Abigail R. Perry

Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

Quantum processors based on linear arrays of trapped ions have achieved exceptional performance, but scaling to large qubit numbers requires realizing two-dimensional ion arrays as envisioned in the quantum charge-coupled device (QCCD) architecture. Here we present a scalable method for the control of ion crystals in a grid-based surface-electrode Paul trap and characterize it in the context of transport operations that sort and reorder multispecies crystals. By combining cowiring of control electrodes at translationally symmetric locations in each grid site with the sitewise ability to exchange the voltages applied to two special electrodes gated by a binary input, site dependent operations can be achieved using only a fixed number of analog voltage signals and a single digital input per site. In two separate experimental systems containing nominally identical grid traps, one using $^{171}\mathrm{Yb}^{+}$-$^{138}\mathrm{Ba}^{+}$ crystals and the other $^{137}\mathrm{Ba}^{+}$-$^{88}\mathrm{Sr}^{+}$, we demonstrate this method by characterizing the conditional intrasite crystal reorder and the conditional exchange of ions between adjacent sites on the grid. Averaged across a multisite region of interest, we measure subquanta motional excitation in the axial in-phase and out-of-phase modes of the crystals following these operations at exchange rates of 2.5 kHz. In this initial demonstration, the logic controlling the voltage exchange occurs in software, but the applied signals mimic a proposed hardware implementation using crossover switches. These techniques can be further extended to implement other conditional operations in the QCCD architecture such as gates, initialization and measurement.

We report on the first demonstration of transport of a multispecies ion crystal through a junction in an RF Paul trap. The trap is a two-dimensional surface-electrode trap with an X junction and segmented control electrodes to which time-varying voltages are applied to control the shape and position of potential wells above the trap surface. We transport either a single $^{171}$Yb$^+$ ion or a crystal composed of a $^{138}$Ba$^+$ ion cotrapped with the $^{171}$Yb$^+$ ion to any port of the junction. We characterize the motional excitation by performing multiple round-trips through the junction and back to the initial well position without cooling. The final excitation is then measured using sideband asymmetry. For a single $^{171}$Yb$^+$ ion, transport with a $4\;\mathrm{m/s}$ average speed induces between $0.013\pm0.001$ and $0.014\pm0.001$ quanta of excitation per round trip, depending on the exit port. For a Ba-Yb crystal, transport at the same speed induces between $0.013\pm0.001$ and $0.030\pm0.002$ quanta per round trip of excitation to the axial center of mass mode. Excitation in the axial stretch mode ranges from $0.005\pm0.001$ to $0.021\pm0.001$ quanta per round trip.