We propose a scheme to implement Kitaev's honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum simulators. We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom. We address the challenge of probing the physics of Majorana fermions, while having only access to the original composite spin degrees of freedom. Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive. The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically-prepared states. By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators. arXiv:2211.09777
We analyze a new class of time-periodic dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space volume preserving) yet possess no symplectic structure. As a result, the dynamics of the system cannot be derived from any time-dependent Hamiltonian. In the high-frequency limit, we find that the magnetization dynamics features a long-lived metastable plateau, whose duration is controlled by the fourth power of the drive frequency. However, due to the lack of an effective Hamiltonian, the system does not evolve into a strictly prethermal state. We propose a Hamiltonian extension of the system using auxiliary degrees of freedom, in which the original spins constitute an open yet nondissipative subsystem. This allows us to perturbatively derive effective equations of motion that manifestly display symplecticity breaking at leading order in the inverse frequency. We thus extend the notion of prethermal dynamics, observed in the high-frequency limit of periodically-driven systems, to a nonsymplectic setting. arXiv:2208.09005
The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations. While they are well established theoretically and also experimental realizations for simple few-body systems already exist, a verification in the quantum many-body regime is still missing. Closing this gap becomes crucial in the light of the rapid development of quantum technologies, since it represents a natural test for the validity of the laws of quantum thermodynamics in closed systems, on the one side, and the utility of modern quantum simulators to reveal and scrutinize fundamental principles of nature, on the other. We verify the quantum Jarzynski equality and the Crooks relation in systems with up to sixteen interacting qubits on digital quantum computers. We overcome present-day limitations in the preparation of thermal ensembles and in the measurement of work distributions. Our analysis reveals a novel dissipative nonequilibrium regime, where a fast unitary drive compensates for dissipation and restores the validity of Jarzynski's equality.
Periodically driven (Floquet) quantum systems have become a paradigm for their capability to engineer and sustain stable long-lived states where energy absorption can be controllably suppressed. However, this approach is often restricted to specific initial states, typically aligned parallel to the driving field. In collaboration with Ajoy lab at UC Berkeley, we propose the engineering of robust closed spin orbits on the Bloch sphere. Our approach combines micromotion, which enables the engineering of a time-periodic family of Hamiltonians, with key concepts from the eigenstate thermalisation hypothesis, and Floquet pre-thermalisation. Our idea is experimentally demonstrated in a model system of long-range strongly interacting C13 nuclear spins in diamond with an intrinsic decoherence time of 1.5 ms. Using dynamical stabilisation we demonstrate the ability to excite and track robust designer trajectories for a lifetime of tens of seconds, corresponding to an increase in decoherence time of more than 4 orders of magnitude. Our results suggest new ways to stabilise strongly-coupled quantum systems through periodic driving, and portend powerful applications of rigid spin orbits in quantum sensing.
Variational quantum algorithms stand at the forefront of simulations on near-term and future fault-tolerant quantum devices. While most variational quantum algorithms involve only continuous optimization variables, the representational power of the variational ansatz can sometimes be significantly enhanced by adding discrete optimization variables, as is exemplified by the generalized quantum approximate optimization algorithm (QAOA). However, the hybrid discrete-continuous optimization problem poses a challenge for optimization. In collaboration with the Lin group at UC Berkeley and the Ying group at Stanford, we propose a new algorithm called MCTS-QAOA, which combines a Monte Carlo tree search method with an improved natural policy gradient solver to optimize the discrete and continuous variables in the quantum circuit. MCTS-QAOA has excellent noiseresilience properties and outperforms prior algorithms.
Quantum simulators and computers require optimal control techniques for state preparation. At the same time, the number of qubits is increasing at a rapid rate which poses a challenge for finding optimal control strategies in the many-body regime. We propose a novel approach for controlling quantum many-body systems based on reinforcement learning. The quantum many-body problem is tackled by leveraging matrix product states for both representing the quantum system and as a trainable deep learning ansatz for the reinforcement learning agent. The framework allows us to reach far larger system sizes than approaches based purely on neural networks while retaining the general advantages of deep learning methods such as generalizability and robustness to noise. We demonstrate that our agent can perform universal state preparation for a small number of spins, control a many-body spin chain of N=32 sites, and prepare ground states in the critical region of the Ising model. Our work opens up the door to further research at the intersection of tensor network-based machine learning and reinforcement learning.
In collaboration with the Ajoy lab at UC Berkeley, we observed long-lived Floquet prethermal discrete time crystalline (PDTC) order in a three-dimensional position-disordered lattice of interacting dipolar-coupled 13C nuclei in diamond. We demonstrate a novel strategy of "two-frequency" driving, involving an interleaved application of slow and fast drives that simultaneously prethermalize the spins with an emergent quasi-conserved magnetization along the x-axis, while enabling continuous and highly resolved observation of their dynamic evolution when periodically kicked away from x. The PDTC order manifests itself in a robust period doubling response of this drive-induced quasi-conserved spin magnetization interchanging between x and -x. We obtain movies of the time-crystalline response with a clarity and throughput orders of magnitude greater than previous experiments. Such rapid measurement enables detailed characterization of the entire PDTC phase diagram, rigidity and lifetime, informing on the role of prethermalization towards stabilizing the DTC response.
Check out our preprint arXiv:2201.02162