Master Thesis Defense: Daniel Guerrero Domínguez

On Protocols for Secure Implementation of Deutsch’s Algorithm Using One-Way Quantum Computing

In this work we aim to understand and mathematically describe the concept of one-way quantum computing (1WQC), a class of measurement-based quantum computing (MBQC). Our ultimate goal is to investigate protocols that demonstrate a quantum advantage in the paradigm of 1WQC in the presence of errors. We center our study on Deutsch's algorithm, a particular case of the Deutsch-Jozsa (DJ) algorithm, which showcases a quantum advantage in the oracle model. When the DJ algorithm is implemented in practice, to say that we have demonstrated a quantum advantage we have to take into account potentially flawed implementations of the oracle. In particular, many existing implementations have the caveat that even a classical computer might be able to solve the problem if given access to a faulty oracle. To address this limitation, we propose schemes that leverage nonlocal games. By employing these games we show that, for a specific 1WQC implementation of Deutsch's algorithm, claiming a quantum advantage requires a certain level of trust in the experimental setup's performance.