Quantum simulation of molecular electronic structure is among one of the promising applications of quantum computers. From an implementation standpoint, decomposition into factors of an exponential of a sum of operators is at the core of the construction of quantum circuits. In particular Lie-Trotter formulas provide the aforementioned (approximate) factorization such that the simulation is accomplished in terms of sequential operators that can be translated into computational gates. However, in spite of their relevance, a systematic approach to reduce the inherent error associated to Trotterization in the electronic structure problem is still lacking.<br/>On the other hand, a Lie algebraic framework for efficient decomposition and subsequent measurement of electronic Hamiltonians has been introduced recently. The latter is based on the formulation of the electronic Hamiltonian as a sum of contributions where each one can be rendered into a Cartan sub-algebra (<i>i.e.</i> a sub-algebra spanned by mutually commutative elements) form by means of single-particle rotations. In this work, we implement a strategy to find Hamiltonian partitions that minimize Trotterization error while preserving the Cartan sub-algebra character of the fragments. We discuss the limitations as well as the advantages of our procedure with respect to other popular decomposition schemes, such as matrix factorization approaches.

Cartan sub-algebra based approach to minimize Trotterization error on a quantum computer

ACS Spring 2022

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