Realizing topologically ordered states on a quantum processor

K J Satzinger¹, Y-J Liu^{2

3}, A Smith^{2

4

5}, C Knapp^{6

7}, M Newman¹, C Jones¹, Z Chen¹, C Quintana¹, X Mi¹, A Dunsworth¹, C Gidney¹, I Aleiner¹, F Arute¹, K Arya¹, J Atalaya¹, R Babbush¹, J C Bardin^{1

8}, R Barends¹, J Basso¹, A Bengtsson¹, A Bilmes¹, M Broughton¹, B B Buckley¹, D A Buell¹, B Burkett¹, N Bushnell¹, B Chiaro¹, R Collins¹, W Courtney¹, S Demura¹, A R Derk¹, D Eppens¹, C Erickson¹, L Faoro⁹, E Farhi¹, A G Fowler¹, B Foxen¹, M Giustina¹, A Greene^{1

10}, J A Gross¹, M P Harrigan¹, S D Harrington¹, J Hilton¹, S Hong¹, T Huang¹, W J Huggins¹, L B Ioffe¹, S V Isakov¹, E Jeffrey¹, Z Jiang¹, D Kafri¹, K Kechedzhi¹, T Khattar¹, S Kim¹, P V Klimov¹, A N Korotkov^{1

11}, F Kostritsa¹, D Landhuis¹, P Laptev¹, A Locharla¹, E Lucero¹, O Martin¹, J R McClean¹, M McEwen^{1

12}, K C Miao¹, M Mohseni¹, S Montazeri¹, W Mruczkiewicz¹, J Mutus¹, O Naaman¹, M Neeley¹, C Neill¹, M Y Niu¹, T E O'Brien¹, A Opremcak¹, B Pató¹, A Petukhov¹, N C Rubin¹, D Sank¹, V Shvarts¹, D Strain¹, M Szalay¹, B Villalonga¹, T C White¹, Z Yao¹, P Yeh¹, J Yoo¹, A Zalcman¹, H Neven¹, S Boixo¹, A Megrant¹, Y Chen¹, J Kelly¹, V Smelyanskiy¹, A Kitaev^{1

6

7}, M Knap^{2

3

13}, F Pollmann^{2

3}, P Roushan¹

Affiliations

¹ Google Quantum AI, Mountain View, CA, USA.
² Department of Physics, Technical University of Munich, 85748 Garching, Germany.
³ Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany.
⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.
⁵ Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UK.
⁶ Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.
⁷ Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA.
⁸ Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA.
⁹ Laboratoire de Physique Theorique et Hautes Energies, Sorbonne Université, 75005 Paris, France.
¹⁰ Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
¹¹ Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA.
¹² Department of Physics, University of California, Santa Barbara, CA, USA.
¹³ Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.

PMID: 34855491
DOI: 10.1126/science.abi8378

Realizing topologically ordered states on a quantum processor

K J Satzinger et al. Science. 2021.

. 2021 Dec 3;374(6572):1237-1241.

doi: 10.1126/science.abi8378. Epub 2021 Dec 2.

Authors

Affiliations

¹ Google Quantum AI, Mountain View, CA, USA.
² Department of Physics, Technical University of Munich, 85748 Garching, Germany.
³ Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany.
⁴ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.
⁵ Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UK.
⁶ Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.
⁷ Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA.
⁸ Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA.
⁹ Laboratoire de Physique Theorique et Hautes Energies, Sorbonne Université, 75005 Paris, France.
¹⁰ Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
¹¹ Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA.
¹² Department of Physics, University of California, Santa Barbara, CA, USA.
¹³ Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.

PMID: 34855491
DOI: 10.1126/science.abi8378

Abstract

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

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Programming a quantum phase of matter.
Bartlett SD. Bartlett SD. Science. 2021 Dec 3;374(6572):1200-1201. doi: 10.1126/science.abl8910. Epub 2021 Dec 2. Science. 2021. PMID: 34855480

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Realizing topologically ordered states on a quantum processor

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Realizing topologically ordered states on a quantum processor

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