Partitioning Pauli Operators: in Theory and in Practice

Abstract

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in the variational quantum eigensolver. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the measurement process. In this thesis, we look both at the task of partitioning all Pauli operators of a xed length and of partitioning a random subset of these Pauli operators. We rst show how Singer cycles can be used to optimally partition the set of all Pauli operators, giving some insight to the structure underlying many constructions of mutually unbiased bases. Thereafter, we show how graph coloring algorithms promise to provide speedups linear with respect to the lengths of the operators over currently-implemented techniques in the measurement step of the variational quantum eigensolver.