Quantum computing with atomic qubit arrays: confronting the cost of connectivity

TL;DR

The paper analyzes connectivity challenges in quantum computing with neutral-atom qubit arrays, contrasting long-range Rydberg gates and atom-transport approaches as routes to scalable entanglement. It evaluates three architectural strategies—long-range interactions, transport-based connectivity, and lattice surgery—for implementing logical operations, highlighting timing, range, and measurement bottlenecks, and discusses the promise of two-species architectures for fast mid-circuit measurements. A key takeaway is that achieving fault-tolerant scale will hinge on markedly improving gate fidelity, mitigating motional heating and leakage, and enabling rapid, high-fidelity mid-circuit measurements and cooling; while HP-NISQ progress may push practical devices sooner, FTQC will require large, robust, and highly interconnected hardware, potentially aided by alternative codes such as $q$LDPC$. The work provides a framework to compare connectivity modalities on realistic timescales and shapes hardware roadmaps for scalable neutral-atom quantum processors.

Abstract

These notes present a review of the status of quantum computing with arrays of neutral atom qubits, an approach which has demonstrated remarkable progress in the last few years. Scaling digital quantum computing to qubit counts and control fidelities that will enable solving outstanding scientific questions, and provide commercial value, is an outstanding challenge, not least because of the requirement of connecting and entangling distant qubits. Long-range Rydberg gates and physical motion outfit atomic qubit arrays with tools for establishing connectivity. These tools operate on different timescales and with distinct levels of parallelization. We analyze several prototypical architectures from the perspective of achieving fast connectivity for circuits with large scale entanglement, as well as fast cycle times for measurement based quantum error correcting codes. Extending Rydberg interactions to multiple atomic species has emerged as a promising route to achieving this latter requirement.

Figures (9)

• Figure 1: A bifurcated scenario for the development of quantum computers beyond the current NISQ era. High performance NISQ (HP-NISQ) for beyond classical capabilities requires moderate increases in qubit count and a substantial increase in gate fidelity. Quantum error correction and Fault Tolerant Quantum Computing(FTQC) will require orders of magnitude more qubits and a moderate increase in gate fidelity.
• Figure 2: Contour plot of $\log_{10}(\log_{10}(C)),$ the double logarithm of the classical calculational cost as a function of number of qubits and gate infidelity.
• Figure 3: Representative measurements of neutral atom qubit states in free space reported in the literature. The results are quantified in terms of the measurement time and the generalized fidelity given by the state detection fidelity $F$ times the atom retention probability $1-P_{\rm loss}$ . The experiments a,b,g,h with the shortest integration times used single photon counting detectors and all others used cameras: a Fuhrmanek2011, b Gibbons2011, c Kwon2017, d Martinez-Dorantes2017, e TYWu2019, f Covey2019a, g Shea2020, h Chow2023, i Huie2023, j Lis2023, k Norcia2024, l RTao2024, m SMa2023, n Scott2025.
• Figure 4: Experimental results for Rydberg $\sf CZ$ gate fidelity. The atomic species are Rb (red circles), Cs (blue squares), Sr (purple triangles), Yb (green diamonds). References: a Wilk2010, b Isenhower2010, c Zhang2010, d Maller2015, e Jau2016, f YZeng2017, g Levine2018, h Picken2019, i Levine2019, j Graham2019, k Madjarov2020, l Graham2022, m ZFu2022, n Schine2022, o Evered2023, p SMa2023, q King2024, r Radnaev2025, s Finkelstein2024, t ACao2024, u Muniz2025, v MChow2024, w Peper2025, x Chinnarasu2025, y Tsai2025.
• Figure 5: Generic Rydberg gate based on excitation of two atoms in a ground state $|1\rangle$ to Rydberg states that interact with energy $V$ and decay to other states with lifetime $\tau_{\rm R}$. The time dependent Rydberg excitation pulses $\Omega_1(t), \Omega_2(t)$ need not be the same for the two atoms.