Partitioning Pauli Operators: in Theory and in Practice
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Date
2019-09-04
Authors
Jena, Andrew
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
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.
Description
Keywords
Clifford group, Pauli operators, partitioning, graph coloring, Singer cycles, VQE, variational quantum eigensolver, MUBs, mutually unbiased bases, symplectic representation, NP-hard