Realization Of Quantum Purification Protocol And Dynamics Identification Algorithm On Nuclear Magnetic Resonance Systems

Over the past several decades, tremendous progress has been made to advance the information technology with unique quantum properties. As the classical information processing units start to approach the quantum limit and it is impossible to simulate a quantum system with classical Turing machines, big e?ort has been made to advance the techniques of quantum information processing. The research on quantum information processing exhibits speed-ups in several problems, such as the factorization of a large number and searching an unsorted database, and the possibility of simulating a large quantum systems.Nuclear spin manipulated by means of nuclear magnetic resonance(NMR) have been among the first experimental systems to realize quantum algorithms and quantum simulations. Since nuclear spins have long decoherence time, and the control techniques has been well developed since the birth of NMR about 60 years ago, NMR provides a good platform for performing quantum information processing tasks.In this thesis, first, we briefly introduce the history of information technology as well as quantum information processing. Then, start from the basic postulates of quantum mechanics, we introduce the basic ideas of quantum information processing and some physical implementations. Subsequently, the basic principles of nuclear magnetic resonance based on Fourier transformation is presented in details. With the knowledge of the basic ideas of quantum information and the basic principles of nuclear magnetic resonance, we examined how to implement quantum information processing tasks based on DiVincenzo’s five criteria.With the above introductions, we could be able to realize some quantum information processing tasks on a nuclear magnetic resonance spectrometer.Single qubits are the building blocks of quantum information processing. To protecting qubits against the environmental noise is of vital importance, Cirac et. al. proposed a single qubit purification protocol to protect obtain single qubits with high fidelity from those with with low fidelity almost one and a half decades ago. However, no full implementation has been realized since the realization requires accurate manipulation of the qubits and a full implementation of a complex quantum network. Here, we introduce our implementation of the single qubit purification protocol. The experimental results and the theoretical predictions agree well with each other, which shows that the protocol is e?ective and universal.To accomplish quantum information processing tasks with a unique quantum system, a characterization of the system is required, based on what can we manipulate the quantum system. Theoretically, quantum process tomography is a way of fully characterization scheme for identifying the system. However, quantum process tomography requires a large number of experiments which makes it almost impossible to be performed on only a small size of system. A quantum Hamiltonian identification algorithm base on measurement time traces of only some observables has been proposed very recently. With a nuclear magnetic resonance quantum information processor, we realized the identification algorithm with di?erent forms of Hamiltonian based on the free induction decay signals. The results from the quantum Hamiltonian identification algorithm and those form classical Fourier transformation are compared, from which, we can see that this approach provides almost the same amount of information with that of Fourier transformation. At last, we benchmarked the identification algorithm using numerical simulations.