Experimental Quantum Computation Based On Nuclear-spin System

The research on quantum computation is a very active and fast moving sub-ject, encompassing many different fields of research (computer science, quantum mechanic, mathematics, for instance). The quantum computer can solve cer-tain problems with exponentially speedup over classical counterparts, e.g. the Shor’s quantum algorithm for prime factorization. This powerful ability have at-tracted enormous research interest all over the world, including various research institutes, governments and IT companies. With the well-developed control tech-nology, Nuclear Magnetic Resonace (NMR) has been widely utilized for many of the first experimental demonstrations in quantum computation. In this thesis, I will concentrate on the experimental implementation of quantum algorithms using nuclear-spin systems.The contents are as follows:1. The first chapter is mainly the review of the theoretical background of quan-tum computation. Starting from the definition of qubits, the basic concep-tion of quantum computation are illustrated. Then a variety of candidate for physical realization of quantum computation are introduced and analyzed.2. In Chapter2, the NMR techniques and how it could be used for quantum computation are described. The commonly used pulse techniques for quan-tum control are also reviewed in this part.3. Chapter3mainly focus on the experimental realization of several quantum algorithms. Specifically, we extended the PEA method to a more general case and solved the ground-state problem by utilizing a approximate tri-al state. We experimentally obtained the eigenvalue to the10-5decimal digit and distilled the ground-state fidelity to more than80%. As another application of the PEA method, the quantum algorithm for solving linear equations is also realized using the NMR technique.4. Chapter4is another important practical application of quantum computer, called quantum simulation. We review the method of compressed quan-tum simulation, which proposed that certain N-qubit quantum circuit could be faithfully simulated by quantum simulator with only O(log(N)) qubits. Then, by utilizing an NMR quantum simulator with only five qubits, we experimentally simulated the property of ground-state magnetization of an32-spin chain.5. Chapter5is my conclusion and perspective.In summary, we have experimentally realized several useful algorithms in the field of quantum computation. These work has given us much practical ex-perience on how to build the quantum computer. Beyond the proof-of-principle experiments, the techniques and methods developed for high-fidelity quantum con-trol could also be expanded to other more general, scalable quantum computer implementations.