Quantum error correction (QEC) [1,2] is essential for the realization of large-scale quantum computers [3,4]. However, due to the complexity of operating on the encoded ‘logical’ qubits [5,6], understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement the key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors [6,7], demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding [8,9]. We then investigate logical entanglement using transversal gates and lattice surgery [10–12], and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes [13,14], enabling arbitrary-angle synthesis with polylogarithmic overhead [5,15]. Finally, we develop mid-circuit qubit re-use [16], increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations [17–20] with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic & entropy removal, judiciously using physical entanglement in logic gates & magic state generation, and leveraging teleportations for universality & physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.
The power of quantum computation derives from algorithmic methods that exploit the availability of quantum superposition and entanglement to perform computations that are intractable with classical devices. The race is on to develop hardware that will unleash the promise of quantum algorithms. A handful of different types of hardware are currently being developed with the greatest efforts directed at superconducting, quantum-dot, trapped-ion, photonic, and neutral-atom approaches [1]. While all approaches have strengths and weaknesses, and are at different stages of development, the challenge of creating a practical design that can be scaled to a million or more qubits has not yet been met with any of the existing platforms. One may wonder if we really need a million qubits for a useful quantum computer. The answer depends on our ambition level. On the one hand it is widely believed that a quantum computer with less than 100 reliable qubits will be able to demonstrate a quantum advantage for a well defined computational problem [2]. Demonstration of a quantum computational advantage will generate great excitement in the halls of academia, but will have little broader import. A problem of great practical interest such as ab initio design of chemicals for increasing the yield of fertilizers for crop production, to name but one example, may also require just a few hundred qubits, provided computational sequences with circuit depth of 1010 or more operations can be reliably performed [3]. However, given the current performance of qubit hardware, which has demonstrated error rates not less than ∼10−3, computations with depth 1010 will only produce random outcomes of negligible value. The solution lies in the construction of error-correction circuitry operating on logical qubits, each composed of many physical qubits, which will enable logical error rates many orders of magnitude smaller than physical error rates. Although error correction is remarkably efficient for classical computing devices—Hamming codes detect and correct errors while only requiring roughly 10% overhead in the number of physical bits—quantum error correction is notoriously expensive. New approaches to error correction are the subject of intensive research with one promising direction being the development of codes that are optimized to suppress the dominant error mechanism in a particular physical platform [4,5]. Nevertheless, with physical error rates of 10−4, a plausible target for current qubit systems, the overhead required to reach logical error rates of 10−10 may be measured in thousands of physical qubits for each logical qubit. Thus a quantum computer able to perform deep calculations on a few hundred logical qubits could require a million physical qubits. A consequence of the cost of quantum error correction is that any viable approach to large-scale quantum computing needs to combine high-fidelity quantum logic operations with a capability for integrating large numbers of physical qubits. From this perspective neutral-atom qubits appear particularly promising [6] as they have already demonstrated control of more qubits than any other platform with recent experiments in 1D [7], 2D [8,9], and 3D [10] geometries showing control of up to 50 atomic qubits. Large qubit arrays can potentially be prepared in 1D, 2D, or 3D geometries. The number of proximal qubits increases with the dimensionality, which is advantageous for implementation of error correction code words, and points towards a preference for 2D or 3D arrays. On the other hand, the added overhead of compensating crosstalk incurred when targeting atoms inside a 3D volume makes parallel operations on multiple qubits challenging. A 2D geometry, as shown schematically in Fig. 1, may be an optimal choice since qubit control and measurement can be performed with lasers propagating normal to the plane of the array so that individual qubit sites can be addressed independently. With demonstrated array periods of a few micrometers we require a footprint of less than 1 mm2 for 104 qubits. Conceptual picture of a 2D neutral-atom qubit array. a) High-numerical-aperture lenses project several different wavelengths of light for control and measurement of the qubits. Specific choices of optical wavelengths depend on the atomic species. Not shown are optics for initial laser cooling, transport to the array, beam scanning, and imaging for qubit measurement. b) Averaged fluorescence image of 49 atomic qubits on a 2D grid with |
3.8μm| spacing [8]. From a fundamental perspective the prospects for scaling neutral-atom systems are particularly promising due to the exceptionally large ratio between coherent and incoherent coupling rates. Neutral-atom qubits are encoded in hyperfine ground states for which coherence times of the order of 10 s have been demonstrated [10]. This implies a dephasing rate |
γ∼0.1s−1|. The coherent coupling that enables quantum logic operations is switched on by exciting atoms to high-lying Rydberg states with principal quantum number close to 100 [11,12]. Rydberg excited atoms at spacings of a few micrometers in an optical lattice interact coherently with rates |
g>109s−1|. The ratio between desired coherent coupling and residual incoherent dephasing of g/γ ∼ 1010 establishes a figure of merit that is enabling for scalability. To our knowledge only trapped ions can claim a similar g/γ ratio [13], but without a correspondingly direct path towards controlling thousands of qubits in a single processing unit. Although the g/γ ratio is exceptionally favorable for neutral-atom qubits a complete set of universal gate operations has not yet been demonstrated with high fidelity. Single-qubit gates in large 2D and 3D arrays have reached fidelity |
F∼0.999| [8,10]. However, the highest demonstrated fidelity for two-qubit entanglement mediated by Rydberg-state interactions is |
F<0.8| [6,14,15], a value that is well short of the theoretical limit of |
F>0.9999| [16,17]. There is healthy optimism within the research community working with neutral-atom qubits that combining improved laser sources with reduced noise, better cooling to reduce motional dephasing, and control of stray electric fields that perturb Rydberg atoms will lead to substantially improved gate fidelity in the near future. Recent results with better filtering of laser phase noise have already demonstrated remarkable improvement in ground–Rydberg entanglement [18]. The outlook for the next few years appears very promising. We anticipate that with advances in lasers, optical lattices for atom trapping, deterministic rearrangement and loading of atoms in multi-dimensional arrays [19,20], and optics for fast beam scanning it will be possible to increase the number of physical qubits in a single neutral-atom module to at least 104. A challenging yet plausible path to a million-qubit processor can then be contemplated by connecting 100 such modules with atom–photon entanglement channels [21]. Beyond the potential for advancing the state of the art in computation, development of techniques for single-atom control inside large multi-atom arrays will enable other applications of quantum science including metrology and time-keeping. Rydberg interactions that are at the heart of a neutral-atom quantum computer may lead to multi-atom entanglement and Heisenberg scaling of atomic-clock precision [22]. This work was supported by the NSF and ARL CDQI.
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys could be broken using Shor's algorithm with fewer than a million noisy qubits. Although such machines do not yet exist, the availability of smaller, cloud-accessible quantum processors and open-source implementations of Shor's algorithm raises the question of what key sizes can realistically be factored with today's platforms. In this work, we experimentally investigate Shor's algorithm on several cloud-based quantum computers using publicly available implementations. Our results reveal a substantial gap between the capabilities of current quantum hardware and the requirements for factoring cryptographically relevant integers. In particular, we observe that circuit constructions still need to be highly specific for each modulus, and that machine fidelities are unstable, with high and fluctuating error rates.
Efficient quantum error correction and fault-tolerant quantum computing require scalable, high-fidelity long-range connectivity. In neutral-atom quantum computers, this is commonly achieved through atom transport, but shuttling introduces latency and motional heating that worsen with system size. Here, we introduce a neutral-atom architecture based on static atomic buses, in which auxiliary mediator atoms enable long-range entangling operations without qubit transport. The architecture naturally supports long-range stabilizer measurements in high-rate LDPC codes and transversal logical gates between neighboring surface-code patches, enabling a modular framework for efficient logical memories, Clifford computation, and magic-state distillation. To realize these capabilities, we co-design optimal-control protocols for bus-mediated controlled-Z gates that incorporate both microscopic neutral-atom dynamics and architectural constraints. We obtain smooth bus-mediated gates with fidelities approaching 99.9% and durations of a few hundred nanoseconds by combining time-optimal control with interaction-flatness and robustness constraints. Large-scale simulations of quantum error correction and logical entangling operations between neighboring surface-code patches predict more than an order-of-magnitude improvement in logical error rates compared with atom-shuttling architectures under realistic noise. The architecture achieves logical gate times of approximately 100 us and quantum-error-correction cycle times of about 1 ms for code distances d<12. These results establish static atomic buses as a practical alternative to atom shuttling for scalable fault-tolerant neutral-atom quantum computing.
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to implement such codes makes their physical realization challenging. Here, we propose a hardware-efficient scheme to perform fault-tolerant quantum computation with high-rate qLDPC codes on reconfigurable atom arrays, directly compatible with recently demonstrated experimental capabilities. Our approach utilizes the product structure inherent in many qLDPC codes to implement the non-local syndrome extraction circuit via atom rearrangement, resulting in effectively constant overhead in practically relevant regimes. We prove the fault tolerance of these protocols, perform circuit-level simulations of memory and logical operations with these codes, and find that our qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits at a realistic physical error rate of
10−3. We further find that less than 3000 physical qubits are sufficient to obtain over an order of magnitude qubit savings compared to the surface code, and quantum algorithms involving thousands of logical qubits can be performed using less than
105 physical qubits. Our work paves the way for explorations of low-overhead quantum computing with qLDPC codes at a practical scale, based on current experimental technologies.
Recent advancements in neutral atom platforms have enabled exploration of early fault-tolerant (FT) architectures for applications with quantum advantage, such as quantum dynamics simulations. An efficient fault-tolerant architecture has both spatially efficient quantum error correction codes (low qubit overhead), and efficient methodologies (transversal based gates, extractor based gates, etc.) for logical computation, to minimize overall execution time. Achieving the right balance between space and time can be critical for enabling early FT demonstrations of quantum advantage.
In this work, we identify bottlenecks in existing spatially efficient schemes, which tend to be very serial, and do not take advantage of unutilized space. We introduce a teleportation-based scheme that leverages the reconfigurable connectivity of neutral atoms to parallelize logical operations. Our approach achieves up to \textbf{
∼3× speedup} over extractor architectures at no extra space cost and achieves the best spacetime performance among other viable architectures before accounting for external \textit{resource-states}. To rigorously evaluate performance, we construct explicit quantum advantage benchmarks and \textit{simulate} compilation to a fault-tolerant instruction set, including low-level gate scheduling and shuttling patterns, and resource-state nondeterminism. We find that our speedups still apply and report exact space-time cost along with success probabilities, identifying architectures capable of achieving quantum advantage \textbf{with as little as
11,495 atoms and a runtime of
∼15 hours}.