Towards Quantum Utility on NISQ Hardware

Quantum utility in the noisy intermediate-scale quantum (NISQ) era requires hardware-focused design to maximize resources and minimize the effects of noise and decoherence. In studying quantum simulation and optimization, this involves choosing the optimal bases, hardware type, and quantum algorithm. In this dissertation, I present past work in 5 projects. The first is a proposition to obtain non-Abelian anyons in the Z₂ lattice gauge theory system on neutral atom hardware. We perform numerical simulations of the quantum processor and present a scheme for quantum computation using the anyons. Then we solve the weighted MaxCut and low autocorrelation binary sequences (LABS) problems using the quantum imaginary time evolution (QITE) algorithm, and compare with state of the art classical and quantum methods. In the third project, we solve power grid optimization problems on Rydberg neutral atom hardware using 2 hardware-centric algorithms and benchmark the processor noise. Then, the analog nature of the neutral atom platform is used to study the entanglement dynamics of the critical Ising model and experimentally compute an entanglement witness. Finally, a NISQ-suitable quantum chemistry algorithm is developed for ground state calculations on superconducting quantum hardware and compared to classical methods. To conclude, I give directions for future work.