Quantum Cellular Automata on a Dual-Species Rydberg Processor

TL;DR

This work realizes quantum cellular automata on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform a myriad of quantum protocols.

Abstract

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. We realize QCAs on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform a myriad of quantum protocols. With simple pulse sequences, we explore many-body dynamics and generate a variety of entangled states, including GHZ states, 96.7(1.7)%-fidelity Bell states, 17-qubit cluster states, and high-connectivity graph states. The versatility and scalability of QCAs offers compelling routes for scaling quantum information systems with global controls, as well as new perspectives on quantum many-body dynamics.

Figures (5)

• Figure 1: Dual-species quantum cellular automaton.(A) Classical cellular automata repeatedly apply an update rule to a grid of "cells", leading to complex dynamics from simple initial states. (B) Replacing the classical cells and update rules with qubits and unitary steps (e.g. controlled qubit rotations) yields a quantum cellular automaton (QCA). These unitary steps can be applied by global controls, facilitating simple manipulation of complex quantum systems from a separable initial state. (C) Averaged fluorescence image of our rubidium (blue) and cesium (yellow) Rydberg qubit array, which is used to implement QCAs. Unitary operations are applied via global lasers, and AOD tweezers (red) are used to control initialization. (D, E) Rabi oscillations between the ground and excited states (blue/yellow data) are driven by species-selective lasers. Presence of a neighboring atom in the Rydberg state induces a blockade effect, preventing excitation of the driven atom (gray data). Solid lines are fits to damped cosines. (F) Spectroscopy of the Rydberg transition reveals that the free-space resonance frequency (yellow data) can be strongly shifted using AOD tweezers (red data), shielding selected atoms during initialization. Solid lines are fits to Lorentzians. (G) Applying alternating Rb/Cs $\pi$-pulses on the 35-qubit array implements the PXP automaton. Tracking the Rydberg state population over time, we observe a periodic "vacuum orbit", where at each time step at most one species is excited.
• Figure 2: Quasiparticles in the PXP QCA.(A) A domain wall state is initialized and then evolved under global PXP unitary steps. (B) By identifying the position of the domain wall in each shot of the experiment, we build a quasiparticle position histogram for each time step, revealing its linear motion and reflection. Initializing states with more domain walls, we further observe the dynamics of (C) two- and (D) three-quasiparticle configurations. When two quasiparticles collide (red squares), there is an interaction which modifies their trajectory. (E) By over- or under-rotating our global $\pi$-pulses, we deviate from the integrable regime of the PXP automaton. For a 15-atom chain initialized in $\ket{0}$, increasing the deviation from $\pi$ results in an increasingly fast saturation of the quasiparticle number. Exponential fits are a guide to the eye. (F) Looking at a single time step (6 $\pi$-pulses) on a 35-atom array, we see the quasiparticle number distribution shifts further upwards as the rotation angle deviates from $\pi$. We note a small horizontal shift, which we attribute to a slight miscalibration of the pulses.
• Figure 3: Growing GHZ states with the PXP QCA.(A) When a single qubit is initialized in a superposition state (here, $\ket{+}=(\ket{0}+\ket{1})/\sqrt{2}$), applying PXP unitary steps causes the superposition to spread out across the array, growing a GHZ state. (B) GHZ state fidelity is probed at each time step using population (top) and parity (bottom) measurements, shown here for time steps 2 (left, Rb) and 6 (right, Cs). Solid lines are fits to cosines. (C) Plotting the GHZ state fidelity versus number of pulses, we verify entanglement over many time steps, up to a size of 4 single-species qubits (solid bars) or 5 dual-species qubits (striped bars).
• Figure 4: Bell and Cluster states.(A) Applying a $2\pi$-pulse to one species (here Rb) leaves all computational states unchanged, but provides a phase depending on the state of neighboring atoms. This effects a CZ gate on the Cs atoms, and the Rb atom(s) can be traced out. (B) With two Cs atoms in the $\ket{+}$ state, a $2\pi$ pulse on a central Rb atom creates the Bell state $(\ket{1+}-\ket{0-})/\sqrt{2}$. Population (top) and coherence (bottom) measurements indicate a Bell state fidelity of 96.7(1.7)%. Solid line is a fit to a model function parametrized by realistic error sources supp. (C) Using the same sequence on a 33-atom chain generates a 17-qubit 1D cluster state. Pauli stabilizer measurements on the Cs atoms verify entanglement across any cut of the Cs chain toth2005entanglement.
• Figure 5: Graph State QCA.(A) Starting with a chain of 5 Cs and 4 Rb atoms in the ground state, applying multiple Graph State unitary steps builds and unbuilds complex entanglement on Cs. These states are equivalent to graph states under single-qubit transformations of some qubits, indicated with dashed outlines. (B) Expectation values for Pauli string operators in the Graph State QCA. For each pair of bars, the lower bar's Pauli string is indicated on the left axis, where $R$ is any unit-length combination of Pauli $X$ and $Y$supp; the upper bar is the same string under the replacement $R\leftrightarrow Z$. Outlined bars are experimental results, yellow bars are analytic ideal values. (C)$U$- and (D)$D$-operators are a subset of the aforementioned Pauli strings, corresponding to upward-moving and downward-moving gliders.