Quantum Inference Protocol : from origination to application

• Main Author: Ho, Matthew Shu Hui
• Other Authors: Gu Mile
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Science::Physics
• Online Access: https://hdl.handle.net/10356/153399
• Institution: Nanyang Technological University

We are at the interface of two hot research areas – modelling of stochastic processes with causal models in quantitative science, and quantum simulation on real quantum devices. Classical causal models first made its appearance in 1989 with the aim of extracting a stochastic process’ underlying dynamics in order to do statistically faithful predictions. Research into causal models expanded into the quantum regime where it was shown that quantum models could outperform classical models; quantum models had equal predictive capabilities but had less memory requirement. This kickstarted the exploratory research into building more optimal quantum models with lower memory requirements. However, all quantum models required prior knowledge of classical causal models. Errors that occurred in classical models due to finite-length stochastic processes were automatically inherited by quantum models. The Quantum Inference Protocol was developed to circumvent the problem of inheriting errors from classical causal models by bypassing the requirement of using classical causal models to build quantum models. These quantum models feature probabilities that are inferred through frequency counting. In Chapter 4, we demonstrate the equivalence between inferred quantum models from the Quantum Inference Protocol and exact quantum models obtained from classical models. We provide analytical reasoning and two examples to validate and justify the efficacy of the Quantum Inference Protocol. With the increasing popularity of open source cloud quantum computing, Chapter 5 introduces an algorithm to reconstruct the relevant unitary operator for the inferred quantum model. Additionally, we provide a separate algorithm to decompose the unitary operator into elementary quantum gates that are implementable on real quantum devices. This sees a natural progression to apply the inferred quantum models on a fully functioning quantum device, since previous works focused on exploratory work in the ideal noiseless scenario. Due to hardware limitations, quantum devices are inherently noisy, reducing the accuracy of the measurement outcomes. We seek to apply error mitigation techniques to reduce the effects of noise from quantum devices. In Chapter 6, we outline the full procedure for an error mitigation method known as probabilistic cancellation method before conducting simulations with noise models from real quantum backends. Our results indicate that error mitigation aids in suppressing the effects of noise for statistical distributions. On second side of the same coin, we apply the Quantum Inference Protocol to extract the dynamics of elementary cellular automata in Chapter 7. We show that our inferred quantum models are able to identify varying degrees of complexity in cellular automata, offering a fresh perspective in the form of a hybrid classification scheme.