Time-crystalline eigenstate order on a quantum processor

@article{Mi2021TimecrystallineEO,
  title={Time-crystalline eigenstate order on a quantum processor},
  author={Xiao Mi and Matteo Ippoliti and Chris Quintana and Amy Greene and Zijun Chen and Jonathan A. Gross and Frank Arute and Kunal Arya and Juan Atalaya and Ryan Babbush and Joseph C. Bardin and Jo{\~a}o Basso and Andreas Bengtsson and Alexander Bilmes and Alexandre Bourassa and Leon Brill and Mick Broughton and Bob B. Buckley and David A. Buell and Brian Burkett and Nicholas Bushnell and Benjamin Chiaro and Roberto Collins and William Courtney and Dripto M. Debroy and Sean Demura and Alan R. Derk and Andrew Dunsworth and Daniel Eppens and Catherine Erickson and Edward Farhi and Austin G. Fowler and Brooks Foxen and Craig Gidney and Marissa Giustina and Matthew P. Harrigan and Sean D. Harrington and Jeremy P. Hilton and Alan K. Ho and Sabrina Hong and Trent Huang and Ashley Huff and William J. Huggins and L. B. Ioffe and Sergei V. Isakov and Justin Iveland and Evan Jeffrey and Zhang Jiang and Cody Jones and Dvir Kafri and Trinjhna Khattar and Seon Kim and Alexei Kitaev and Paul V. Klimov and Alexander N. Korotkov and Fedor Kostritsa and David Landhuis and Pavel Laptev and Joonho Lee and Kenny Lee and Aditya Locharla and Erik Lucero and Orion Martin and Jarrod R. McClean and Trevor Mccourt and Matthew J. McEwen and Kevin C. Miao and Masoud Mohseni and S. Montazeri and Wojciech Mruczkiewicz and Ofer Naaman and Matthew Neeley and Charles J. Neill and Michael Newman and Murphy Yuezhen Niu and Thomas F. O' Brien and Alexander Opremcak and Eric P. Ostby and Bálint Pató and Andre Petukhov and Nicholas C Rubin and Daniel Thomas Sank and Kevin J Satzinger and Vladimir Shvarts and Yuan Su and Doug Strain and Marco Szalay and Matthew D Trevithick and Benjamin Villalonga and Theodore White and Z. Yao and Ping Yeh and Juhwan Yoo and Adam Zalcman and Hartmut Neven and Sergio Boixo and Vadim N. Smelyanskiy and Anthony Megrant and Julian Kelly and Yu Chen and S. L. Sondhi and Roderich Moessner and Kostyantyn Kechedzhi and Vedika Khemani and Pedram Roushan},
  journal={Nature},
  year={2021},
  volume={601},
  pages={531 - 536}
}
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… 

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