A categorical order theory of pulse scheduling in gate-based quantum computing

Abstract

We define a preorder on a vector space of complex valued integrable functions on the non-negative real numbers. This preorder is then used to develop a scheduling theory for microwave pulse schedules with an application for quantum computer experiments on superconducting circuits. The scheduling theory is further developed in a categorical framework using a subcategory of Ord, the category of preordered sets and order-preserving mappings between them. The developed theory is then applied to create a Python library which translates IBM OpenPulse schedules to Quantify schedules. Further, this library was then used to conduct single qubit characterisation experiments. Performed experiments include: resonator spectroscopy, two-tone spectroscopy, Rabi oscillation, relaxation time (T1) and qubit state discrimination experiments.