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Quantum processors of today are already capable of surpassing classical supercomputers on certain specialized tasks [1]. A current milestone for the quantum information science community is the fulfilment of quantum computational advantage on a practical problem of interest. The beginning of this talk will outline our technical progress on realizing various high-fidelity quantum gates on Google’s Sycamore processor, such as iSWAP and CPHASE. We then focus on two experiments studying many-body phenomena that have previously proven elusive on all quantum computing or simulation platforms: discrete time-crystals (DTC) and quantum scrambling.

In the DTC work, we implement Floquet dynamics on a 1D chain of 20 superconducting qubits [2]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing a non-equilibrium phase of matter [3]. 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. In the quantum scrambling work [4], we deploy a full 2D grid of 53 qubits and implement quantum circuits with tunable complexity. By measuring the quantum fluctuation of out-of-time-ordered correlators (OTOCs), we resolve the two key requisites of quantum scrambling: operator spreading and operator entanglement. Results from the most complex quantum circuits require ~100 hours to simulate on a CPU core via best-known classical algorithms, indicating the potential for achieving practical quantum advantage in the near term.

[1] Google AI Quantum and Collaborators, Nature **574**, 505 (2019).

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

[3] M. Ippoliti, K. Kechedzhi, R. Moessner, S. Shivaji, V. Khemani, PRX Quantum (In press).

[4] X. Mi, P. Roushan, C. Quintana, K. Kechedzhi, V. Smelyanskiy, Y. Chen *et al.*, arXiv:2101.08870 (2021).