The quantum approximate optimization algorithm - perspectives of analog compilation and incoherent evolution.

Abstract

The current challenges of quantum computing development pertain to mitigating the effect of noise on the device. The problems of this era, in which Noisy Intermediate-Scale Quantum (NISQ) computers must be used in the absence of error-correcting schemes, are the focus of this thesis. In one theme of the thesis, we investigate the drop in performance incurred by Quantum Approximate Optimization Algorithm (QAOA) applied to constraint optimization problems Max-kSAT and Max-kXOR, finding that significant changes in performance occur for increasing the number of literals k per constraint. We also investigate the use of annealing-inspired schedules for QAOA, demonstrating that linear schedules outperform those of Trotterized Quantum Annealing. A second theme of the thesis concerns the co-design of devices for QAOA. Firstly, we consider the tradeoffs in the decomposition of ZZ-generated gates into CZ- and CNOT- gates, with depolarizing and coherent errors affecting each decomposition differently. We find analytical and numerical evidence that both decompositions attain comparable gate fidelities for low noise. We investigate QAOA in the digital-analog scheme, in which individual control of two-qubit gates is relinquished in favor of a global interaction, with device control occurring only via single-qubit gates. We demonstrate that QAOA in this scheme produces the same results as its digital counterpart for fast single-qubit gates.