#### Event Title

A new measure of distance between quantum states: Exploring optimal transformations between qubit ground states

#### Research Mentor(s)

Armin Rahmani

#### Description

Advancements in controllable quantum bits have created a desire for new mathematical and computational methods which allow for greater authority over such systems. By applying techniques in optimal control theory to the dynamics of two highly tunable "Gmon" qubits, we provide not only computational tools for analyzing controllable quantum systems, but also novel applications of the data generated by these methods. By constraining the parameters in the Hamiltonian of the Gmon qubit architecture, we can define a "minimum transition time" between permissible ground states as the absolute minimum time needed to transform one ground state to another via unitary evolution. That evolution is dictated by how the parameters in the Hamiltonian change over time, called the protocol of the transition. We then create an algorithm which finds those minimum transition times as a function of initial and final ground states by solving for the optimal protocol, and we demonstrate various novel applications of this data. These applications show the richness of optimal control in quantum theory and may serve as starting points for future research.

#### Document Type

Event

#### Start Date

May 2018

#### End Date

May 2018

#### Location

Physics and Astronomy

#### Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

#### Language

English

#### Format

application/pdf

A new measure of distance between quantum states: Exploring optimal transformations between qubit ground states

Physics and Astronomy

Advancements in controllable quantum bits have created a desire for new mathematical and computational methods which allow for greater authority over such systems. By applying techniques in optimal control theory to the dynamics of two highly tunable "Gmon" qubits, we provide not only computational tools for analyzing controllable quantum systems, but also novel applications of the data generated by these methods. By constraining the parameters in the Hamiltonian of the Gmon qubit architecture, we can define a "minimum transition time" between permissible ground states as the absolute minimum time needed to transform one ground state to another via unitary evolution. That evolution is dictated by how the parameters in the Hamiltonian change over time, called the protocol of the transition. We then create an algorithm which finds those minimum transition times as a function of initial and final ground states by solving for the optimal protocol, and we demonstrate various novel applications of this data. These applications show the richness of optimal control in quantum theory and may serve as starting points for future research.