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Revising measurement process in the variational quantum eigensolver: Is it possible to reduce the number of separately measured operators?

Abstract

Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit subspaces. The number of such parts rapidly grows with the size of the molecule. This increases the computational cost and can increase uncertainty in the measurement of the energy expectation value because elements from different parts need to be measured independently. To address this problem we introduce a more efficient partitioning of the qubit Hamiltonian using fewer parts that need to be measured separately. The new partitioning scheme is based on two ideas: 1) grouping terms into parts whose eigenstates have a single-qubit product structure, and 2) devising multi-qubit unitary transformations for the Hamiltonian or its parts to produce less entangled operators. The first condition allows the new parts to be measured in the number of involved qubit consequential one-particle measurements. Advantages of the new partitioning scheme resulting in severalfold reduction of separately measured terms are illustrated on the H2 and LiH problems.

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Publication details

The article was received on 14 Dec 2018, accepted on 11 Feb 2019 and first published on 12 Feb 2019


Article type: Edge Article
DOI: 10.1039/C8SC05592K
Citation: Chem. Sci., 2019, Accepted Manuscript
  • Open access: Creative Commons BY license
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    Revising measurement process in the variational quantum eigensolver: Is it possible to reduce the number of separately measured operators?

    A. Izmaylov, T. Yen and I. G. Ryabinkin, Chem. Sci., 2019, Accepted Manuscript , DOI: 10.1039/C8SC05592K

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