The Variational Power of Quantum Circuit Tensor Networks

TL;DR

This paper investigates the expressive power of quantum circuit tensor networks for representing many-body ground states, demonstrating their advantages over traditional tensor networks and other quantum circuits in terms of expressiveness and compactness.

Contribution

It introduces an adaptive optimization method for quantum circuit tensor networks and benchmarks their performance against standard tensor networks and other architectures.

Findings

Quantum circuit tensor networks are more expressive than other quantum circuits for studied models.

They can be more compact than standard tensor networks.

Extrapolated depths suggest potential quantum advantage in representing ground states.

Abstract

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D/2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground-states.