiosity drives people to constantly reveal its mysterious veil. Meanwhile, people certainly expect that the quantum mechanics can bring a revolution to the civilization of human society. When quantum mechanics is combined with other different disciplines, such as mathematics, information science, computing science and material science, a skyscraper of science appears on the horizon. It consists of two components: quantum information and quantum computation. It’s easy to verify that quan-tum information has a strong storage capacity, which is unreachable for classical information. Moreover, quantum information has many characteristics differen-t from classical information, such as entanglement, no-cloning theorem, collapse in measurement. These characteristics may change our ways of information s-torage, communication and processing in future. Based on the new information carrier-quantum system, quantum computing science is developing quickly. Com-pared with classical counterparts, some quantum algorithms may provide higher efficiency. Sometimes they even provide an exponential speedup. Scientists are working hard for the great vision of quantum information and quantum com-putation. During this process, humans keep improving our own capability of manipulating quantum systems. There is no doubt that this period, during which the applications of quantum mechanics and humans’quantum technology develop very quickly, is significant in the developmental history of science.However, there are many difficulties hindering people from big-scale quantum information processing. Among these difficulties, decoherence is the biggest one. Decoherence can severely destroy the coherent property of quantum systems, so the question "how to suppress decoherence" is always a hot research subject. Un-der the theoretical framework of "decoherence-free subspace", scientists have pro-posed a number of methods for decoherence protection, including passive methods and active methods. Among these methods, fault-tolerant quantum computation which is based on quantum error correction code theory is considered as the basic framework of future big-scale quantum computing circuits. However, to achieve universal fault-tolerant quantum computation, some special states, called "magic states", have to be introduced to the computing circuits. Realization of highly reliable quantum computing requests that magic states possess very high purity. This requirement makes "magic state distillation" attract a lot of attention.In all potential physical systems which might be used to realize quantum computers, nuclear magnetic resonance (NMR) system always occupy the leading position in the area of quantum computation and quantum simulation, depending on its relatively mature control technology and long decoherence time. A lot of quantum algorithms and quantum simulations have been experimentally demon-strated in NMR system. Besides, many techniques developed in NMR have been transplanted to other systems, such as ion traps and superconducting. circuits. Although there is a bottleneck lying in the scalability of traditional liquid NMR system, at present liquid NMR system is still a very good platform for quantum information processing. Moreover, with the development of solid state NMR and the combination with electron spin control, nuclear control system is moving into a new stage.Based on the above background, I introduce my works in this thesis:(1). In the first two chapters, I introduce the overall background, including quan-tum information science and NMR quantum information processor.(2). The third chapter is about quantum information protection. I introduce three kinds of methods for protecting quantum information:quantum Zeno effect, dynamical decoupling, quantum error correction. I also explain how they can prevent decoherence and errors using the theory of invariant subspace.(3). In the fourth chapter, I introduce my work on dynamic quantum Zeno effect. Different from conventional quantum Zeno effect which is based on projection measurements, the dynamical version gives one exclusive phenomenon-"the critical measurement time effect". This special phenomenon inspires peo-ple to look at quantum measurements from the dynamical perspective. We experimentally demonstrated the dynamic quantum Zeno effect with NM-R system and we also observed the critical measurement time effect in our experiment. Moreover, we provide an experimental demonstration of an en-tanglement preservation mechanism based on such a dynamic quantum Zeno effect.(4). In the fifth chapter, I introduce how to use quantum Zeno effect to protect unknown quantum states. Based on a Zeno-like effect,"operator quantum Zeno effect", we propose a scheme which can protect n-qubit system with just two ancillary qubits. Compared with the conventional method, which implements quantum zeno effect with the measurements of stabilizers of one quantum error correction code, our scheme needs less ancillary qubits and requires indeed no entanglement operator for encoding.(5). The sixth chapter is about universal fault-tolerant quantum computation. In this chapter, the topic of magic state distillation is drawn out.(6). In the seventh chapter, I introduce my work on magic state distillation. We propose a hybrid method for magic state distillation, which aims to take advantage of different MSD protocols. It further integrates all of the currently known distillable ranges and extends the T-type distillable range to the stabilizer octahedron edges. Moreover, the hybrid scheme has the remarkable advantage of saving qubit resources.(7). The last chapter is my conclusion and perspective.