Experimental Studies Of Adiabatic Quantum Computation Via Nuclear Magnetic Resonance System

It is expected that quantum computing will have great advantages over classicalcomputing in some problems. Adiabatic quantum computing solves a computationalproblem via an adiabatic evolution, where the ground state of the final Hamiltonian ofthe evolution encodes the solution to the problem. Adiabatic quantum computing pro-vides an effective approach to quantum algorithm design. Over the last half a century,nuclearmagneticresonance (NMR)techniqueshave undergonesignificant developmen-t. These techniques can be used to realize quantum computation and offer many advan-tages, such as long decoherence time and ease of operation. This thesis focused on NMRimplementation of quantum algorithms, including the following three parts:First, we have demonstrated the adiabatic quantum algorithm for the modified Si-mon’s problem (MSP) in a NMR quantum information processor. In our experiment,the adiabatic evolution was discretized into several steps (Trotter steps), each step beingsimulated using unitary operations. In this part, we focus on the effect of the numberof Trotter steps and evolution time on the experiment results. We found that there is atrade-off between satisfying the adiabatic condition and reducing NMR experimental er-ror. As the number of steps and evolution time increase, the adiabatic condition is bettersatisfied, and the evolution will have a higher probability of reaching the ground stateof the final Hamiltonian. However, with more Trotter steps and longer evolution time,pulse imperfections and decoherence worsen and dominate the variation in the resultfidelity after certain step number. An optimal Trotter step number and run time wereindicated by our results. The trade-off with increasing the Trotter steps and evolutiontime restricts the performance of adiabatic quantum algorithms.Second, we have improved the adiabatic quantum algorithm for the MSP by usingthe method of enhanced symmetry of the Hamiltonian and demonstrated the improvedalgorithm via NMR system. The experimental result of the improved algorithm is betterthan Rao’s algorithm with the same run time and number of Trotter steps. This work ver-ifiedthemethodforimprovingadiabaticquantumcomputingperformancebymodifyingadiabatic quantum algorithm designs.Third, we have demonstrated the quantum deletion algorithm in a three-qubit N-MR system. The GRAPE algorithm was used to obtain an optimized NMR pulse se- quence. Furthermore, we have reconstructed the experimental output via the methodfor Maximum-Likelihood quantum state reconstruction and obtained a more reasonableexperimental result.