In many extended systems strong correlation is localized in spatially separated subunits. This feature can be leveraged to lower the computational cost of quantum calculations, not only using classical algorithms, but also quantum algorithms. A recently developed method in our group, LAS-UCC, combines a localization of the wave function with quantum phase estimation (QPE) performed only on local fragments and the variational quantum eigensolver (VQE) for inter-fragment correlation. LAS-UCC is used to compute the energy of large molecules in which strong correlation is localized with subunits. This algorithm provides accuracy above that of both the VQE using the UCCSD ansatz on the whole system, and the classical localized active space self-consistent field (LASSCF) method upon which it builds.<br/><br/>In this work, we explore the limits of the LAS-UCC method in terms of the required number of ancilla qubits and gate depths, as well as the accuracy with respect to an exact diagonalization (FCI). The goal of this study is to provide an efficient way to simulate the wave functions of the fragment systems on a quantum computer using QPE and then use the VQE to re-capture any correlation between nearby fragments. Thus, errors arising due to trotterization, the scaling of the Hamiltonian for QPE, as well as similar errors for the VQE step, will provide insight into the efficiency of the method. In order to model real systems, keeping the error sources in mind, we then apply the LAS-UCC method as implemented on a quantum simulator using Qiskit to compute the total energies of conjugated organic molecules, and compare it to the classical LASSCF method.

Exploring the LAS-UCC method on a quantum simulator

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