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Realizing topologically ordered states on a quantum processor

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arxiv 2104.01180 v1 pith:YS2BYIJL submitted 2021-04-02 quant-ph cond-mat.str-el

K. J. Satzinger , Y. Liu , A. Smith , C. Knapp , M. Newman , C. Jones , Z. Chen , C. Quintana
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X. Mi A. Dunsworth C. Gidney I. Aleiner F. Arute K. Arya J. Atalaya R. Babbush J. C. Bardin R. Barends J. Basso A. Bengtsson A. Bilmes M. Broughton B. B. Buckley D. A. Buell B. Burkett N. Bushnell B. Chiaro R. Collins W. Courtney S. Demura A. R. Derk D. Eppens C. Erickson E. Farhi L. Foaro A. G. Fowler B. Foxen M. Giustina A. Greene J. A. Gross M. P. Harrigan S. D. Harrington J. Hilton S. Hong T. Huang W. J. Huggins L. B. Ioffe S. V. Isakov E. Jeffrey Z. Jiang D. Kafri K. Kechedzhi T. Khattar S. Kim P. V. Klimov A.N. Korotkov F. Kostritsa D. Landhuis P. Laptev A. Locharla E. Lucero O. Martin J. R. McClean M. McEwen K. C. Miao M. Mohseni S. Montazeri W. Mruczkiewicz J. Mutus O. Naaman M. Neeley C. Neill M. Y. Niu T. E. O'Brien A. Opremcak B. Pató A. Petukhov N. C. Rubin D. Sank V. Shvarts D. Strain M. Szalay B. Villalonga T. C. White Z. Yao P. Yeh J. Yoo A. Zalcman H. Neven S. Boixo A. Megrant Y. Chen J. Kelly V. Smelyanskiy A. Kitaev M. Knap F. Pollmann P. Roushan
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classification quant-phcond-mat.str-el
keywords quantummattertopologicalcodeerrororderorderedprocessor
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abstract

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction.

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  1. Lower-depth local encoding circuits for the surface code

    quant-ph 2025-09 conditional novelty 7.0 of 10

    Depth-d local encoding circuits for the rotated surface code, built from depth-2 growth steps, with a proof that any inductive construction needs depth d+O(1).

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