Tensor-network based variational approach to calculating ground state properties of interacting quantum systems with superconducting qubits*

Variational quantum-classical hybrid algorithms have recently emerged as a promising application for near-term quantum devices. In superconducting circuits, recent demonstrations of this algorithm with up to four qubits have probed the energy landscapes of simple molecules and spin chains. As these devices scale to increasingly larger numbers of qubits, the choice of ansatz for the variationally-optimized wavefunction becomes more important. An ideal ansatz combines two desiderata: the ability to represent a large portion of the n-qubit Hilbert space, specifically highly-entangled states; and a circuit depth which scales polynomially with the qubit number. Recently, classical methods based on tensor networks have become popular for compactly handling wavefunctions of interacting systems which possess a high degree of entanglement. Motivated by their successes, we apply tensor network ansatze to the variational quantum eigensolver in an experimental setting: an superconducting quantum processor comprising eight transmon qubits. Our approach is intended to study ground-state properties of interacting systems, e.g. spin chains. Here we detail the experimental protocol and present preliminary data.