Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches

• URL: http://arxiv.org/abs/2208.08272v1
• Date: Wed, 17 Aug 2022 13:08:05 GMT
• Title: Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
• Authors: Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, and Artur F. Izmaylov
• Abstract summary: We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. The main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity.
• Score: 0.18374319565577155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity. It is derived that the lowest possible LCU 1-norm for a given Hamiltonian is half of its spectral range. This lowest norm decomposition is practically unattainable for general Hamiltonians; therefore, multiple practical techniques to generate LCU decompositions are proposed and assessed. A technique using symmetries to reduce the 1-norm further is also introduced. In addition to considering LCU in the Schr\"odinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm.

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