Universal Dynamics with Globally Controlled Analog Quantum Simulators

Abstract

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems realize universal quantum dynamics under global control? Here we establish a necessary and sufficient condition for universal quantum computation using only global pulse control, proving that a broad class of analog quantum simulators is, in fact, universal. We further extend this framework to fermionic and bosonic systems, including modern platforms such as ultracold atoms in optical superlattices. Moreover, we observe that analog simulators driven by random global pulses exhibit information scrambling comparable to random unitary circuits. In a dual-species neutral-atom array setup, the measurement outcomes anti-concentrate on a $\log N$ timescale despite the presence of only temporal randomness, opening opportunities for efficient randomness generation. To bridge theoretical possibility with experimental reality, we introduce \emph{direct quantum optimal control}, a control framework that enables the synthesis of complex effective Hamiltonians while incorporating realistic hardware constraints. Using this approach, we experimentally engineer three-body interactions outside the blockade regime and demonstrate topological dynamics on a Rydberg-atom array. Experimental measurements reveal dynamical signatures of symmetry-protected-topological edge modes, confirming both the expressivity and feasibility of our method. Our work opens a new avenue for quantum simulation beyond native hardware Hamiltonians, enabling the engineering of effective multi-body interactions and advancing the frontier of quantum information processing with globally-controlled analog platforms.

Figures (14)

• Figure 1: Expressivity of globally controlled analog quantum simulators. (a) An analog quantum system driven by uniform global control fields (red) together with an additional symmetry-breaking field (green) that breaks reflection symmetry. Any global field that violates this symmetry suffices. Here we illustrate this with a green field applied only to the right half of the system. We prove that the presence of such a symmetry-breaking control is both necessary and sufficient for universal quantum computation. The symmetry-breaking Hamiltonian $H_{\mathrm{break}}$ only needs to satisfy $R H_{\mathrm{break}} R^{-1} \neq H_{\mathrm{break}}$, where $R$ denotes the reflection operator. (b) Schematic illustration of the proof strategy based on group representation theory. Uniform global controls enable near-independent control of local fields and interactions, up to a residual reflection symmetry that couples qubits at mirrored positions (e.g., the first and last sites). Using representation theory, we show that any additional symmetry-breaking control suffices to lift this constraint and complete the controllable space.
• Figure 2: Information scrambling in globally driven quantum systems. (a) Dual-species neutral-atom array driven by spatially uniform and temporally random global pulses, and illustration of the rescaled output probability distribution $D p(z)$, where $D$ is the Hilbert space dimension. A uniform distribution yields a delta peak at $D p(z)=1$, while random Haar states follow the Porter–Thomas distribution, corresponding to an anti-concentrated output. In contrast, non-anti-concentrated distributions exhibit long tails, indicating enhanced probabilities for specific outcomes. (b) Histograms of rescaled output probabilities for a dual-species atom array with interatomic spacing $d = 8.9~\mu\mathrm{m}$ under random global pulses. As the evolution time increases, the distribution transitions from non-anti-concentrated to anti-concentrated. See \ref{['app:scrambling']} for details. (c) Relative error of the averaged collision probability $\mathcal{Z}$ with respect to Haar-random states for different system sizes. (d) Defining the characteristic anti-concentration time $T^*$ by a relative error threshold $\epsilon = 5\%$, we observe a logarithmic scaling $T^* \propto \log N$.
• Figure 3: Experimental realization of symmetry-protected topological dynamics using optimal control. (a) Symmetry-protected topological Hamiltonian. A pair of decoupled Kitaev chains, which host topological edge modes, can be mapped to a qubit model with three-body interactions known as the cluster-Ising model. Due to experimental constraints, only measurements in the Z-basis are available. A key dynamical signature distinguishing boundary from bulk qubits is that the Z expectation values of the boundary qubits remain unchanged under evolution with the ZXZ Hamiltonian. (b) Schematic of the experimental setup. Rydberg atom arrays are globally driven by time-dependent Rabi frequency $\Omega(t)$ and detuning $\Delta(t)$. Atoms are spaced beyond the blockade radius $R_b$blockade, resulting in position fluctuations due to residual atomic temperature. Optimal quantum control is employed to design global pulses that mitigate errors and also satisfies machine constraints. (c) Overview of optimal control pulses used in the experiments. Time-dependent control waveforms $\Omega(t)$ and $\Delta(t)$ are engineered to simulate the effective SPT Hamiltonian. Constraints such as maximum slew rate, amplitude bounds, and finite time resolution are incorporated in the control optimization.
• Figure 4: Comparison between direct and indirect quantum optimal control methods. (a) Schematic illustration of indirect v.s. direct quantum optimal control. The indirect method (left) optimizes only the control pulses $\mathbf{u}_k$, with intermediate states $x_k$ determined solely by the Schrödinger equation. In contrast, the direct method (right) simultaneously optimizes both the control pulses and intermediate states, treating the Schrödinger equation as a constraint — allowing traversal of unphysical regions during optimization (visualized as discrete jumps in state space). Therefore, they explore different loss landscape during optimization as shown in the lower panel. (b) Comparison of final unitary fidelities achieved by GRAPE (indirect) and the direct method, targeting a effective evolution time $\tau/J_{\text{eff}}=0.8$ under realistic machine constraints. GRAPE results are shown for three regularization strengths $r$ that penalize the second derivative to impose pulse smoothness. For each $r$, 100 GRAPE runs with random initializations are shown as violin plots; the thick bar marks the interquartile range and the white marker indicates the median. Two smooth pulse control obtained from the direct method (Pulse 1 with $T=1.2\mu\mathrm{s}$ and Pulse 2 with $T=3.6\mu \mathrm{s}$) are marked for comparison. (c) Typical examples of optimized pulses for Rabi frequency $\Omega(t)$ (MHz) and detuning $\Delta(t)$ (MHz) using GRAPE and the direct method (Pulse 1).
• Figure 5: Characterizing noise in experiment using time-resolved Rydberg density. (a) Control pulses ($\Omega(t)$ and $\Delta (t)$) obtained from the direct method (Pulse 2) targeting effective evolution time $\tau/J_{\text{eff}}=0.8$. (b) $\langle Z_i \rangle = 1 - 2\langle n_i \rangle$ measured at the end of the pulse sequence for a three-atom chain initially prepared in the ground state. While the ideal unitary evolution predicts two peaks at atom 1 and atom 3, experimental results (red) deviate from the ideal simulation (blue), indicating the presence of noise. (c) Time-resolved scan of ($\langle Z_i \rangle$) for all three atoms during pulse application. Six separated three-atom clusters were measured in experiments in parallel (light to dark blue). Black stars indicate noiseless simulation results, and red stars represent noisy simulations incorporating Rydberg decay (incoherent error) and drifts in $\Omega(t)$ and $\Delta(t)$ (coherent error). The apparent deviation for $t>1.5\mu \mathrm{s}$ from ideal dynamics highlights the impact of realistic experimental imperfections. Each experiment consists of 1000 measurement shots, and the size of the experimental error bars (standard deviation) is smaller than that of the markers.

Theorems & Definitions (67)

• Theorem 1: Minimal requirement for universal quantum computation on a qubit chain
• Definition 1: Dynamical Lie Algebra
• Remark 1
• Definition 2: The Baker-Campbell-Hausdoff formula
• Definition 3: Dynamical Lie Algebra
• Definition 4: Repertoire of unitary dynamics deutsch
• Lemma 2
• proof
• Lemma 3
• proof