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1. Logical quantum processor based on reconfigurable atom arrays

   https://doi.org/10.1038/s41586-023-06927-3  

   Bluvstein, Dolev; Evered, Simon J.; Geim, Alexandra A.; Li, Sophie H.; Zhou, Hengyun; Manovitz, Tom; Ebadi, Sepehr; Cain, Madelyn; Kalinowski, Marcin; Hangleiter, Dominik; et al (December 2023, Nature)

   Abstract Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)^2–6for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy^2–4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays⁷, our system combines high two-qubit gate fidelities⁸, arbitrary connectivity^7,9, as well as fully programmable single-qubit rotations and mid-circuit readout^10–15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code⁶distance fromd = 3 tod = 7, preparation of colour-code qubits with break-even fidelities⁵, fault-tolerant creation of logical Greenberger–Horne–Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks^16,17, we realize computationally complex sampling circuits¹⁸with up to 48 logical qubits entangled with hypercube connectivity¹⁹with 228 logical two-qubit gates and 48 logical CCZ gates²⁰. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling^21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors. 

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2. Fault-Tolerant Quantum Computation Using Large Spin-Cat Codes

   https://doi.org/10.1103/PRXQuantum.5.020355  

   Omanakuttan, Sivaprasad; Buchemmavari, Vikas; Gross, Jonathan A; Deutsch, Ivan H; Marvian, Milad (June 2024, PRX Quantum)

   We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous-variable cat encoding. With this, we can correct the dominant error sources, namely processes that can be expressed as error operators that are linear or quadratic in the components of angular momentum. Such codes tailored to dominant error sources can exhibit superior thresholds and lower resource overheads when compared to those designed for unstructured noise models. A key component is the gate that preserves the rank of spherical tensor operators. Categorizing the dominant errors as phase and amplitude errors, we demonstrate how phase errors, analogous to phase-flip errors for qubits, can be effectively corrected. Furthermore, we propose a measurement-free error-correction scheme to address amplitude errors without relying on syndrome measurements. Through an in-depth analysis of logical gate errors, we establish that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. We consider a specific implementation based on neutral-atom quantum computing, with qudits encoded in the nuclear spin of 87Sr, and show how to generate the universal gate set, including the rank-preserving gate, using quantum control and the Rydberg blockade. These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing. 

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3. On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement

   https://doi.org/10.4230/lipics.itcs.2025.16  

   Bergamaschi, Thiago; Liu, Yunchao (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Meka, Raghu (Ed.)

   Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state [Raussendorf et al., 2005] offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward [Bravyi et al., 2020]. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman’s clustering-of-errors argument [Gottesman, 2014]. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement. 

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4. Architectural mechanisms of a universal fault-tolerant quantum computer

   Bluvstein, Dolev; Geim, Alexandra_A; Li, Sophie_H; Evered, Simon_J; Bonilla_Ataides, J_Pablo; Baranes, Gefen; Gu, Andi; Manovitz, Tom; Xu, Muqing; Kalinowski, Marcin; et al (June 2025, arXivorg)

   Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, 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 all 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, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations 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 and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems. 

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5. Emergent Unitary Designs for Encoded Qubits from Coherent Errors and Syndrome Measurements

   https://doi.org/10.1103/bnld-2chd  

   Cheng, Zihan; Huang, Eric; Khemani, Vedika; Gullans, Michael J; Ippoliti, Matteo (August 2025, PRX Quantum)

   Unitary $k$ -designs are distributions of unitary gates that match the Haar distribution up to its $k\mathrm{th}$ statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical qubits is nontrivial due to the need for magic gates, which can require a large resource overhead. In this work, we propose an efficient approach to generate unitary designs for encoded qubits in surface codes by applying local unitary rotations (“coherent errors”) on the physical qubits followed by syndrome measurement and error correction. We prove that, under some conditions on the coherent errors (notably including all single-qubit unitaries) and on the error-correcting code, this process induces a unitary transformation of the logical subspace. We numerically show that the ensemble of logical unitaries (indexed by the random syndrome outcomes) converges to a unitary design in the thermodynamic limit, provided that the density or strength of coherent errors is above a finite threshold. This “unitary design” phase transition coincides with the code’s coherent error threshold under optimal decoding. Furthermore, we propose a classical algorithm to simulate the protocol based on a “staircase” implementation of the surface code encoder and decoder circuits. This enables a mapping to a $(1+1)$ -dimensional monitored circuit, where we observe an entanglement phase transition (and thus a classical complexity phase transition of the decoding algorithm) coinciding with the aforementioned unitary design phase transition. Our results provide a practical way to realize unitary designs on encoded qubits, with applications including quantum state tomography and benchmarking in error-correcting codes. 

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