Experimental Study Of Holonomic Gates And Other Quantum Algorithms In Nuclear Magnetic Resonance Systems

Based on quantum mechanics,quantum computation executes computational tasks corresponding to a specific algorithm by encoding quantum states into information and gets data from measurements.Since quantum states combine superposition and entanglement,quantum computation has two advantages compared with classical computation: First,quantum computation gains exponential speed-up over classical computation;Secondly,quantum computation has the ability of dealing some certain problems which classical computation is inaccessible to.A lot of famous quantum algorithm,such as Shor's factoring algorithm and Grover's searching algorithm,put classical encryption system in danger,thus more and more scientists start studying quantum computation.There are many physical apparatuses for realizing quantum computation.As one of them,nuclear magnetic resonance(NMR)quantum computation has the advantages of long coherent time and sophisticated control techniques,and is used to realize quantum algorithms and quantum simulation of small-to-medium scale.In this thesis,we first introduce basic principles of quantum computation,and then simply introduce the theory of NMR spectrometer and explain the basic pulse control techniques and advanced pulse sequence optimization method,finally,we focus on studying some problems in front of quantum computation related to the above techniques and methods,such as the problems of improving the control precision of quantum gates and the limit of quantum speed-up.As discussed below:· The first experimental study of Forrelation problem that can largest separate quantum from classical query complexities.Since the value of Forrelation is sensitive to the experimental data,we use optimized pulse to keep the error rate under 1% in experiment.A realization of 2-fold and 3-fold Forrelation algorithms on a 3-qubit NMR quantum information processor,proves the quantum query complexity of solving Forrelation problem is under tens.This work is a prototype experiment that proves 'quantum supremacy'given the current technology and in the presence of experimental noise.· The first experimental realization of single-shot nonadaibatic holonomic one-qubit quantum gates.As a promising model of quantum computation,nonadiabatic holonomic quantum computation has advantages of fault-tolerance to some certain errors during the process and short running time.All the previous schemes of nonadiabatic holonomic one-qubit quantum gates have to use at least two sequentially implemented gates to realize a general one-qubit gates,our work realizes singleshot general quantum gates using an ancillary qubit on a 2-qubit NMR quantum information processor based on the recent schemes and characterizes them with quantum process tomography.