Experimental Investigation Of Quantum Simulation Based On Solid-state Spins In Diamond

As a fundamental theory to describe nature at the smallest scales of energy levels of atoms and subatomic particles,quantum mechanics together with the theory of rela-tivity is considered to be the two basic pillars of modern physics.Since the discovery of quantum mechanics,physicists have come to realize that it is difficult to quantita-tively describe quantum systems,especially when the system is large.This is because the resources that a classical computer needs to simulate a quantum system grow expo-nentially with the system dimension.In order to overcome this difficulty,it is necessary to build a machine which operates quantum mechanically,namely a quantum simula-tor.However,for actual physical systems,their quantum properties are very fragile and can be easily destroyed by environmental noise.So build of a quantum simulator is not an easy task.To this end,many of the world's top research groups and technology companies have invested a lot of manpower and material resources,making quantum simulation one of the most active research areas both in physics and engineering.It is also the area which this thesis will focus on.The physical systems that can realize quantum simulation are also varied.Among them,the nitrogen-vacancy(NV)center in diamond has become one of the most im-portant candidate systems for quantum simulation because it has excellent coherence properties and can be easily polarized,manipulated and read out even in room tempera-ture.In recent years,the quantum control techniques of NV center have been advanced.For example,fault-tolerant universal quantum gates and quantum error correction have been realized.This paves the way toward NV center-based quantum simulation.In this thesis,we describe a series of research related to quantum simulation based on a home-bulit optically detected magnetic resonance setup,including three parts:1.By precisely manipulating the NV electron spin and the adjacent nuclear spin,a digital quantum simulator is realized to simulated a generalized counterfactual calculation(CFC)protocol.Counterfactual calculations have been previously im-plemented in optical systems,but the counterfactual efficiency was theoretically limited to be poorer than random guessing.We use the NV system to simulate a generalized CFC protocol and achieve a high efficiency beyond the classical limit for the first time.2.By fine tuning the Hamiltonian of a two-qubit system consisted by the NV elec-tron spin and the adjacent nuclear spin,a analog quantum simulator is realized to simulate a topology system,and a clear topological phase transition is observed.The key point is the effective Hamiltonian of NV system can be controlled by the applied microwave and radiofrequency pulses,to be similar with the Hamiltonian of the topology system to be studied.By changing the adjustable parameters,the behavior of the topology system in different phases can be directly predicted.3.A scheme for realizing large-scale quantum simulator using external spins of di-amond is studied and preliminary experiments are conducted.Taking advantage of the relatively easy preparation of external spins of diamond rather than inter-nal spins,we can perform quantum simulation on the external spins which can be initialized and read out by the nearby NV center.As an preliminary demon-stration,we have realized the coupling between NV center and a single electron spins on the diamond surface.To detect multi-electron spins,we propose and experimental demostrated a zero-field electron spin resonance method.