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Quantum Cellular Automata on a Dual-Species Rydberg Processor
Ryan White, Vikram Ramesh, Alexander Impertro, Shraddha Anand, Francesco Cesa, Giuliano Giudici, Thomas Iadecola, Hannes Pichler, Hannes Bernien
TL;DR
Scaling coherent control is a challenge for large quantum devices, motivating QCAs that use global operations on static, locally interacting arrays. This work realizes dual-species Rydberg QCAs, demonstrating quasiparticle dynamics, GHZ growth, and mediated entanglement, including 96.7(1.7)%-fidelity Bell states and a 17-qubit cluster state. The experiments show that a small set of global controls supports varied many-body and quantum-information protocols, while the demonstrated system remains one-dimensional and faces interaction and coherence limitations.
Problem
Scaling coherent control for large quantum devices is difficult, motivating globally controlled protocols that retain universal dynamics with locally interacting qubits.
Method
The authors implement dual-species QCAs on alternating rubidium–cesium Rydberg arrays, using independent global species control, blockade interactions, and a mediated entangling gate.
Results
96.7(1.7)% Bell-state fidelity was achieved, alongside a 17-qubit cluster state and quasiparticle, GHZ, and graph-state protocols.
Takeaways & Limitations
A minimal set of global controls supports diverse QCA protocols spanning many-body dynamics and quantum-state generation.
Takeaways & Limitations
The experiments use one-dimensional atomic chains, and high-fidelity gates are limited by finite interactions, residual interactions, and phase noise.
Abstract
from arXiv · showhide
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem: universal dynamics can be achieved using only a static qubit array and global control operations. Despite an extensive history of theoretical explorations and proposals, QCAs have not been experimentally explored in the context of highly-scalable globally-controlled systems. Here we realize QCAs on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform multiple quantum protocols. Seeding an automaton with different initial states, we explore many-body dynamics of quasiparticles and grow GHZ states across both species, highlighting the flexibility of our approach. We further develop a second automaton using a novel mediated entangling gate, enabling generation of 96.7(1.7)%-fidelity Bell states, 17-qubit cluster states, and high-connectivity graph states. Our results demonstrate that simple global controls enable access to a rich variety of applications through the QCA framework. The versatility and scalability of QCAs present compelling opportunities for the development of quantum information systems, as well as new perspectives on quantum many-body dynamics.
INTRODUCTION
Quantum cellular automata use repeated local unitary updates implemented through global controls, offering a route to complex dynamics without individually controlling every qubit. This work realizes that framework on a dual-species Rydberg array and implements a PXP automaton with blockade-mediated, species-alternating updates.
- Motivation: Global controls applied to locally interacting qubits are proposed to limit control complexity as scalable quantum devices grow.QCAs are one framework for such globally controlled protocols.
- Dual-species platform: The experiment implements QCAs on alternating rubidium and cesium arrays of up to 35 neutral-atom qubits.Independent species addressability and nearest-neighbor Rydberg blockade support the protocols.
- Dual-species platform: Species-selective global lasers drive Rabi oscillations, while neighboring Rydberg excitations produce blockade that prevents resonant excitation.AOD light shifts can detune selected atoms for initialization or basis-selective measurement.
- PXP automaton: Alternating Rb/Cs π-pulses implement a discretized PXP automaton because blockade makes each species’ flip conditional on neighboring qubit states.The unitary uses Pauli X operations projected by neighboring ground-state projectors.
- PXP automaton: Starting from the ground-state vacuum, the automaton alternately excites Rb and Cs configurations, producing a periodic vacuum orbit.The observed cycle repeats every six π-pulses and is associated with nonthermal eigenstates of the driven system.
QUASIPARTICLES IN THE PXP AUTOMATON
The PXP QCA uses initialized domain walls and superposition seeds to probe quasiparticle motion, interactions, non-integrable behavior, and entanglement growth. Its dynamics reveal moving and reflecting quasiparticles, collision-dependent trajectories, tunable quasiparticle proliferation, and GHZ states spanning one or both species.
- Quasiparticle dynamics: A domain wall moves across the array with fixed velocity and reflects, providing a quasiparticle whose position can be tracked over time.Multiple domain walls enable measurements of two- and three-quasiparticle dynamics.
- Quasiparticle dynamics: When quasiparticles collide, their trajectory changes: motion takes two π-pulses after collision instead of three for independent quasiparticles.This difference directly identifies an interaction between the quasiparticles.
- Quasiparticle dynamics: As rotation angles deviate from π, quasiparticles proliferate more rapidly and their number distribution shifts upward, indicating tunable departure from the integrable PXP regime.The shift is minimized near π, where the ideal PXP automaton is recovered.
- GHZ-state growth: GHZ entanglement is verified over multiple time steps, reaching 4 single-species qubits and 5 dual-species qubits.At dual-species steps, fidelity is estimated using later-time parity measurements because direct parity readout is obstructed.
- GHZ-state growth: A superposition seed spreads across the array under PXP steps, growing a GHZ state whose light cone reflects superposed vacuum and two-quasiparticle evolutions.Population probabilities near 50% provide the expected light-cone signature.
MEDIATED GATE AND CLUSTER STATES
A mediated Rb gate bypasses Cs blockade constraints by implementing pairwise CZ operations, enabling Bell and cluster-state preparation and a Graph State QCA with propagating entanglement.
- Mediated gate: The mediated 2π-pulse returns Rb to |0⟩ while applying a blockade-dependent phase, implementing an effective CZ gate between neighboring Cs atoms.This lets the Rb atoms serve as auxiliary qubits while the Cs data qubits remain outside one another’s blockade radius.
- Bell and cluster states: 96.7(1.7)% Bell-state fidelity was measured on Cs atoms prepared through an Rb-mediated gate.Population and coherence measurements were combined after flagging and SPAM correction.
- Bell and cluster states: A 33-atom alternating chain generated a 17-qubit Cs cluster state, with every measured stabilizer exceeding 0.5 and mean value 0.80(1).ZXZ and XZX stabilizer measurements verified entanglement across the Cs chain.
- Graph State QCA: The Graph State QCA alternates global Cs π/2 rotations with parallel Rb-mediated CZ gates, building longer-range entanglement before unwinding it.A single step is equivalent to the Bell/cluster preparation sequence.
- Graph State QCA: The Graph State QCA produces entanglement structures equivalent to graph states under single-qubit transformations.The protocol is named for this state-generation property.
- Graph State QCA: Measured Pauli-string expectations identify coherence across multiple steps, while U- and D-gliders translate in opposite directions through the array.The glider operators correspond to localized information-carrying structures under the automaton dynamics.
DISCUSSION AND OUTLOOK
The dual-species Rydberg platform supports scalable QCA implementations with global controls, quasiparticle dynamics, multipartite entanglement, and localized-glider propagation. The demonstrated protocols are currently restricted to one-dimensional chains, although the authors describe extensions to two-dimensional arrays and longer coherence times.
- Discussion: The platform combines neutral-atom scalability, globally addressed Rydberg interactions, and independent control of two species to implement QCAs.These capabilities support multiple QCA protocols using global controls.
- Discussion: The PXP automaton probes quasiparticle many-body dynamics and generates multi-qubit GHZ states, while the mediated gate produces Bell and 17-qubit cluster states.The mediated gate also enables the Graph State QCA, which generates and propagates localized gliders.
- Outlook: The experiments are restricted to one-dimensional chains, with proposed extensions to two-dimensional arrays through new trapping geometries and reshaped uniform laser beams.The authors also identify improved intensity stability, pulse control, and hyperfine clock qubits as routes to longer coherence.
1. Experimental platform
The experiment uses alternating Rb–Cs chains in independently controlled optical tweezers, dual-species rearrangement, blockade-mediated interactions, selective Stark-shift addressing, and stabilized Rydberg lasers.
- Dual-species trapping and rearrangement: The dual-species array uses Rb and Cs atoms in optical tweezers, with 5.3 µm spacing and additional loading columns for rearrangement.The two species are trapped with separate SLMs and arranged in a single experimental column.
- Dual-species trapping and rearrangement: The rearrangement procedure fills empty rows and the central column, removes excess atoms when needed, and repeats correction rounds before experiments.Data are retained only after final fluorescence imaging verifies successful rearrangement.
- Dual-species trapping and rearrangement: Per-atom rearrangement succeeds with probabilities of 94% for Rb and 92% for Cs.Large arrays can still have low acquisition rates, so SPAM correction is used instead of loading-based selection in one dataset.
- Rydberg control: The chosen stretched states and magnetic field simplify optical pumping and Rydberg excitation while enabling state isolation through Zeeman splittings.Rydberg transitions are described as insensitive to the magnetic field for the selected states.
- Rydberg control: The van der Waals interaction gives a next-nearest-neighbor ratio V_NNN/V_NN ≈ 1/26 = 1.6%, supporting the blockade condition V_NN ≫ Ω ≫ V_NNN, V_NNNN.The shorter interaction range helps suppress longer-range effects relative to nearest-neighbor blockade.
- Rydberg laser frequency noise measurements: All four Rydberg lasers are locked to one ULE cavity, with frequency-noise power spectral density mostly below 10^4 Hz^2/Hz except for resonant peaks and the noisier 420 nm laser.The laser noise was characterized with fiber-based Mach–Zehnder interferometers and a 10 m delay line.
- AOD light shifts: AOD-generated AC Stark shifts selectively detune Cs atoms, achieving a mean shift of 35 MHz and uniformization within 3% standard deviation.The shift exceeds approximately 11Ω, suppressing Rydberg excitation at targeted sites.
2. Simulations
The simulations model the dual-species dynamics with quantum trajectories on systems of up to 11 atoms, representing each atom as a three-level system. For the 17-site cluster state, tensor-network methods are used because exact simulation is out of reach.
- Quantum-trajectory simulations: Quantum trajectories simulate systems of up to 11 atoms, including 6 Rb and 5 Cs atoms.Each atom is modeled with |0⟩, |e⟩, and |1⟩ levels, with |e⟩ as the intermediate excitation state.
- Quantum-trajectory simulations: The trajectory dynamics include intermediate-state scattering, Rydberg decay, laser phase noise, position fluctuations, and intensity fluctuations.
- Cluster-state simulations: Tensor-network methods model the 17-site cluster state with three levels per atom and no noise.Remaining deviations from an ideal cluster state arise from finite blockade strength, next-nearest-neighbor interactions, and finite intermediate-state detuning.
3. PXP QCA, quasiparticles
The PXP automaton is implemented as alternating species-selective Floquet pulses and exhibits a period-3 cycle under ideal nearest-neighbor interactions. Van der Waals interactions cause leakage from this cycle, while quasiparticles are identified from local bitstring patterns and interact during collisions.
- Automaton dynamics: A Floquet step consists of alternating even- and odd-site pulses, and the ideal PXP automaton repeats every 3 Floquet steps.
- Quasiparticle identification: Domain-wall quasiparticles are detected using mutually exclusive four-qubit bitstrings 0001, 1000, and 1001.At chain edges, three-qubit identifiers 001 and 100 identify the two edge quasiparticle types.
- Measurement caveat: Quasiparticle-number estimates at multiple-of-three time steps are omitted because atom loss can make nominal vacuum states appear as two-particle states.
4. GHZ states
The PXP automaton generates GHZ states from seeded superpositions, with fidelity measured through populations and parity. Dual-species GHZ steps require a conservative lower-bound estimate because blockade prevents direct parity measurement.
- GHZ-state generation: GHZ states arise when the PXP automaton spreads an initial |+⟩ seed across the array.
- Fidelity measurement: GHZ fidelity is measured using population terms and parity B(ϕ)=⟨R⊗N(ϕ)⟩, with R(ϕ)=cos(ϕ)X+sin(ϕ)Y.The parity sweep is fit to a cosine to estimate the generalized GHZ fidelity.
- Dual-species GHZ states: At time steps 1, 4, and 7, the dual-species GHZ state has the form |010⟩+|101⟩ rather than |000⟩+|111⟩.
- Dual-species GHZ states: Because blockade obstructs parity measurement for dual-species states, later-time-step parity provides a conservative lower-bound estimate.The estimate assumes that additional pulses do not increase state coherence and is compared with numerical simulations.
- Comparison with simulations: Experimental fidelities decay on a timescale similar to simulations, although simulations consistently predict higher fidelities.This discrepancy suggests additional uncaptured noise or small detuning errors.
5. Mediated gate
A mediated gate uses an auxiliary atom to entangle two data atoms while returning the auxiliary to |0⟩. The optimized protocol supports Bell-state preparation and parallel nearest-neighbor CZ layers for cluster-state generation, with complete stabilizer measurements of a 17-atom cluster state.
- Mediated-gate protocol: A mediated gate entangles two data atoms through an auxiliary initialized in |0⟩, which returns deterministically to |0⟩.
- Mediated-gate protocol: In the ideal blockade regime, a 2π auxiliary pulse produces a conditional phase and implements a CZ gate on the data atoms.
- Mediated-gate protocol: Finite interspecies and intraspecies interactions, together with systemic phase noise, limit the fidelity of the simplest mediated-gate protocol.The authors incorporate an echo technique to cancel these effects.
- Gate optimization: The optimized detuning is Δ≈1.25Ω, selected by minimizing |⟨Z1⟩⟨Z2⟩| after applying the gate to |++⟩.
- Cluster-state generation: Parallel mediated CZ gates between adjacent data qubits generate a one-dimensional cluster state, whose stabilizers can be measured in two basis settings.The stabilizers are Si=Zi−1XiZi+1, with modified boundary operators.
- Cluster-state verification: Complete stabilizer measurements of the 17-atom cluster state compare fitted cosine amplitudes with noiseless simulations.
6. Graph State Automaton
The Graph State Automaton combines global single-qubit rotations with mediated entangling operations to probe graph-state dynamics and benchmark stabilizer structure. Noisy simulations agree substantially better with measured operator values, although some contrast loss remains unexplained.
- Automaton design: The nominal automaton step applies a global Hadamard followed by global CZ gates between neighboring qubits.At the integrable Clifford point, the dynamics can be probed through Pauli measurements and mapped to free fermions.
- Experimental implementation: Experimentally, the step uses a global π/2 rotation and mediated entangling gate, with a π/2 laser-phase shift compensating edge–bulk asymmetry.Up to five steps are applied to arrays containing five Cs and four Rb atoms.
- Measurement: Stabilizer measurements sweep α to identify Pauli strings whose readout reaches unit expectation at the appropriate rotation.Unlisted operators and those marked N/A are not predicted to vary with α.
- Comparison with simulation: Noisy simulations agree significantly better with experimental graph-state operator values than ideal analytic predictions, though some contrast loss remains unaccounted for.The comparison uses the maximum absolute fit value or the absolute mean when the operator varies with α.
7. Correction of state preparation and measurement (SPAM) errors
The experiment calibrates preparation, detection, imaging, and recapture errors, then uses a linear SPAM error model to infer the underlying probability distribution. These corrections are applied to assess implemented operations more faithfully.
- Calibration scope: SPAM calibration covers state preparation, readout, imaging discrimination, imaging survival, and atom recapture after the sequence.The resulting parameters are summarized in Extended Data Table 3 and used throughout the manuscript.
- State preparation: Optical pumping prepares Rb and Cs in their respective ground states with fidelities of 99.43(5)% and 99.03(5)%, respectively.The fidelities are obtained from measured pumping and depumping time constants.
- Imaging discrimination: Imaging discrimination errors arise from overlap between occupied and empty-tweezer fluorescence distributions, producing false-positive and false-negative rates.These rates are extracted directly from the overlap area relative to the total distribution area.
- Imaging survival and recapture: Thermal motion during trap-off evolution causes drop-time-dependent recapture loss, while finite vacuum lifetime produces baseline loss even at zero drop time.For a two-atom Bell-state measurement, t_drop = 1.5 µs was used, limiting ground-state detection fidelity to 95.9(3)% for Cs.