Measuring All Compatible Operators in One Series of Single-Qubit Measurements Using Unitary Transformations

Journal of Chemical Theory and Computation
Tzu-Ching YenArtur F Izmaylov

Abstract

The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or compatible operators simultaneously. Unfortunately, the current hardware permits measuring only a much more limited subset of operators that share a common tensor product eigen-basis. We introduce unitary transformations that transform any fully commuting group of operators to a group that can be measured on current hardware. These unitary operations can be encoded as a sequence of Clifford gates and let us not only measure much larger groups of terms but also to obtain these groups efficiently on a classical computer. The problem of finding the minimum number of fully commuting groups of terms covering the whole Hamiltonian is found to be equivalent to the minimum clique cover problem for a graph representing Hamiltonian terms as vertices and commutativity between them as edges. Tested on a set of molecular electronic Hamiltonians with up to 50 thousand terms, the introduced technique allows for the reduction of the number of separately measurable operator groups down to few hundreds, thus ach...Continue Reading

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Nov 15, 2018·Journal of Chemical Theory and Computation·Ilya G RyabinkinArtur F Izmaylov
Nov 21, 2019·Journal of Chemical Theory and Computation·Artur F IzmaylovVladyslav Verteletskyi

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Citations

Jun 3, 2021·Entropy·Oliver G MaupinAndrew J Landahl
Jun 3, 2021·Entropy·Michael KreshchukPeter J Love
Dec 10, 2020·Journal of Chemical Theory and Computation·Robert A LangArtur F Izmaylov
Nov 12, 2021·The Journal of Physical Chemistry. a·Robert H LavroffAnastassia N Alexandrova
Nov 12, 2021·The Journal of Physical Chemistry Letters·Robert H LavroffAnastassia N Alexandrova
Nov 12, 2021·The Journal of Physical Chemistry. B·Robert H LavroffAnastassia N Alexandrova

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