Improved variational quantum eigensolver via quasi-dynamical evolution

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 favourable 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 quasi-dynamical 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. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits. 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.

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• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
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• Information flow in parameterized quantum circuits
• Simulator Demonstration of Large Scale Variational Quantum Algorithm on HPC Cluster
• Quantum annealer accelerates the variational quantum eigensolver in a triple-hybrid algorithm
• Reverse quantum annealing assisted by forward annealing
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• Slice-Wise Initial State Optimization to Improve Cost and Accuracy of the VQE on Lattice Models