Accurately computing electronic properties of a quantum ring

TL;DR

This paper demonstrates an accurate quantum simulation of electronic properties in a condensed-matter system using superconducting qubits, achieving high fidelity in measuring energy eigenvalues and probing complex phenomena like disorder and persistent currents.

Contribution

It provides an experimental blueprint for high-precision quantum simulation of condensed-matter systems with superconducting qubits, including methods to mitigate errors and analyze electronic properties.

Findings

Reconstructed the band-structure of a 1D wire with ~0.01 rad accuracy.

Achieved robust measurement of eigenenergies with statistical uncertainty of 1e-4 rad.

Observed avoided level crossings and persistent currents in simulated disordered systems.

Abstract

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 rad, whereas typical energy scales are of order 1 rad. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 rad. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits.