Experimental Study Of Quantum Simulation In NMR Systems

Recently, quantum computation has attracted increasing interest. Different fromclassical computation, quantum computation makes use of the principles of quantummechanics, such as the principles of entanglement and superposition, to perform dataprocessing. Quantum computers outperform classical computers in some problems, es-pecially in simulating quantum systems. Quantum simulation is an important part of thequantum computation study, and it is one of the goals that urges people to study quantumcomputation.Researchershavebeenmakinggreateffortstoexperimentallyrealizequantumcom-putation. Small-scale demonstrations of quantum algorithms and quantum simulationshave been performed in several potential physical systems, one of which is the nucle-ar magnetic resonance (NMR) system. Because of its long coherence time and simplecoherent controls, the NMR system is an important testbed for quantum algorithms andquantum simulations. This thesis is focused on quantum simulations of certain quantumcomputation models and quantum phenomena utilizing liquid-state NMR systems. Theresearch conducted in this thesis is as follows：1. We realized the first experimental demonstration of a universal gate set of nona-diabatic holonomic quantum computation. In our experiments, the realized gates werecharacterized using quantum process tomography, and the experimental results agreedwell with the theoretical predictions. Holonomic quantum computation is robust againstcertain types of control errors. Nonadiabatic holonomic quantum computation not onlyhasthisadvantage, butalsoavoidsthelongrun-timerequirementofadiabaticholonomicquantum computation. Therefore nonadiabatic holonomic quantum computation is lesssusceptible to decoherence.2. Wesimulatedthequantumtunnelingphenomenonusingthedigitalquantumsim-ulationalgorithm. Wediscretizedtheone-dimensionalspacedegreeandthetimedegree.The wave function of a particle was encoded in the computational bases of the quantumprocessor. We implemented the evolution operator by using a sequence of quantumgates, and thus realized the simulation of the evolution of a particle’s probability dis-tribution in a one-dimensional double-well potential. In the experiments, the tunnelingof the particle’s probability distribution from one potential well to the other, and the oscillation of the probability distribution within one potential well, can be observed.3. We experimentally demonstrated anyonic fractional statistics by simulating asix-qubit Kitaev spin-lattice model using a seven-qubit NMR system. We prepared theground state of this model and realized anyon creation, braiding and fusion operations.By detecting a probe qubit, we observed a phase change of the system caused by any-on braiding. As anyon braiding is equivalent to two successive particle exchanges,this phase change reflects the difference between anyons and the particles in three-dimensional space, i.e. bosons and fermions. Thus, we succeeded in the demonstrationthat anyons obey fractional statistics.