Realizing topologically ordered states on a quantum processor
Kevin J. Satzinger, Yu-Jie Liu, Adam Smith, Christina Knapp, Michael Newman, C. Jones, Z. Chen, Chris Quintana, Xiao Mi, A. Dunsworth, C. Gidney, I. L. Aleǐner, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, R. Barends, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, B. Chiaro, Roberto Collins, William Courtney, Sean Demura, Alan R. Derk, Daniel Eppens, C. W. Erickson, L. Faoro, E. Farhi, Austin G. Fowler, Brooks Foxen, Marissa Giustina, Alex Greene, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Sabrina Hong, T. Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, E. Jeffrey, Z. Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Tanuj Khattar, Seon Kim, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Matt McEwen, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, J. Mutus, Ofer Naaman, M. Neeley, C. Neill, M. Y. Niu, Thomas E. O’Brien, Alex Opremcak, Bálint Pató, A. Petukhov, Nicholas C. Rubin, D. Sank, V. Shvarts, Doug Strain, Marco Szalay, Benjamin Villalonga, T. White, Z. Jamie Yao, P. Yeh, Juhwan Yoo, Adam Zalcman, Hartmut Neven, Sergio Boixo, A. Megrant, Yu Chen, J. Kelly, Vadim Smelyanskiy, Alexei Kitaev, Michael Knap, Frank Pollmann, P. Roushan
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.