MAQCY: Modular Atom-Array Quantum Computing with Space-Time Hybrid Multiplexing

TL;DR

MAQCY introduces a modular neutral-atom quantum computing architecture that uses space-time hybrid multiplexing to achieve universal quantum computation with globally controlled operations on dual-species Rydberg atom arrays. Central to MAQCY is the Q-Pair, a dual-species unit whose data qubit can be a single atom or a superatom and whose auxiliary qubit enables coherent information flow under global pulses; space-time multiplexing via temporal translations $ ilde{\mathcal{T}}$ and SWAPs $\tilde{\mathcal{S}}$ provides all-to-all connectivity while allowing in-situ atom replacement. The protocol supports arbitrary single-qubit gates and two-qubit gates (CZ, CP, CX) through a set of global pulse sequences and a mobile interposer superatom, demonstrated by a three-qubit quantum Fourier transform realized with global operations and atom transport. The proposed dual-Yb platform ($^{171}\mathrm{Yb}$ data and $^{174}\mathrm{Yb}$ auxiliary) offers long coherence clock states and spectrally distinct Rydberg transitions, enabling scalable execution with potential mid-circuit erasure and memory-based error mitigation toward fault-tolerance. Overall, MAQCY achieves linear physical-qubit overhead, $O(N)$, in contrast to previous $O(N^2)$ schemes, and outlines a practical pathway to large-scale quantum computing using globally controlled, multiplexed neutral-atom arrays.

Abstract

We present a modular atom-array quantum computing architecture with space-time hybrid multiplexing (MAQCY), a dynamic optical tweezer-based protocol for fully connected and scalable universal quantum computation. By extending the concept of globally controlled static dual-species Rydberg atom wires [1], we develop an entirely new approach using Q-Pairs, which consist of globally controlled and temporally multiplexed dual-species Rydberg blockaded atom and superatom pairs. Space-time hybrid multiplexing of Q-Pairs achieves O(N) linear scaling in the number of required physical qubits, while preserving coherence and mitigating circuit-depth limitations through in-situ atom replacement. To demonstrate MAQCY's versatility, we implement a three-qubit quantum Fourier transform using only global operations and atom transport. We also propose a concrete implementation using ytterbium isotopes, paving the way toward large-scale, fault-tolerant quantum computing.

Figures (11)

• Figure 1: MAQCY; Modular atom-array quantum computing protocol with space-time hybrid multiplexing.(a) Space-time hybrid array of Q-Pairs. A Q-Pair consists of a dual-species atomic pair: a red circle (data qubit, species $A$) and a blue square (auxiliary qubit, species $B$). Local control is realized using a superatom$-$an ensemble of atoms$-$indicated by a star-shaped background. Each Q-Pair is encoded in a hybrid mode $(t_k, s_l)$ as $\left|\Psi(t_k, s_l)\right\rangle$. (b) Zoned architecture for experimental realization. All Q-Pairs are arranged in the interaction zone, where a driving laser couples ground and Rydberg states. The laser is applied only within this zone. Rydberg blockade mediates correlations within a blockade volume (indicated by a dotted circle). During temporal mode translation, $\tilde{\mathcal{T}}: t_k \rightarrow t_{k+1}$, atoms from the reservoirs replace those in the interaction zone. (c) Energy-level diagrams of the dual-species AEAs. The two atomic species are spectrally distinguishable, allowing global laser beams to address individual atoms in each Q-Pair. A superatom (e.g., with $N=4$ atoms) functions as an effective data qubit and serves as a local (target) data qubit in the MAQCY protocol. Additional details are provided in the main text.
• Figure 2: Temporal mode translation operator $\tilde{\mathcal{T}}_{1}$: single-atom to single-atom transfer.(a) Two successive pulses, $\hat{X}_{A}\hat{X}_{B}$, transfer quantum information from the data qubit (species $A$) to the auxiliary qubit (species $B$) under the Rydberg blockade condition. The replacement operation $\hat{D}_{A}$ removes the $A$ atom at temporal mode $t_{k}$ and loads a fresh $A$ atom at $t_{k+1}$. (Inset: Details of the atom replacement operation. The old data qubit is shuttled to the reservoir, while a new data qubit is delivered to the interaction zone to form the Q-Pair for the next temporal mode.) Iterating this sequence translates the temporal mode from $t_{k}$ to $t_{k+1}$. (b) The Rydberg blockade suppresses the doubly excited state $\left| r_{A} r_{B} \right\rangle$, enabling the $\hat{X}_{A}\hat{X}_{B}$ pulse pair to facilitate coherent information flow between the two atoms.
• Figure 3: Superatom-based single-qubit wire-gates$\vec{\mathcal{U}}_\nu = \tilde{\mathcal{T}}_\nu \bar{\bar{\mathcal{U}}}_A$, $\nu = 2, 3, 4$, with $\bar{\bar{\mathcal{U}}}_A = \bar{X}_A$. (a) For $\nu = 2$, $\bar{\bar{\mathcal{U}}}_A$ is applied to a single-atom $A$ in the Q-Pair at temporal mode $t_k$, and the atom at $t_{k+1}$ that replaces it is a ground-state superatom $A$, denoted by $\left|\bar{g}_A\right\rangle$. (b) For $\nu = 3$, $\bar{\bar{\mathcal{U}}}_A$ is applied to a superatom $A$ at $t_k$, and the atom at $t_{k+1}$ that replaces it is a ground-state single-atom $A$, denoted by $\left|g_A\right\rangle$. (c) For $\nu = 4$, $\bar{\bar{\mathcal{U}}}_A$ is applied to a superatom $A$ at $t_k$, and the atom at $t_{k+1}$ that replaces it is a ground-state superatom $A$, denoted by $\left|\bar{g}_A\right\rangle$. The temporal mode translation operators $\tilde{\mathcal{T}}_\nu$ in (a)-(c) are defined in Eq. (\ref{['EqTG']}).
• Figure 4: Two-qubit controlled-Z (CZ) gate implementation. The displacement operator $\bar{D}_B^{\rm in}$ inserts an auxiliary superatom $B$ between the two Q-Pairs. A global pulse sequence $\tilde{\mathcal{U}}_B$ mediates interactions between superatom $B$ and the data qubits of the Q-Pairs. Finally, the operator $\bar{D}_B^{\rm out}$ removes superatom $B$, leaving only the two Q-Pairs. (Inset) The global operation $\tilde{\mathcal{U}}_B$ assigns a relative phase of $\pi$ to both single-atom and superatom states of species $B$. Due to the Rydberg blockade, excitation is forbidden if both data qubits are in the Rydberg state $\left|r_A r_A\right\rangle$. This blockade induces a relative $\pi$ phase shift, thereby implementing the CZ gate.
• Figure 5: Two-qubit global CNOT wire-gate $\vec{\mathcal{CX}}^{(s_1,s_2)}_{1,3}$. (a) The CNOT gate is implemented by sandwiching a CZ gate between two Hadamard gates on the target qubit. This is realized using the global Hadamard gate $\bar{\bar{\mathcal{H}}}$ defined in Eq. (\ref{['EqHWG']}). (b) Experimental realization of the global CNOT wire-gate $\vec{\mathcal{CX}}^{(s_1,s_2)}_{1,3}$