Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits

TL;DR

This paper demonstrates the experimental creation of continuous matrix product states in superconducting circuits to approximate the ground state of an interacting Bose gas, bridging classical and quantum simulation methods.

Contribution

It introduces a novel experimental approach to realize and probe continuous matrix product states using circuit QED, enabling exploration of strongly correlated quantum systems.

Findings

Successfully approximated the ground state of the Lieb-Liniger Hamiltonian

Demonstrated the potential to explore exotic multicomponent models

Provided insights into entanglement properties of matrix product states

Abstract

Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate and experimentally probe the properties of such systems. In this work we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states - a class of states which has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics (cQED) system we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to exotic models involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.