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Accurately computing the electronic properties of a quantum ring


A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform1,2,3,4. However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate 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 measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10−4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation5,6 and paves the way to study new quantum materials with superconducting qubits.

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Fig. 1: Engineering a one-dimensional system with energy, momentum and flux.
Fig. 2: Measuring the single-particle band structure.
Fig. 3: Synthetic flux as a probe of local disorder.
Fig. 4: Inferring current and conductance from avoided level crossings.

Data availability

The data presented in this study can be found in the Dryad repository located at

Code availability

The Python code for processing the data presented in this study can be found in the Dryad repository located at


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We acknowledge discussions with B. Altshuler and L. Faoro. We thank J. Platt, J. Dean and J. Yagnik for their executive sponsorship of the Google Quantum AI team, and for their continued engagement and support. We thank A. Brown and J. Platt for reviewing and providing advice on the draft of the manuscript.

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Authors and Affiliations



C.N. designed and executed the experiment. C.N. and P.R. wrote the manuscript. C.N., T.M. and V. Smelyanskiy wrote the Supplementary Information. V. Smelyanskiy, S.B., T.M., Z.J., X.M., L.B.I. and C.N. provided the theoretical support and analysis techniques, the theory of Floquet calibration and the open system model. Y.C., V. Smelyanskiy and H.N. led and coordinated the project. Infrastructure support was provided by the hardware team. All authors contributed to revising the manuscript and the Supplementary Information.

Corresponding authors

Correspondence to P. Roushan, Y. Chen or V. Smelyanskiy.

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The authors declare no competing interests.

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Peer review information Nature thanks Jonas Bylander, Frank Wilhelm and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary Information

This file contains Supplementary Sections A-G, including Supplementary Figures 1-15 – see contents page for details.

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Neill, C., McCourt, T., Mi, X. et al. Accurately computing the electronic properties of a quantum ring. Nature 594, 508–512 (2021).

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