Features and Applications of Random Unitaries
Name
kong-linghang-phd-physics-2022-thesis.pdf
Description
Thesis PDF
Size
1.54 MB
Format
Adobe PDF
Checksum (MD5)
627d8c50c4562ab1b69ec0f31d40f11b
Author(s)
Kong, Linghang
Advisor(s)
Harrow, Aram
Date Issued
February 2022
Publisher
Massachusetts Institute of Technology
Abstract
Random unitary model plays essential roles in the study of many-body quantum systems, and have many applications in the field of quantum information. In this thesis we will explore some features and applications of this model. We will first study the scrambling property of random circuits (i.e., sequential applications of random unitaries according to some interaction geometry). We will analyze the behaviors of two commonly used measures of scrambling, out-of-time-ordered correlation and entanglement, and show that the corresponding notions of scrambling can be fundamentally different. Then we will study one application of random unitaries, which is generation of near-optimal covariant quantum error-correcting codes (i.e., codes that obey some symmetry). We will show that quantum codes with U(1) and SU(d) symmetry could be generated using random unitaries with the corresponding symmetry, and the error rates of such codes typically saturate the fundamental limits. Finally, we will explore another application of random unitaries, the randomized benchmarking protocol. We will extend the randomized benchmarking framework in previous work to the setting of a continuous gate set. This allows us to benchmark arbitrary quantum gates in a unified way, which accommodates the need posed by experiments.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
In Copyright - Educational Use Permitted
Copyright MIT
Persistent DSpace Link
