Observation of Time-Crystalline Eigenstate Order on a Quantum Processor*

Quantum processors of today are already capable of surpassing classical supercomputers on certain specialized tasks. A current milestone for the quantum information science community is the fulfilment of quantum computational advantage on a practical problem of interest. Studying many-body phases of matter offers unique opportunities toward this coveted goal since many outstanding questions remain surrounding the critical behaviors of quantum phases. Here we report on the experimental observation of a non-equilibrium phase of matter, the discrete time crystal (DTC). A DTC breaks time-translational symmetry and displays spatio-temporal quantum order in all of its eigenstates, a feature dubbed “eigenstate order”. We implement Floquet dynamics on a 1D chain of 20 superconducting qubits [1]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing the non-equilibrium phase [2]. We carefully validate the phase structure of the DTC by probing the average response of all eigenstates belonging to the Floquet unitary. Using a suitable choice of order parameter, we further identify the location of the MBL-ergodicity crossover via experimentally observed finite-size effects. These results open a direct path to studying quantum phase transitions and critical phenomena on NISQ quantum processors.

[1] X. Mi, M. Ippoliti, K. Kechedzhi, V. Khemani, P. Roushan et al.,  arXiv:2107.13571 (2021).

[2] M. Ippoliti, K. Kechedzhi, R. Moessner, S. Shivaji, V. Khemani,  PRX Quantum 2, 030346 (2021).