Making and identifying quantum resources

Doctoral thesis, 2023

This thesis aims to investigate the properties of quantum systems that serve asvaluable resources for information processing and their advantages over classicalsystems in specific tasks. While quantum computers have shown the ability tosolve certain problems faster than classical computers, understanding the precisereasons behind this advantage remains a challenging task. The focus of thisresearch lies in identifying and generating the quantum states that contributeto achieving quantum advantages.
The study begins by examining the distinctive characteristics of quantumsystems in comparison to classical systems. Specifically, the thesis explorescontinuous-variable quantum computing, where quantum information is storedin continuous quantum variables. This stands in contrast to the more widelystudied discrete-variable quantum processing in qubits. The investigation seeksto elucidate the potential of continuous-variable quantum computing and shedlight on the specific states and operations that can provide quantum advantages.
The research explores the conversion of different quantum states throughclassical operations, investigating the feasibility of transforming tri-squeezedstates into cubic phase states (Paper A), converting binomial states into resourcestates for universal quantum computing (Paper B), and creating twophotonstates from single-photon states without single-photon detectors (PaperC). These studies reveal the possibility of achieving high-fidelity conversions withmoderate success probabilities, uncovering valuable insights into the potentialof these states as quantum resources.
Additionally, the thesis expands the research scope to encompass quantumadvantage in random walks (Paper D). Random walks are fundamental to algorithmssolving diverse computational problems, and the investigation aims tounderstand how quantum walkers can outperform classical walkers in certainscenarios. The analysis examines the behavior of quantum walkers, utilizingsuperposition states that occupy multiple nodes simultaneously. The studyinvestigates the potential application of neural networks in identifying graphstructures where quantum walkers exhibit advantages, with the goal of enhanciing accuracy and understanding the underlying mechanisms.By exploring the properties of quantum states and measurement techniques,this thesis contributes to a deeper understanding of quantum resources andadvantages in computing.