Digital Quantum Simulation of the Rabi Model Assisted via Shortcut to Adiabaticity

Author: Pablo García Azorín
Advisor(s): Xi Chen
Master in Quantum Science and Technology
Publication year: 2022
Abstract: Since the very early stages of quantum computation, the use of quantum computers as platforms for the simulation of quantum systems was thought to offer computational advantage over the use of classical computers. Recently, a new paradigm between Adiabatic Quantum Computation performed in gate-based Digital Quantum Computers was demonstrated, which combines the strength of the adiabatic algorithm to encode and solve a broad range of problems, with the generality of digital quantum computing that allows the implementation of a wider range of interactions and is compatible with error correction protocols. In this thesis we cover the digital quantum simulation of the Rabi model, making an emphasis in the simulation of the time-dependent variation, with a time-dependent interaction term. With this generalization, the problem can be understood as an Adiabatic Quantum Computation problem, making it feasible for the implementation making use of the new paradigm of Digitized-Adiabatic Quantum Computing. To enhance the performance of the algorithm, we study the addition of Digitized Shortcuts to Adiabaticity, exploring the computation of a Counter-diabatic term with the recently proposed approximation method of the nested formula and proposing a novel way of performing the simulation via the Counter-diabatic term, reducing the circuit depth required. From the study of a simple model, we intend to understand the effect of adding STA techniques into the simulation, with a view to their future extension to more complex systems, where they could be beneficial in the approach towards quantum advantage.
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