Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant (FT) implementations. In this paper, we investigate the performance of QEC schemes taking into account that quantum gates and measurements are themselves error-prone. We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information, such as the number of flag qubits and quantum gates. Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults. The derived bounds highlight fundamental limitations in Shor-style FT-QEC performance and quantify how circuit imperfections degrade error correction capabilities, under the assumption of depolarizing noise.

Reliable quantum computation requires fault-tolerant protocols to prevent errors from propagating during syndrome extraction in quantum error correction. We present a novel fault-tolerant syndrome extraction technique for CSS codes, which we refer to as the cut-cat state scheme. While each ancilla qubit interacts non-fault-tolerantly with a pair of data qubits, we introduce additional cat stabilizer measurements to identify and correct the resulting hook errors. Our approach maintains the key benefit of cat-based extraction, i.e., parallelized data qubit interactions, while reducing the number of simultaneous qubits required by more than half. Compared to flag-based state-of-the-art protocols, the cut-cat scheme offers a notable advantage in terms of two-qubit gate count as the code distance increases.

Quantum computers are highly vulnerable to noise, necessitating the use of error-correcting codes to protect stored data. Errors must be continuously corrected over time to counteract decoherence using appropriate decoders. Therefore, fast decoding strategies capable of handling real-time syndrome extraction are crucial for achieving fault-tolerant quantum computing. In this paper, we introduce the bubble clustering (BC) decoder for quantum surface codes, which serves as a low-latency replacement for MWPM, achieving significantly faster execution at the cost of a slight performance degradation. This speed boost is obtained leveraging an efficient cluster generation based on bubbles centered on defects, and avoiding the computational overhead associated with cluster growth and merging phases, commonly adopted in traditional decoders. Our complexity analysis reveals that the proposed decoder operates with a complexity on the order of the square of the number of defects. For moderate physical error rates, this is equivalent to linear complexity in the number of data qubits.

In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric errors are critical to mitigating the impact of such impairments. To this aim, several asymmetric quantum codes have been proposed. These include variants of surface codes like the XZZX and ZZZY surface codes, tailored to preserve quantum information in the presence of error asymmetries. In this work, we propose two classes of Calderbank, Shor and Steane (CSS) topological codes, referred to as cylindrical and Möbius codes, particular cases of the fiber bundle family. Cylindrical codes maintain a fully planar structure, while Möbius codes are quasi-planar, with minimal non-local qubit interactions. We construct these codes employing the algebraic chain complexes formalism, providing theoretical upper bounds for the logical error rate. Our results demonstrate that cylindrical and Möbius codes outperform standard surface codes when using the minimum weight perfect matching (MWPM) decoder.

This paper elaborates on the idea of building grant-free channel access schemes from non-orthogonal multiple access ones, and proposes an explicit such scheme based on sparse code multiple access (SCMA). In the designed protocol, SCMA codebooks and pilots are chosen by users in a fully uncoordinated fashion, with multiple pilots associated with the same codebook to aid codebook detection. A modified two-stage SCMA decoder is proposed, where a low-complexity collision resolution algorithm, working on a super-constellation, and an SCMA message passing detector are iteratively applied. Numerical results, integrated by analysis in the high signal-to-noise ratio regime, highlight a potential for the proposed scheme in the context of massive uncoordinated machine-type uplink.

Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used PauliXor PauliZoperators in a square structure, these codes can be improved by rotating the lattice or incorporating a mix of generators in the XZZX variant. However, a comprehensive theoretical analysis of the logical error rate for these variants has been lacking. To address this gap, we present theoretical formulas based on recent advancements in understanding the weight distribution of stabilizer codes. For example, over an asymmetric channel with asymmetryA= 10 and a physical error ratep→ 0, we observe that the logical error rate asymptotically approachespL→ 10p2for the rotated [[9, 1, 3]] XZZX code andpL→ 18.3p2for the [[13, 1, 3]] surface code. Additionally, we observe a particular behavior regarding rectangular lattices in the presence of asymmetric channels. Our findings demonstrate that implementing both rotation and XZZX modifications simultaneously can lead to suboptimal performance. Thus, in scenarios involving a rectangular lattice, it is advisable to avoid using both modifications simultaneously.

One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing and quantum Internet. We here analyze the performance of surface codes, one of the most important class for practical implementations, on both symmetric and asymmetric quantum channels. We derive approximate expressions, confirmed by simulations, to evaluate the performance of surface codes and of XZZX codes, and provide a metric to assess the advantage of codes with respect to uncoded systems. Our findings allow to characterize the performance by means of analytical formulas of surface codes, like, for example, the [[13, 1, 3]], the [[23, 1, 3/5]], the [[33, 1, 3/7]], and the [[41, 1, 5]] surface codes.