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Paper 1

Quantum Lego Power-up: Designing Transversal Gates with Tensor Networks

ChunJun Cao, Brad Lackey

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.03542

arXiv

2603.03542

Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains difficult within the stabilizer formalism or CSS constructions alone. We show that these limitations can be overcome using tensor-network frameworks such as the quantum lego formalism, where transversal gates naturally appear as global or localized symmetries. Within the quantum lego formalism, small codes carrying desirable symmetries can be "glued" into larger ones, with operator-flow rules guiding how logical symmetries are preserved. This approach enables the systematic construction of codes with addressable transversal single- and multi-qubit gates targeting specific logical qubits regardless of whether the gate is Clifford or not. As a proof of principle, we build new finite-rate code families that support strongly transversal $T$, $CCZ$, $SH$, and Gottesman's $K_3$ gates, structures that are challenging to realize with conventional methods. We further construct holographic and fractal-like codes that admit addressable transversal inter-, meso-, and intra-block $T$, $CS$, and $C^\ell Z$ gates. As a corollary, we demonstrate that the heterogeneous holographic Steane-Reed-Muller black hole code also supports fully addressable transversal inter- and intra-block $CZ$ gates, significantly lowering the overhead for universal fault-tolerant computation.

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Paper 2

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Xiangjun Mi, Frank Mueller

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.06257

arXiv

2510.06257

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen codes. To address this gap, we propose \textbf{QuBA}, a Bayesian graph neural decoder that integrates attention to both dot-product and multi-head, enabling expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop \textbf{SAGU }\textbf{(Sequential Aggregate Generalization under Uncertainty)}, a multi-code training framework with enhanced cross-domain robustness enabling decoding beyond the training set. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving a reduction of on average \emph{one order of magnitude} in logical error rate (LER), and up to \emph{two orders of magnitude} under confident-decision bounds on the coprime BB code $[[154, 6, 16]]$; (ii) QuBA also surpasses state-of-the-art neural decoders, providing an advantage of roughly \emph{one order of magnitude} (e.g., for the larger BB code $[[756, 16, \leq34]]$) even when considering conservative (safe) decision bounds; (iii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

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