Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
Authors
Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, Artur F. Izmaylov
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 Schrödinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm.
4 comments
AKim
Also, what's the definition of a molecular structure Hamiltonian - basically N-particle system with Coulomb forces or something else?
afizmaylov
2) The space for unitaries and hermitian operators is the same, it is 2^N dimensional Hilbert space of states for N qubits.
3) Molecular electronic Hamiltonian is a second-quantized form of T_e+ V_ee+V_en+V_nn after the Born-Oppenheimer separation in the total molecular Hamiltonian, here T_e is a kinetic energy of electrons, V_ee-V_nn corresponding Coulomb interactions between electrons and nuclei constituting the molecule.
AKim
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