Metamaterials engineered to host topological states of matter in controllable quantum systems hold promise for the advancement of quantum simulations and quantum computing technologies. In this context, the Su-Schrieffer-Heeger (SSH) model has gained prominence due to its simplicity and practical applications. Here we present the implementation of a gate-tunable, five-unit-cell resonator-based SSH chain on a one-dimensional lattice of superconducting resonators. We achieve electrostatic control over the inductive intracell coupling using semiconductor nanowire junctions, which enables the spectroscopic observation of a transition from a trivial to a topological phase in the engineered metamaterial. In contrast to prior work, our approach offers precise and independent in situ tuning of the coupling parameters, which is critical to directly approximate ideal tight-binding Hamiltonians via the control over local variables. Our results supplement efforts towards gate-controlled superconducting electronics and large controllable resonator-based lattices to enable quantum simulations.@en

Topological properties of quantum systems are among the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically nontrivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets an approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.

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Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking of large-scale dynamical quantum systems represents a major challenge due to lack of efficient tools for their simulation. Here, we present a scalable algorithm based on neural networks for Hamiltonian tomography in out-of-equilibrium quantum systems. We illustrate our approach using a model for a forefront quantum simulation platform: ultracold atoms in optical lattices. Specifically, we show that our algorithm is able to reconstruct the Hamiltonian of an arbitrary sized bosonic ladder system using an accessible amount of experimental measurements. We are able to significantly increase the previously known parameter precision.

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