Improved Variational Quantum Eigensolver Via Quasidynamical Evolution

Physical Review Applied, vol. 19

Abstract

The variational quantum eigensolver (VQE) is a hybrid quantum classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favorable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state-preparation mechanism, in a recursive manner, for a quasidynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground-state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to 40 qubits that manipulate the complete state vector. In addition to systematically finding the ground-state energy, we observe that it avoids barren plateaus, escapes local minima, and works with low-depth circuits. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground-state energies beyond 50 qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.

Authors 4

1. Manpreet Singh Jattana Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, D-52425, Germany

   RWTH Aachen University, Aachen D-52062, Germany

2. Fengping Jin

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, D-52425, Germany

3. Hans A. De Raedt

   University of Groningen · Forschungszentrum Jülich · Jülich Supercomputing Centre · Zernike Institute for Advanced Materials

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, D-52425, Germany

   Zernike Institute for Advanced Materials, University of Groningen, Groningen NL-9747 AG, Netherlands

4. Kristel F. L. Michielsen Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, D-52425, Germany

   RWTH Aachen University, Aachen D-52062, Germany