Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz

TL;DR

This paper introduces a tensor network-enhanced variational quantum eigensolver that accelerates ground-state calculations for complex quantum systems by embedding classical TN solutions into quantum circuits, improving convergence and avoiding local minima.

Contribution

It presents a novel synergistic framework combining tensor networks with VQE, enabling systematic inhomogeneous system analysis and improved optimization without initial parameter guesses.

Findings

Accelerates VQE convergence in complex models

Avoids local minima in Ising model calculations

Demonstrates effectiveness on random transverse-field models

Abstract

In this paper, we introduce a tensor network (TN) scheme into the entanglement augmentation process of the synergistic optimization framework by Rudolph et al. [arXiv:2208.13673] to build its process systematically for inhomogeneous systems. Our synergistic approach first embeds the variational optimal solution of the TN state with the entropic area law, which can be perfectly optimized in conventional (classical) computers, in a quantum variational circuit ansatz inspired by the TN state with the entropic volume law. Next, the framework performs a variational quantum eigensolver (VQE) process with embedded states as the initial state. We applied the synergistic to the ground-state analysis of the all-to-all coupled random transverse-field Ising, XYZ, Heisenberg model, employing the binary multiscale entanglement renormalization ansatz (MERA) state and branching MERA states as TN states with entropic area law and volume law, respectively. We then show that the synergistic accelerates VQE calculations in the three models without an initial parameter guess of the branching-MERA-inspired ansatz and can avoid a local solution trapped by a standard VQE with the ansatz in the Ising model. The improvement of optimizers for MERA in all-to-all coupled inhomogeneous systems, enhancement, and potential synergistic applications are also discussed.