Exploring an efficient and scalable architecture of fault-tolerant quantum computing (FTQC) is vital for demonstrating useful quantum computing. Here, we propose and evaluate a scalable and practical architecture with a cavity-quantum-electrodynamics (CQED) network. Our architecture takes advantage of the stability of neutral atoms and the flexibility of a CQED network. We show a concrete framework for implementing surface codes and numerically analyze the logical error rate and threshold values beyond the simplified circuit-level noise model on several network structures. Although the requirement of CQED parameters is demanding given the current performance of experimental systems, we show that an error-decoding algorithm tailored to our proposed architecture, where the loss information of ancillary photons is utilized, greatly improves the error threshold. For example, the internal cooperativity, a good figure of merit of the cavity performance for quantum computing, required for FTQC is relaxed to 1/5 compared to the normal error-decoding for the surface code. Since our proposal and results can be extended to other LDPC codes straightforwardly, our approach will lead to achieve more reliable FTQC using CQED.
Exploring an efficient and scalable architecture of fault-tolerant quantum computing (FTQC) is vital for demonstrating useful quantum computing. Here, we propose and evaluate a scalable and practical architecture with a cavity-quantum-electrodynamics (CQED) network. Our architecture takes advantage of the stability of neutral atoms and the flexibility of a CQED network. We show a concrete framework for implementing surface codes and numerically analyze the logical error rate and threshold values beyond the simplified circuit-level noise model on several network structures. Although the requirement of CQED parameters is demanding given the current performance of experimental systems, we show that an error-decoding algorithm tailored to our proposed architecture, where the loss information of ancillary photons is utilized, greatly improves the error threshold. For example, the internal cooperativity, a good figure of merit of the cavity performance for quantum computing, required for FTQC is relaxed to 1/5 compared to the normal error-decoding for the surface code. Since our proposal and results can be extended to other LDPC codes straightforwardly, our approach will lead to achieve more reliable FTQC using CQED.
Abstract The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice other factors. Here, we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10 −10 and 10 −24 by more than 90% and 96%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.5% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.
The threshold theorem indicates that if errors are all local and their rates are below a certain threshold, it is possible to implement large scale quantum computation with arbitrarily small error based on active quantum error correction (QEC). However, most fault-tolerant quantum computation (FTQC) schemes require enormous overhead to achieve this rate by increasing either the concatenation levels for concatenated codes or the distance (hence the size) for topological codes. As a result, a logical qubit is usually encoded in more than thousands of physical qubits, even when the error rate is below the threshold. In this thesis, we try to reduce the resource overhead of FTQC. We first study a quantum computation scheme using clouds of atoms trapped on atomic chips. It suggests that this scheme is robust to noise to some extent and has potential to be scalable. Secondly, we propose a FTQC scheme of encoding many logical qubits into large code blocks. The error performance of such scheme is numerically studied. Preparation of various ancilla states necessary for computation is also explored. Thirdly, we explore the idea of introducing energy gap to suppress thermal noise on each qubit. We show that fault-tolerant holonomic quantum computation (HQC) can be implemented in stabilizer codes with the existence of such energy protection. Especially, we studied fault-tolerant HQC in surface codes in detail. This scheme opens the possibility for self-correcting quantum computation in 2D lattice.
Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding.
This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.
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 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.
Fault-tolerant quantum computing (FTQC) is required to execute quantum algorithms capable of tackling computationally intractable problems in chemistry, material science, and cryptography. Noisy Intermediate-Scale Quantum (NISQ) devices remain constrained by physical error rates that degrade quantum coherence over short circuit depths. Quantum error correction (QEC) protects fragile logical states by encoding them into non-local degrees of freedom across topological physical qubit arrays. This research presents a comprehensive architectural and theoretical evaluation of three primary QEC paradigms: planar surface codes, topological color codes, and asymptotic quantum low-density parity-check (qLDPC) codes. We examine error thresholds, transversal gate constraints governed by the Eastin-Knill theorem, magic state distillation (MSD) overheads, lattice surgery, and classical decoding latencies across superconducting transmons, trapped ions, and neutral atom platforms.