Efficient Quantum State Preparation Algorithms

Quantum computing has the potential to address many of the unsolved problems of quantum many-body physics. However, there are serious inefficiencies that must be addressed. In this project, several methods are explored to improve the performance of quantum computing algorithms for quantum state preparation. These include preconditioning methods that increase the probability of success, sampling methods for the density of energy levels, and the reduction of systematic errors due to time step size. As part of the broader impacts of this research proposal, inspiring and diverse public speakers in the field of quantum computing and applications will be invited to present public talks in the Advanced Studies Gateway series. The rodeo algorithm is an efficient quantum computing algorithm that can prepare general eigenstates of quantum Hamiltonians. In this project, the 2D Heisenberg model is used as a benchmark system to develop several methods to accelerate and improve the performance of the rodeo algorithm. The block partition method and the variational rodeo algorithm, two different methods for preconditioning the initial state, will be tested. Stochastic methods with finite energy resolution will then be used to determine the full energy spectrum. Trotter step adiabatic evolution will be used to perform extrapolations to small Trotter step size. This award by the Quantum Information Science program is jointly supported by the Theoretical Nuclear Physics in the Division of Physics within the Directorate for Mathematical and Physical Sciences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.