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Time-crystalline eigenstate order on a quantum processor

Xiao Mi, Matteo Ippoliti, Chris Quintana, Ami Greene, Zijun Chen, Jonathan Gross, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Dripto Debroy, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Joonho Lee, Kenny Lee, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O’Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Yuan Su, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Anthony Megrant, Julian Kelly, Yu Chen, S. L. Sondhi, Roderich Moessner, Kostyantyn Kechedzhi, Vedika Khemani () and Pedram Roushan ()
Additional contact information
Xiao Mi: Google Research
Matteo Ippoliti: Stanford University
Chris Quintana: Google Research
Ami Greene: Google Research
Zijun Chen: Google Research
Jonathan Gross: Google Research
Frank Arute: Google Research
Kunal Arya: Google Research
Juan Atalaya: Google Research
Ryan Babbush: Google Research
Joseph C. Bardin: Google Research
Joao Basso: Google Research
Andreas Bengtsson: Google Research
Alexander Bilmes: Google Research
Alexandre Bourassa: Google Research
Leon Brill: Google Research
Michael Broughton: Google Research
Bob B. Buckley: Google Research
David A. Buell: Google Research
Brian Burkett: Google Research
Nicholas Bushnell: Google Research
Benjamin Chiaro: Google Research
Roberto Collins: Google Research
William Courtney: Google Research
Dripto Debroy: Google Research
Sean Demura: Google Research
Alan R. Derk: Google Research
Andrew Dunsworth: Google Research
Daniel Eppens: Google Research
Catherine Erickson: Google Research
Edward Farhi: Google Research
Austin G. Fowler: Google Research
Brooks Foxen: Google Research
Craig Gidney: Google Research
Marissa Giustina: Google Research
Matthew P. Harrigan: Google Research
Sean D. Harrington: Google Research
Jeremy Hilton: Google Research
Alan Ho: Google Research
Sabrina Hong: Google Research
Trent Huang: Google Research
Ashley Huff: Google Research
William J. Huggins: Google Research
L. B. Ioffe: Google Research
Sergei V. Isakov: Google Research
Justin Iveland: Google Research
Evan Jeffrey: Google Research
Zhang Jiang: Google Research
Cody Jones: Google Research
Dvir Kafri: Google Research
Tanuj Khattar: Google Research
Seon Kim: Google Research
Alexei Kitaev: Google Research
Paul V. Klimov: Google Research
Alexander N. Korotkov: Google Research
Fedor Kostritsa: Google Research
David Landhuis: Google Research
Pavel Laptev: Google Research
Joonho Lee: Google Research
Kenny Lee: Google Research
Aditya Locharla: Google Research
Erik Lucero: Google Research
Orion Martin: Google Research
Jarrod R. McClean: Google Research
Trevor McCourt: Google Research
Matt McEwen: Google Research
Kevin C. Miao: Google Research
Masoud Mohseni: Google Research
Shirin Montazeri: Google Research
Wojciech Mruczkiewicz: Google Research
Ofer Naaman: Google Research
Matthew Neeley: Google Research
Charles Neill: Google Research
Michael Newman: Google Research
Murphy Yuezhen Niu: Google Research
Thomas E. O’Brien: Google Research
Alex Opremcak: Google Research
Eric Ostby: Google Research
Balint Pato: Google Research
Andre Petukhov: Google Research
Nicholas C. Rubin: Google Research
Daniel Sank: Google Research
Kevin J. Satzinger: Google Research
Vladimir Shvarts: Google Research
Yuan Su: Google Research
Doug Strain: Google Research
Marco Szalay: Google Research
Matthew D. Trevithick: Google Research
Benjamin Villalonga: Google Research
Theodore White: Google Research
Z. Jamie Yao: Google Research
Ping Yeh: Google Research
Juhwan Yoo: Google Research
Adam Zalcman: Google Research
Hartmut Neven: Google Research
Sergio Boixo: Google Research
Vadim Smelyanskiy: Google Research
Anthony Megrant: Google Research
Julian Kelly: Google Research
Yu Chen: Google Research
S. L. Sondhi: Princeton University
Roderich Moessner: Max-Planck-Institut für Physik komplexer Systeme
Kostyantyn Kechedzhi: Google Research
Vedika Khemani: Stanford University
Pedram Roushan: Google Research

Nature, 2022, vol. 601, issue 7894, 531-536

Abstract: Abstract Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9–15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (8)

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DOI: 10.1038/s41586-021-04257-w

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