Engineering discrete local dynamics in globally driven dual-species atom arrays

TL;DR

The paper develops a framework to realize discrete local dynamics as Quantum Cellular Automata in globally driven dual-species Rydberg arrays, enabling translation-invariant, discretized updates on static lattice layouts. By introducing mediated gates and decorated gadgets, it implements a broad class of QCAs—including the kicked-Ising model, Floquet Kitaev honeycomb, and digitizations of arbitrary 2-local Hamiltonians—using only global drives and smart layout design, with time- and space-overhead that scale linearly. It also proposes a practical chaos-detection protocol based on a coarse-grained observable g^O(t) that can be measured with minimal experimental resources, enabling near-term exploration of chaotic versus non-ergodic quantum dynamics in large atom arrays. The approach combines quantum control, Floquet engineering, and QCA concepts to significantly simplify experimental requirements while opening a path to study non-equilibrium many-body physics and quantum chaos in programmable, scalable platforms. These advances hold potential for probing complex dynamical phenomena in regimes difficult for classical computation, using near-term neutral-atom quantum simulators.

Abstract

We introduce a method for engineering discrete local dynamics in globally-driven dual-species neutral atom experiments, allowing us to study emergent digital models through uniform analog controls. Leveraging the new opportunities offered by dual-species systems, such as species-alternated driving, our construction exploits simple Floquet protocols on static atom arrangements, and benefits of generalized blockade regimes (different inter- and intra-species interactions). We focus on discrete dynamical models that are special examples of Quantum Cellular Automata (QCA), and explicitly consider a number of relevant examples, including the kicked-Ising model, the Floquet Kitaev honeycomb model, and the digitization of generic translation-invariant nearest-neighbor Hamiltonians (e.g., for Trotterized evolution). As an application, we study chaotic features of discretized many-body dynamics that can be detected by leveraging only demonstrated capabilities of globally-driven experiments, and benchmark their ability to discriminate chaotic evolution.

Figures (11)

• Figure 1: (a, b) For a model defined on a 2D lattice, we construct a sub-division graph, by inserting one new vertex (in yellow) on each edge of the original lattice. We then arrange a dual-species atom array by positioning atoms of the data (blue) and ancillary (yellow) species on the vertices and edges, respectively. The role of the ancillas is to mediate gates between the data atoms. The atom array is then driven in the (nearest-neighbor) Rydberg blockade regime through a global (species-selective) laser. (c) For each atom, we consider two levels: a ground state $\ket{g}$ and a highly excited Rydberg state $\ket{r}$. (d) Gadgets are constructed by placing $S\geq 1$ ancillas on a bond - i.e., between two data atoms. (e) We use optimal control methods to design mediated gates: by controlling the ancillary species, we effectively implement entangling gates on the data atoms. (f) The Floquet driving realizes a discrete local dynamics, where each step corresponds to the application of an update rule $\mathcal{U}$. The latter is said to be synchronous when the interacting updates can be simultaneously applied (i.e., if they commute). (g) Differently, $\mathcal{U}$ is said to be asynchronous if the local interacting updates do not commute - imposing an ordering.
• Figure 2: (a) Circuit depiction of our protocol, where we alternate driving on data and ancillary atoms. The first implements single-qubit gates on the data, while the second physically acts as controlled gates, with the data controlling the evolution of the ancillas - which always return back to $\ket{g}$. Our control knob is the phase profile $\xi(t)$ of the global laser. (b) Since the ancillas are always deterministically mapped back to $\ket{g}$, this effectively results in a circuit on the data only, with entangling gates mediated by the ancillas.
• Figure 3: (a) To implement mediated gates , we drive the ancillary species only, inducing a closed trajectory on the Bloch sphere. This trajectory is conditioned on both the neighboring data atoms being in $\ket{g}$: the geometrical phase $\phi$ is only acquired in this case. This results in an effective entangling gate on the data, as specified by the truth table. (b) Depiction of our circuit notation. Note that we use a diamond symbol to denote the special case where the mediated gate is an effective identity, i.e., $\phi = 2\pi n$ . (c) A cluster of $S$ atoms within a blockade radius behaves as a superatom, oscillating between two effective states $\ket{G_S}\leftrightarrow\ket{R_S}$ with enhanced Rabi frequency $\sqrt{S}\Omega$. (d) Optimal control techniques allow us to simultaneously implement mediated gates through gadgets of various sizes, imprinting arbitrary phases $\phi_S$ to superatoms of size $S$, in parallel.
• Figure 4: (a) For the kicked-Ising model, we alternate the application of single-atom rotations on the data species (implementing the kick term), and gadget pulses on the ancillary species, implementing the Ising layer via mediated gates. (b) For the digitization of an arbitrary $2-$local Hamiltonian, we proceed in three main steps, each operating in a different Pauli basis. (c) The Floquet Kitaev Honeycomb model is implemented by also employing decorated gadgets. (d) We use optimal control to derive time-optimal pulses for the mediated gates of the three steps of our implementation of the Floquet Kitaev honeycomb model. The figure shows the optimal durations $T_\text{min}$ as a function of the target phases $\phi_\alpha=-4\tau J_\alpha$, with $\alpha=X,Y,Z$. These values are shown for $\phi\in[0,\pi]$, holding $T_\text{min}(-\phi_\alpha)=T_\text{min}(\phi_\alpha)$. See Appendix \ref{['sec:optimal_control']} for further details on the numerical procedure.
• Figure 5: (a) A single-qubit $2-$design can be realized through four states $\mathcal{E}_T=\left\{\ket{\mu_1}, \ket{\mu_2}, \ket{\mu_3}, \ket{\mu_4}\right\}$ placed at the vertices of a tetrahedron in the Bloch sphere. (b) An optical tweezer can be used to shift the addressed atoms out of resonance by a detuning $\delta \gg \Omega$ (AC Stark shift). In this way, an atom initialized in $\ket{g}$ cannot be excited to $\ket{r}$ by the driving laser while addressed by the tweezer. (c) Our protocol to initialize the system in a randomly chosen state $\ket{\psi}\in\mathcal{E}_T^N$. The protocol begins by identifying $\ket{\psi}$ of Eq. \ref{['eq: coloring decomposition']} with a coloring of the lattice vertices, and initializing all the atoms in $\ket{g}$. Then, we proceed in four steps, wherein at step $k$ we use the global Rydberg laser to implement the unitary $V_k = U^\dag_{k+1}U_k$ uniformly on all the atoms, where $U_k\ket{g}=\ket{\mu_k}$. Crucially, during the steps we progressively turn off the tweezer light, such that more atoms are addressed. At the end of the protocol, each atom is prepared in the desired tetrahedron state, according to the initial coloring.