Implementing Quantum Simulation Tasks Using Nuclear Magnetic Resonance

Quantum information and quantum computation is a new developing subject, which is based on quantum mechanical theories, and combined with mathemat-ics, computing science and material science etc. The ultimate goal of quantum computation is to establish a new version of computer, which relies on quantum theories, and can exhibit novel, unique and fast quantum properties. For instance, to factor a512-bit integer, we need8400years if we use a MIPS (Million Instruc-tions Per Second) classical computer. However, by utilizing quantum computer it only requires3.5hours! It seems very attractive, but the physical realization, which requires us to control the fragile quantum systems very precisely, is very difficult at current technique. The most feasible task at present is to find and demonstrate an example in experiment, which can really surpass the capacity of classical computers. It has been proved to be possible to perform useful quantum simulation with quantum computers that incorporates as few as30-100qubits, while algorithms require quantum computers with at least a few thousand qubits. Therefore, quantum simulation is one of the hot fields in quantum computation, and also the main object in this thesis.In all potential physical systems which might be used to build quantum com-puters, NMR (nuclear magnetic resonance) is supposed to be the most rapid one in progress. Till now, the most complicated experiment which consists of hundred of logical gates on a12-qubit system has been implemented in NMR. In the mean-while, numerous proposals of quantum algorithms and quantum simulation have been demonstrated in NMR platform, and many control techniques developed in NMR have been extended to other systems, such as ion traps and superconducting circuits. Although there are some limitations like the scalable problem, NMR is still one of the most promising systems to perform the first experiment to outper-form classical computers. All the experiments in this thesis are implemented in NMR, and expected to be a key step towards the goal of surpassing the capacity of classical computers.The goal of this thesis is to implement quantum simulation tasks using NMR systems, and to introduce the experimental achievements obtained during my PhD period. The concepts are as follows: 1. Introduction of the theoretical background from Chapter1to Chapter2. First, we reviewed the history of quantum computation, and described the basic principles of quantum computers. We tried to establish the picture of quantum world in the beginning. In Chapter2, we introduced one major ap-plication of quantum computation, namely, quantum simulation (the other one is quantum alogorithms), including the theories, categories, applications and recent progress.2. In Chapter3, we introduced the NMR techniques using the language of quantum computation. In the end of this chapter, we described the meth-ods of implementing experiments with the strong coupling system, which is relatively novel compared to the traditional weak coupling systems. We proposed a new adiabatic factoring algorithm and factored143in4-qubit strong coupling liquid crystal system. Despite of the long distance from hacking the security system of governments, militaries and banks, we are always working hard towards this target.3. Chapter4is mainly focused on the experiment of solving the database searching problem by quantum random walk searching algorithm. Although the speedup is similar to the famous Grover searching algorithm, the quan-tum random walk searching algorithm is more widely used. This is the first experiment since this algorithm was proposed in2003. We chose a3-qubit strong coupling liquid crystal NMR sample, and solved the problems includ-ing the Hamiltonian fitting, initial state preparation, unitary evolution and measurement.4. Chapter5is simulating quantum chemistry using NMR quantum simula-tors. Starting from the static case, we simulated the ground state energy of the hydrogen molecule, which is the simplest molecule in nature. Then we succeeded in simulating the dynamical problem, which is a one-dimensional chemical reaction. Then we extended the phase estimation algorithm, and obtained the eigenvalues and eigenvectors of a Heisenberg Hamiltonian mod-el in experiment. In the last section of this chapter, we introduced some fur-ther proposals of simulating quantum chemistry, and gave the experimental expectations.5. Chapter6is our conclusion and perspective. In summary, we have completed many experiments of demonstrating the superiority of quantum computation. Although these experiments are proof-of-principle, we expect that some techniques and methods used in these experiments can be expanded to other systems, and provide some confidences in the way to-wards real quantum computers.