Quantum simulation with cold atoms and superconducting qubits

 Two interesting preprints on quantum simulation appeared on arXiv today:

1. Thermalization dynamics of a gauge theory on a quantum simulator, by the USTC team and collaborators. This experiment uses a 71-site optical lattice for cold atoms to simulate the quench dynamics of a one-dimensional U(1) gauge theory. I am not very familiar with U(1) gauge theory and found this paper an informative introduction to the topic, by translating it to the more familiar setting of the Bose-Hubbard model. Basically, the study considers a 1D lattice comprising two detuned sublattices. In the limit where the inter-site hopping is much weaker than the detuning, and the local atom-atom interaction is resonant with the detuning, one can obtain an effective Hamiltonian with a hopping interaction term. Single particle hopping between the two sublattices is forbidden and only pairwise hopping can occur. In the limit of strong interactions, the dynamics becomes constrained to a subset of the full Hilbert space: the deeper sublattice can only be occupied by either 0 or 2 particles, while the shallower sublattice can be occupied by only 0 or 1 particles. This realizes an analogy with U(1) gauge theory by labelling the shallower sublattice as the "matter" field, and the deeper sublattice as the "gauge" field. The experiments then study thermalization in this model when an initial state with uniform "matter" density is quenched. Thus, the dynamics of the Bose-Hubbard model in complex lattices can be mapped onto more exotic gauge fields. It will be interesting to consider this direction further, and whether similar ideas can be realized in photonic lattices with weak and/or mean-field interactions.

2. Observation of Time-Crystalline Eigenstate Order on a Quantum Processor, by the Google AI team and collaborators. This work studies time-crystalline order, which was previously observed using other platforms. Quantum processors are natural for studying periodically-driven phases such as these, owning to description of their dynamics in terms of sequences of Floquet operators. The main innovation in this work appears to be the introduction of continuously-tunable two-qubit CPhase gates, which enables the implementation of strong tunable disorder in an effective Ising interaction between neighbouring qubits. The other two terms comprising the periodic driving are simple single qubit rotations. Using the flexible tunability of their quantum processor, the authors are able to study the stability of the time crystalline order with respect to changes in the system parameters, scaling with the system size (considering a linear chain of up to 20 qubits), and the properties of the entire spectrum of the system.