Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras

Author:

Patel Smik12ORCID,Izmaylov Artur F.12ORCID

Affiliation:

1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto , Toronto, Ontario M5S 3H6, Canada and , Toronto, Ontario M1C 1A4, Canada

2. Department of Physical and Environmental Sciences, University of Toronto Scarborough , Toronto, Ontario M5S 3H6, Canada and , Toronto, Ontario M1C 1A4, Canada

Abstract

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for the evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians we use are defined by the condition that within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras and can, therefore, be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. The application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared to previously used exactly solvable qubit Hamiltonians.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

AIP Publishing

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