Quantum Simulation Of Topological Matter States With NMR System

Starting with quantum computing,this thesis introduces the birth of quantum computing,the basic concepts of quantum computing and quantum simulation,and then we introduce the basic theory of nuclear magnetic resonance quantum computing using spin.After that,we introduce the generation and development of topological order,various topological order models,and the concept and properties of arbitrary sub-models in the topological order model.Then we show that we can realize topological quantum computation by manipulating arbitrary sub-models.A basic problem in the development of topological order is how to distinguish different topological order.Earlier,we distinguished different topological orders by ground state degeneracy.With the further research,we find that different topological orders have the same ground state degeneracy.Then we find that different topological orders can be distinguished by the fusion rules of modular data(S,T matrix)and arbitrary elements.Recent studies have shown that different topological orders can also have the same modulus data,which makes the distinction criteria which we previously thought were almost complete invalid.In order to solve this problem,we propose to distinguish different topological orders from data obtained by semi-braiding operation.By simplifying the model,we design three-bit and four-bit experimental schemes.After semi-braiding operation,a non-trivial phase factor will be generated in the quantum state.Then we simulate it and complete the experiment on a nuclear magnetic resonance quantum simulator.The experimental results prove that our prediction is correct and that the semi-braiding operation is observable for the first time in the laboratory.Our experiments lay a solid foundation for the next step in exploring the most basic criteria for distinguishing topological orders.Next,we will continue to explore,we can use special operators to replace the previous experimental method of quantum state holography measurement of the final state.Because in previous experiments,we used Abel's arbitrary sub-model,we can also try to design a semi-braiding scheme of non-Abel's arbitrary sub-model,so that we can unify Abel's and non-Abel's arbitrary sub-model with semi-braiding experiment to distinguish them.Now the theoretically calculated topological order with the same modulus data needs 49 qubits,and we have no technology to implement it,so we can further search for different topological orders with the same modulus data with fewer bits.