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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The data presented in this study can be found in the Dryad repository located at https://doi.org/10.5061/dryad.4f4qrfj9x.
The Python code for processing the data presented in this study can be found in the Dryad repository located at https://doi.org/10.5061/dryad.4f4qrfj9x.
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885 (2008).
Georgescu, I., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153 (2014).
Polkovnikov, A., Sengupta, K., Silva, A. & Vengalatorre, M. Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys., 83, 863 (2011).
Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).
Qin, M. et al. Absence of superconductivity in the pure two-dimensional Hubbard model. Phys. Rev. X 10, 031016 (2020).
Jiang, H. C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t'. Science 365, 1424–1428 (2019).
Willett, R. et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987).
Dolev, M., Heiblum, M., Umansky, V., Stern, A. & Mahalu, D. Observation of a quarter of an electron charge at the v = 5/2 quantum Hall state. Nature 452, 829–834 (2008).
Willett, R. et al. Interference measurements of non-abelian e/4 & abelian e/2 quasiparticle braiding. Preprint at https://arxiv.org/abs/1905.10248 (2019).
Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).
Neill, C. A Path Towards Quantum Supremacy with Superconducting Qubits. PhD Thesis, Univ. California, Santa Barbara (2017).
Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).
Giamarchi, T. Quantum Physics in One Dimension Vol. 121 (Clarendon, 2003).
Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).
Manovitz, T., Shapira, Y., Akerman, N., Stern, A. & Ozeri, R. Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain. PRX Quantum 1, 020303 (2020).
Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).
Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).
Pal, A. & Huse, D. Many-body localization phase transition. Phys. Rev. B 82, 174411 (2010).
Ponte, P., Papić, Z., Huveneers, F. & Abanin, D. A. Many-body localization in periodically driven systems. Phys. Rev. Lett. 114, 140401 (2015).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Kleemans, N. A. et al. Oscillatory persistent currents in self-assembled quantum rings. Phys. Rev. Lett. 99, 146808 (2007).
Bleszynski-Jayich, A. C. et al. Persistent currents in normal metal rings. Science 326, 272–275 (2009).
Thouless, D., Kohmoto, M., Nightingale, M. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).
Braun, D., Hofstetter, E., MacKinnon, A. & Montambaux, G. Level curvatures and conductances: A numerical study of the thouless relation. Phys. Rev. B 55, 7557 (1997).
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992).
White, S. R. & Huse, D. A. Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S = 1 Heisenberg chain. Phys. Rev. B 48, 3844–3852 (1993).
Kelly, J., O’Malley, P., Neeley, M., Neven, H. & Martinis, J. Physical qubit calibration on a directed acyclic graph. Preprint at https://arxiv.org/abs/1803.03226 (2018).
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.
The authors declare no competing interests.
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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Neill, C., McCourt, T., Mi, X. et al. Accurately computing the electronic properties of a quantum ring. Nature 594, 508–512 (2021). https://doi.org/10.1038/s41586-021-03576-2
Materials Theory (2022)
Scientific Reports (2022)
Nature Communications (2022)