UC Santa Barbara

Quantum computers have many desirable features but are physically challenging to build. They use quantum physics to solve practically motivated yet classically intractable problems, and because the experimental technology is still in its infancy, quantum mechanical devices are susceptible to errors that compromise data integrity. As a result, quantum error correction is necessary to protect important information from such undesirable influences, which inevitably increases the resource overhead to ensure a reliable quantum computation. In this thesis, we develop methods that are relevant to reducing the utilization of physical resources in a quantum computer. The core operations considered here are the so-called stabilizer operations, which have fault-tolerant constructions that are vital to achieving an error-resistant quantum computation. By applying our practices, we achieve small optimizations that have considerable value when implementing quantum algorithms in the near-term, when small quantum systems are much easier to manage than a single large quantum system. We cover two techniques to improve the efficiency of stabilizer operations applied to qubit states.

First, we introduce protocols that can probabilistically recreate an initial input qubit from the output qubit of specific quantum processes. These protocols are ideally suited for recovery purposes, and are designed with potentially many nested layers of stabilizer operations. We subsequently give a precise analysis on the effectiveness of the nested recovery. By integrating recovery at the optimal nesting depth, the resource usage of the relevant quantum processes can be reduced by up to half in expectation. Second, we define a new special arrangement of elementary stabilizer operations for realizing certain quantum computations, which we call a binary in-tree decomposition. We show that such implementations lead to a better process for lowering resource consumption. We then propose an efficient classical algorithm to assemble stabilizer operation sequences with such binary in-tree form. Finally, we demonstrate the merits of the binary in-tree structure on several examples.