Resource overhead problem caused by concatenation in quantum error correction (QEC) is of significant importance for the realization of fault-tolerant quantum computation (FTQC). To attack this problem, we propose a novel scheme by considering integrated FTQC architecture where the concatenation level is controlled dynamically; i.e., less (or more) concatenation levels are imposed by good (or poor) performance gates-we call this scheme "dynamic concatenation" in this sense. Such a dynamic concatenation is realizable in an integrated structure of FTQC, as the information of the concatenation can be communicated between classical system elements (e.g., compiler and system organizer) and the logical qubits in real-time. We derive the effective lower and upper bounds of the length of gate decomposition in order to achieve the practical advantage, namely of reduction of the overall operation time. By considering two non-trivial examples, it is shown that the aforementioned advantage can indeed be achieved in the presented scheme. Our result also provides an important scientific message, i.e., the interplay between "classical" and "quantum" can be helpful in QEC.
Resource overhead problem caused by concatenation in quantum error correction (QEC) is of significant importance for the realization of fault-tolerant quantum computation (FTQC). To attack this problem, we propose a novel scheme by considering integrated FTQC architecture where the concatenation level is controlled dynamically; i.e., less (or more) concatenation levels are imposed by good (or poor) performance gates-we call this scheme "dynamic concatenation" in this sense. Such a dynamic concatenation is realizable in an integrated structure of FTQC, as the information of the concatenation can be communicated between classical system elements (e.g., compiler and system organizer) and the logical qubits in real-time. We derive the effective lower and upper bounds of the length of gate decomposition in order to achieve the practical advantage, namely of reduction of the overall operation time. By considering two non-trivial examples, it is shown that the aforementioned advantage can indeed be achieved in the presented scheme. Our result also provides an important scientific message, i.e., the interplay between "classical" and "quantum" can be helpful in QEC.
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the codes. The codes not only play the role of correcting errors, but the role of polarizing the effective channel. For any independent noise, the most suitable error-correction protocol can be constructed based on the rules of concatenation. The most significant aspect of using the concatenated three-qubit codes is to realize quantum error-correction with the non-ideal gate operations, because the error-correction schemes of the three-qubit codes are simple and modular. For example, for the amplitude damping noise with the initial channel fidelity 0.9, the effective channel fidelity can reach 0.94731 (or 0.961634 with the ideal quantum gate operations) when using the 4 levels concatenated quantum error-correction with the three-qubit codes. The protocol with the three-qubit codes needs 81 qubits and 366 quantum gate operations when the accuracy rate is 0.9995. Meanwhile, when using the 3 levels concatenated quantum error-correction with the five-qubit code, the effective channel fidelity can only reach 0.922798 (or 0.975488 with the ideal quantum gate operations). The protocol with the five-qubit code needs 125 qubits and 1147 quantum gate operations when the accuracy rate is 0.9995. The physical resources costed is multiple of the physical resources costed by realizing the three-qubit quantum error-correction, the protocol has a higher fault tolerance threshold, and no increase in complexity. So, we believe it will be helpful for realizing quantum error-correction in the physical system.
Executing quantum applications with quantum error correction (QEC) faces the gate non-universality problem imposed by the Eastin-Knill theorem. As one resource-time-efficient solution, code switching changes the encoding of logical qubits to implement universal logical gates. Unfortunately, it is still unclear how to perform full-stack fault-tolerant quantum computing (FTQC) based on the changeable logical qubit. Specifically, three critical problems remain unsolved: a) how to implement the dynamic logical qubit on hardware; b) how to determine the appropriate timing for logical qubit varying; c) how to improve the overall system performance for programs of different features. To overcome those design problems, We propose CECQ, to explore the large design space for FTQC based on changeable logical qubits. Experiments on various quantum programs demonstrate the effectiveness of CECQ.
Especially in noisy intermediate-scale quantum (NISQ) devices, fault-tolerant quantum computing cannot be realized without quantum error correction. High error rates in quantum systems stemming from decoherence and gate defects call for effective and flexible QEC systems. This paper presents a novel FPGA-based architecture using dynamic reconfiguration to maximize hardware resources in response to real-time error patterns. Supporting bit-flip, phase-flip, and depolarizing faults among several error correction techniques guarantees high accuracy and little hardware overhead. Scaled for surface code distances up to and beyond, the design combines modular pipelines, adaptive hardware allocation, and error pattern detection. Designed on a Xilinx XC7A50T-CPG236 FPGA, the system showed notable gains over static architecture, averaging 30% lower latency and 20% less resource use overall. Low latency and high throughput are maintained while this dynamic technique enables flexible adaptability to several quantum error models. The outcomes show how well this structure may improve quantum error-correcting systems and enable the incorporation of QEC into useful quantum computer configurations.
Fault-tolerant quantum computing (FTQC) is a form of universal quantum computing that suppresses physical errors via quantum error correction (QEC). On the other hand, it is expected that the available code distance and the T-gate count will be restricted in the early years of FTQC. Meanwhile, quantum error mitigation (QEM) was recently introduced for suppressing errors in noisy intermediate-scale quantum (NISQ) devices; it improves the computation accuracy of near-term quantum algorithms with its overhead being a greater number of samples. In this work, we integrate QEC and QEM into an efficient FTQC architecture that effectively increases the code distance and T-gate count. Our scheme will dramatically alleviate the required qubit count by tens of percent at the cost of a constant multiplicative sampling overhead within 102 in a wide range of regimes from the post-NISQ era to early FTQC regime, which necessitates the order of from 104 to 1010 logical operations. While it has been widely believed that there do not exist useful applications in post-NISQ regimes due to a chasm between the NISQ and FTQC regimes such as overheads for encoding and T-gate distillations, our scheme can continuously bridge the two distinct regimes.
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.
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work, we introduce a hard-decision decoder for concatenated quantum Hamming codes with time complexity polynomial in the block length. This decoder overcomes the limitations of conventional local decoding by leveraging higher-level syndrome information to revise lower-level recovery decisions -- a strategy we refer to as bidirectional decoding. For the concatenated [[15,7,3]] quantum Hamming code under independent bit-flip noise, the bidirectional decoder improves the threshold from approximately 1.56% to 4.35% compared with standard local decoding. Moreover, the decoder empirically preserves the full 3L code-distance scaling for at least three levels of concatenation, resulting in substantially faster logical-error suppression than the 2L+1 scaling offered by local decoders. Our results can enhance the competitiveness of concatenated-code architectures for low-overhead fault-tolerant quantum computation.