Marin Bukov

Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, with improvements of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50kHz range - a challenging frequency regime for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions.

The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations. They are promising tools to benchmark quantum devices and measure free energy differences. While they are well established theoretically and also experimental realizations for few-body systems already exist, their experimental validity in the quantum many-body regime has not been observed so far. Here, we present results for nonequilibrium protocols in systems with up to sixteen interacting degrees of freedom obtained on trapped ion and superconducting qubit quantum computers, which test the quantum Jarzynski equality and the Crooks relation in the many-body regime. To achieve this, we overcome present-day limitations in the preparation of thermal ensembles and in the measurement of work distributions on noisy intermediate-scale quantum devices. We discuss the accuracy to which the Jarzynski equality holds on different quantum computing platforms subject to platform-specific errors. The analysis reveals the validity of Jarzynski's equality in a regime with energy dissipation, compensated for by a fast unitary drive. This provides new insights for analyzing errors in many-body quantum simulators.

I demonstrate the potential of reinforcement learning (RL) to prepare quantum states of strongly periodically driven non-linear single-particle models. The ability of Q-Learning to control systems far away from equilibrium is exhibited by steering the quantum Kapitza oscillator to the Floquet-engineered stable inverted position in the presence of a strong periodic drive within several shaking cycles. The study reveals the potential of the intra-period (micromotion) dynamics, often neglected in Floquet engineering, to take advantage over pure stroboscopic control at moderate drive frequencies. Without any knowledge about the underlying physical system, the algorithm is capable of learning solely from tried protocols and directly from simulated noisy quantum measurement data, and is stable to noise in the initial state, and sources of random failure events in the control sequence. Model-free RL can provide new insights into automating experimental setups for out-of-equilibrium systems undergoing complex dynamics, with potential applications in quantum information, quantum optics, ultracold atoms, trapped ions, and condensed matter.