Quantum Error Correction

Supervised approaches to quantum error mitigation learn a map from noisy circuit outputs to ideal ones, and therefore require the ideal outputs. Producing those ideal outputs demands noiseless classical simulation, whose cost grows exponentially with system size, so supervision is unavailable in exactly the regime where mitigation matters most. We ask whether cheap, individually unreliable signals drawn from circuit structure and hardware calibration can take the place of ideal labels. We assemble sixteen heuristic labeling functions (stabilizer and parity constraints, relaxation and readout characteristics, local depth, gate counts, and neighboring activity), reconcile their disagreements with a probabilistic label model, and read the resulting per-qubit error probabilities as a readout channel whose inverse mitigates the measured distribution. No ideal output enters the training path. On $147{,}000$ five-qubit circuits executed on two IBM devices, the method removes $24.3\%$ (Algiers) and $28.8\%$ (Hanoi) of the Kullback-Leibler divergence to the ideal distribution, against $15.4\%$ and $21.5\%$ for the strongest published analytical baseline, a margin that holds on both devices and lies far outside its bootstrap interval. Supervised neural models trained on ideal distributions remain stronger where such labels exist, and we quantify that gap rather than setting it aside; the method's claim is to the regime where they do not, since the labels they require cannot be computed for the circuits mitigation is needed for. The codes will be released shortly.

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

How much does the noisy measurement add to learned quantum error mitigation? An accuracy table cannot say, because a model handed circuit structure can score well without reading the measurement at all. QEMScore adds the comparison that can. Each simulated circuit carries an exact ideal answer. The learned mitigator is scored beside a capacity-matched control, a model just as flexible that reads the same circuit description but never the measurement. Each method's measurement spend is accounted and not equalized. We run a controlled campaign on simulated circuits and reanalyze two published learned mitigators, Q-LEAR and QRAFT, from their released hardware data. Three findings stand out. First, under familiar within-family conditions (S0) evaluated across two spin-chain families and three seeds, continuous couplings identify the target, and the control that never reads the measurement matches 87.7 to 100.5 percent of the mitigator's gain over an affine fit to the circuit description. A plain polynomial in the coupling parameters, fitted after the campaign, beats the mitigator on all six evaluations, reflecting the selected learners' capacity. Second, for these selected learners, matching most of the gain is not matching the accuracy: on five of six evaluations the mitigator removes 19.5 to 74.5 percent of the error the capacity-matched control leaves, a learner-specific gap rather than a measurement requirement. Third, on released hardware data where descriptors only partially identify queries, the findings differ: flexible models of the descriptors show negligible mean gain over affine fits in Q-LEAR, and measurement inputs carry predictive gains in both Q-LEAR and QRAFT. These comparisons reflect representation- and protocol-specific behavior rather than an isolated cross-regime difference. A learned mitigator's accuracy should therefore be reported beside such controls.

Structured spatial data require quantum encodings that preserve geometric relations, expose measurable observables, and remain implementable on finite-depth hardware. This work introduces a quantum representation and circuit architecture for rigid-body transformations and specializes it to Denavit--Hartenberg kinematics of serial open-chain manipulators. Each translational contribution is factorized into a classical metric magnitude and a signed unit direction encoded by a single-qubit Bloch vector, while parameterized rotations reproduce the ordered propagation of frame directions. A selector register prepares probabilities proportional to the contribution magnitudes, and the reduced state of a designated readout qubit encodes their normalized weighted sum. The retained classical scale then reconstructs the metric end-effector position. Two additional readout qubits encode terminal-frame axes, providing a compact and geometrically interpretable pose interface. At the ideal expectation-value level, measured Pauli observables reproduce the corresponding classical kinematic quantities. Alternative circuit architectures realize the same representation with different tradeoffs in qubit count, circuit depth, controlled operations, and measurement requirements. Validation on a serial manipulator yields numerically negligible position and orientation reconstruction errors under ideal simulation. Finite-shot simulations, noisy executions, transpilation analysis, and a hardware demonstration further characterize statistical error, noise sensitivity, and implementation overhead without asserting computational advantage.

A key subtask of quantum error correction is to extract a syndrome that, if nontrivial, signals an error. The number of possible ways to extract a syndrome grows exponentially with the syndrome size, and these implementations vary greatly in fault tolerance, as measured by their logical error rates. This creates a natural search problem: find an implementation with a low logical error rate. Previous work solves this problem but sacrifices either solution quality or scalability. In this paper, we use reinforcement learning and importance sampling to outperform previous work at all scales. Compared with the state of the art automatic scheduling tools AlphaSyndrome and PropHunt, our tool reduces the logical error rate by 25.9% and 71.7% on average, respectively, culminating with a reduction of 97.8% for a surface code with distance 15.

Quantum-inspired classical algorithms have dequantized several quantum machine learning routines by replacing quantum linear-algebra subroutines with classical counterparts. However, the sampler based on quantum singular value transformation (QSVT) for learning with optimized random features is not covered by existing dequantization frameworks, because the matrix to be inverted is not itself available through sampling access. In this work, we develop a classical algorithm to address this type of quantum-advantage candidate. Our method samples heavy indices, reduces the transformation to a small principal block, and outputs a sparse classical representation with operator-norm guarantees. Applying this method dequantizes the sampler for optimized random features, giving a classical sampler with prescribed accuracy and polynomially related runtime. These results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable.

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

Quantum low-density parity-check (qLDPC) codes can encode multiple logical qubits using sparse parity checks, yet searching for useful finite-length instances remains a challenging design problem because code performance must be optimized while satisfying practical constraints. Motivated by recent advances in artificial-intelligence agents for scientific discovery, we develop a multi-agent framework for discovering practical qLDPC codes. The framework combines specialist proposal and review, persistent scientific memory, long-horizon evolution of executable programs, and deterministic construction and evaluation within a closed-loop search. These programs instantiate coset-orbit balanced-product codes, providing a search space that includes bicycle and lifted-product constructions as well as non-normal subgroup actions. To incorporate practical constraints, we restrict the search to binary CSS codes with block length $n\leq400$ and overall weight $w\leq10$. Within this regime, the framework discovers codes with leading or competitive rate--distance performance in every weight class considered, with representative instances including $[[288,16,18]]$ at $w=7$, $[[288,18,18]]$ at $w=9$, and $[[234,28,18]]$ at $w=10$. The search also uncovers structurally distinct, high-performing constructions, including a $[[336,12,\leq24]]$ candidate and a $[[368,18,16]]$ code, both of which are genuine balanced-product constructions with non-normal subgroup actions. When evaluated under code-capacity depolarizing noise using a common BP-OSD decoding protocol, the discovered codes also exhibit low logical failure rates. Together, these results provide hardware-relevant finite-length candidates for further experimental evaluation and show how structured agentic search can contribute to scientific discovery.

Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables efficient online optimization using only syndrome measurements collected during normal error correction. We prove convergence to an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.

Conventional BB84 Quantum Key Distribution (QKD) systems rely on a fixed 11% Quantum Bit Error Rate (QBER) threshold to detect eavesdropping. However, stealthy attacks can remain below this threshold while still compromising channel security. This paper proposes a temporal QBER based machine learning framework for detecting and classifying eavesdropping attacks in BB84 QKD systems. Rather than relying on average session level QBER, the framework extracts 63 physics-informed temporal features capturing burst behavior, temporal instability, basis dependent asymmetry, and QBER loss interactions. Random Forest, XGBoost, and Support Vector Machine with a Radial Basis Function kernel (SVM-RBF) classifiers are evaluated on seven eavesdropping attacks and a normal channel scenario under noisy and lossy conditions. Averaged over ten independent runs, XGBoost achieves the best performance with 88.01% (0.47%) accuracy and a macro F1 score of 0.8803, while SVM-RBF performs comparably, confirming the robustness of the proposed features. Evaluated as a binary attack-versus-normal detector for comparison with conventional monitoring, a fixed 11% QBER threshold achieves only 25.82% accuracy with a False Negative Rate (FNR) of 0.8477, whereas the proposed framework reduces the FNR to 0.0198, substantially improving detection of stealthy attacks that evade threshold-based monitoring. SHapley Additive exPlanations based (SHAP) explainability shows that physics-informed temporal and channel derived features are highly discriminative for identifying eavesdropping strategies. These results demonstrate that temporal QBER driven machine learning provides an accurate, explainable, and practical framework for multi attack security monitoring in BB84 QKD systems.

Fault-tolerant quantum computing (FTQC) relies on quantum error correction to suppress physical errors and preserve logical information at scale. In practice, however, performance is constrained not only by physical noise but also by the latency of classical decoders processing rapidly generated syndrome data. This challenge is exacerbated by hardware noise that is strong, heterogeneous, and nonstationary, as well as by the simulation-to-hardware distribution shift that can substantially degrade fixed neural decoders. We present QAdapt, a noise-adaptive neural pre-decoding framework for surface-code quantum error correction. QAdapt captures local spatiotemporal correlations in syndrome data, sequentially adapts to evolving noise conditions while mitigating catastrophic forgetting, and forwards the residual syndrome to a conventional global decoder. Across 110 synthetic out-of-distribution noise configurations for rotated surface-code memory circuits, QAdapt consistently reduces the logical error rate relative to the neural pre-decoding baseline. On Google's Willow benchmark data, without target-domain fine-tuning, it achieves reductions of up to 5.79 percent in logical error rate and 9.32 percent in backend decoding latency on the residual syndrome. These results demonstrate that QAdapt provides a practical and decoder-compatible approach to improving the robustness and backend decoding efficiency of quantum error correction under evolving hardware noise.

Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and $14$ total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.

Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure, but the most accurate measures for that require costly decoder-level information. We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data. The method trains a supervised classifier to distinguish between syndromes from low- and high-noise regimes, and then uses the classifier's output as an abort score for new runs, without requiring logical-error labels, correction operators, or code-specific likelihood calculations. We validate the approach in three complementary settings: circuit-level simulations of the Gross bivariate-bicycle code, code-capacity simulations of the surface code, and experimental logical magic-state distillation data from the QuEra neutral-atom processor. In the Gross and surface codes, learned syndrome post-selection reduces the conditional logical error rate at a fixed acceptance rate, with performance comparable to syndrome-weight filtering. For the surface code, the learned classifier reveals a post-selection transition distinct from the conventional decoding threshold. In the experimental data, the machine-learning score outperforms syndrome-weight post-selection and, when combined with logical-gap filtering, improves the output fidelity beyond using the logical gap alone. These results show that syndrome-only learning provides a scalable and hardware-compatible route to improving the reliability of quantum error correction.

We propose a unified meta-decoding framework for quantum error correction that learns syndrome-to-recovery mappings across multiple stabilizer codes and noise settings, without requiring separate decoders for each configuration. The benchmark includes FiveQubit, Steane, Planar3x3, and Planar5x5 codes, four noise families, and five evaluation regimes: interpolation, unseen-p transfer, unseen-noise transfer, few-shot unseen-code adaptation, and few-shot held-out-size adaptation. We compare a classical Meta-MLP teacher-trained baseline with variational quantum circuit (VQC) meta-decoders selected through hardware-aware quantum architecture search over qubit count, circuit depth, and entangling topology. The Meta-MLP achieves teacher-label accuracies of 0.9993, 0.9118, 0.9342, 0.6304, and 0.7548 across the five regimes, while the hardware-aware VQC achieves 0.9400, 0.8495, 0.8415, 0.5678, and 0.7143. However, logical-level evaluation shows that high teacher-label accuracy alone is insufficient in the most challenging Planar5x5 setting. During interpolation, the raw logical-failure ratios relative to the teacher are 12.08 and 25.91 for the Meta-MLP and VQC, respectively, whereas confidence-gated fallback reduces them to 1.71 and 1.11. These results support confidence-aware selective recovery rather than unconditional teacher replacement.

Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension $D$. In hypervector decomposition, the objective is to recover $F$ constituent hypervectors, each drawn from a codebook of size $N$, from a bound target hypervector. This requires searching over $N^F$ candidate tuples, making the task computationally prohibitive at scale. Recent quantum approach provides a quadratic search advantage, but typically rely on qubit-inefficient $O(D)$-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to $O(\log D)$. The framework introduces logarithmic hypervector and binding encodings, together with a reversible hypervector lookup operator for circuit-level manipulation of dense hypervectors. Combined with a modified Dürr-Høyer search procedure, the method preserves $O(\sqrt{N^F})$ search complexity while substantially reducing qubit usage. Experimental results validate correct similarity computation, accurate decomposition in executable regimes, and significantly improved qubit scaling over baselines based on explicit $D$-qubit hypervector encodings, achieving up to $2{,}000\times$ fewer qubits.

Can AI agents visually comprehend quantum circuit diagrams and generate verified executable code--and at what cost? We present Quantum Circuit Vision, a cost-aware evaluation framework for multimodal AI agents on quantum circuit visual understanding. We construct a 132-circuit benchmark spanning 13 categories ($1$--$10$ qubits) with executable Amazon Braket code and unitary-fidelity verification. Evaluating three frontier Claude-family models at different capability-cost tiers with $n=5$ repeated trials, we find that the mid-tier model (Sonnet 4.6, $1.30\times$ credits) offers the most favorable balance on the cost-accuracy frontier: 91% pass rate on the core subset at 18% of the per-call cost of the strongest model (Opus 4.6), whose accuracy advantage is not statistically significant (paired $t$: $p=0.083$). Logistic regression confirms that circuit depth--not qubit count--is the primary predictor of failure ($p<0.001$). Chain-of-thought prompting shows no statistically significant effect (all $p>0.18$, $n=5$), suggesting that visual pattern recognition outweighs explicit reasoning strategy for structurally coupled diagrams. We propose a cascade routing strategy (cheap $\rightarrow$ expensive models) that achieves 84% accuracy at 38% of single-model cost, demonstrating that model routing dominates prompt engineering as a cost lever. We release QCV-Dataset (132 circuits, 5 modalities, 1,931 files) on Hugging Face Hub as an open evaluation infrastructure with structured metadata for discoverability, interoperability, and responsible AI documentation, and all evaluation code, cost logs, and verification scripts on GitHub for full reproducibility.

We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris--Rips filtration of S&P500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding $n_k$ simplex indices into $O(n_k^{1/κ})$ qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of\cite{Sciorilli25} does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over $n=4$--$12$ qubits. The classical stage matches ripser~\cite{bauer2021ripser} on all 190 sliding windows (2007-2009). On the real market Laplacians ($β_1=1$--$22$), warm-starting from a classical null-space surrogate allows PCE-VQE to recover $β_1$ exactly at every scale, placing the obstacle in the optimisation landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC $0.818$, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC $0.009$, $0.515$) shows the calibration does not generalize across crisis regimes.

Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances $d \in \{3,5,7,9,11\}$ under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near $4.6 \times 10^{5}$ samples s$^{-1}$ at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance $d=7$. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.

Quantum convolutional neural networks (QCNNs) combine the power of quantum computing and classical CNN for computational speedup in classification tasks. However, noise levels on state-of-the-art quantum devices remain too high for practical QCNN execution. In addition, despite the reliable surface code providing a method for error rates below a threshold value, they have a prohibitively large qubit cost. Recently introduced bivariate bicycle (BB) codes are of particular interest for their high error threshold, constant encoding rate, and linear code distance. Through simulation with realistic hardware noise sources, we demonstrate that a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate compared to numerical simulations. Addressing both limitations, we propose a distance-4 BB quantum error-correction (QEC) technique for QCNNs. In doing so, we validate that our low-overhead QEC technique for QCNNS represents a step toward practical QCNNs.

Large language models can generate plausible quantum code, but it is unclear whether they can reliably target the specific software development kit (SDK) version requested by the user. We study this problem as API drift and introduce quantum-api-drift, a benchmark for measuring version fidelity, defined here as execution success on the requested SDK version, cross-version compatibility, failure modes, and documentation-guided repair in LLM-generated quantum SDK code. We instantiate the benchmark with Qiskit, a representative quantum SDK that underwent substantial interface changes across v0.43, v1.3, and v2.0. We evaluate 17 models on 50 tasks with 3 samples per prompt, yielding 450 generated samples and 1,350 executions per model. Sixteen models are tested in a matched REST API setting with a 1024-token output cap, while GPT-5.4 (Codex CLI) is reported separately as a reference configuration. Across the 16 matched REST models, diagonal Pass@1 ranges from 0.02 to 0.85. Claude Opus 4.7 is strongest on v0.43 and v2.0, while Grok 4.20 is strongest on v1.3 at 0.513. Error profiles differ systematically by model strength: weaker models fail mainly with broken imports, while stronger models more often reach deprecation-level failures. Documentation-guided repair succeeds for 0.19 to 0.59 of repair attempts overall and is consistently much more effective for migration to v2.0 than to v1.3. The benchmark artifacts are publicly available at https://github.com/arasyi/quantum-api-drift. These results show that version alignment is a distinct evaluation axis for quantum code generation and that API drift remains only partly recoverable even with migration guidance.

Foundation decoders, a class of high-capacity neural decoders, are leading candidates for fault-tolerant quantum computing, with accurate and efficient decoding at large code distances. However, their construction often faces a steep scaling barrier, as larger code distances rapidly amplify the cost of syndrome generation and neural optimization. To address this bottleneck, here we devise neural transfer unification (NTU), a unified framework for efficient foundation decoders. A central feature of NTU is its ability to align decoding tasks across code distances via algebraic structures shared by scalable code families, which enables knowledge learned on smaller codes to accelerate large-scale decoder training. We instantiate NTU as NTU-Transformer, a transformer-based neural decoder tailored for planar surface codes and bivariate bicycle codes. For planar surface codes under circuit-level noise, NTU-Transformer outperforms correlation-aware matching on the $[\![361,1,19]\!]$ code and further scales to the $[\![625,1,25]\!]$ code, where it exceeds standard matching through transfer adaptation. For the bivariate bicycle code with $[\![72,12,6]\!]$, it surpasses Relay-BP in the low-physical-error regime. These results establish our proposal as a scalable route to amortized cross-distance training of foundation decoders for fault-tolerant quantum processors.

Quantum computers could outperform classical machines on important problems, but only if the errors that pervade quantum hardware can be corrected at scale. Quantum low-density parity-check (qLDPC) codes offer a promising route to this goal by combining sparse parity checks with finite encoding rate and growing distance, but their construction remains a challenging discrete design problem. Here we introduce structured concept evolution (SCE), a search framework that pairs a large language model with a structured algebraic mutation grammar to discover lifted-product code families, a class of CSS qLDPC codes. Instead of asking the LLM to design codes from first principles, SCE evolves structured concepts consisting of algebraic specifications paired with executable programs that realize them, using hierarchical mutations that modify the group algebra, protograph geometry, or base space. Running SCE, we discover a diverse set of competitive code families, ranging from abelian constructions to families over non-abelian groups beyond those underlying standard designs such as bivariate-bicycle codes, and characterize them under code-capacity depolarizing noise with BP+OSD decoding. These results are obtained with lightweight models (GPT-5.4-mini and GPT-5.4-nano).

Hyperdimensional Computing (HDC) is a robust computational framework inspired by human cognition characterized by simple and efficient operations within high-dimensional vector spaces. Quantum-enhanced Hyperdimensional Computing (QeHDC) extends classical HDC by leveraging quantum mechanical properties to enhance computational efficiency. In this paper, we propose a novel Quantum HDC framework featuring a one-pass training method, leveraging sinusoidal and quantum encoding to project classical data into quantum amplitude states efficiently. Our framework introduces an innovative reference-state-based quantum binding operation realized via quantum circuits. Furthermore, we propose a density-matrix-based superclass generation strategy employing eigenvalue decomposition to extract critical quantum state features effectively, enabling a more accurate and robust class representation. Experimental evaluations conducted on standard benchmark datasets demonstrate our approach's superior performance, robustness to noise, and computational feasibility compared to traditional classical and existing quantum-enhanced approaches. The results highlight the practical benefits and potential of Quantum HDC for quantum-enhanced classification tasks and pave the way for future advancements in quantum-inspired computational paradigms.

Modern AI systems increasingly solve a task not with a single model call but with several imperfect agents working together: some propose pieces of a solution, others verify them, and the results are combined. These systems often outperform any single model, yet it is rarely clear why they succeed or when they will fail. We model such a system as message passing on a sparse graph, the structure that underlies low-density parity-check (LDPC) codes, and extend the density-evolution machinery of coding theory to this richer setting. In our model a task is a set of coupled binary subclaims, and an agent architecture is a sparse, role-typed factor graph whose check nodes are noisy Boolean verifier nodes, each computing a local Boolean function of the subclaims it touches. Three distinct failure modes, all modeled as erasures (an agent abstaining, a verifier returning no usable output, and a message lost between two agents), propagate as the agents exchange set-valued messages. The check agents combine these messages by a single logical-forcing rule that specializes to XOR, AND, OR, implication, and Horn constraints. This is more than a relabeling of LDPC theory: the verifier functions are nonlinear and value-asymmetric, and the three failure modes do not reduce to a single effective channel, so they require new threshold, finite-length, and converse results rather than a direct reuse of parity-check density evolution. We prove a density-evolution theorem that predicts the asymptotic fraction of unresolved subclaims on random role-typed architectures, with an extension to deterministic, locally tree-like graph sequences. The XOR case recovers the classical LDPC recursion on the binary erasure channel (BEC); the AND case exposes an asymmetry between positive and negative verifier certificates.

Efficient quantum error correction is essential for the advancement of quantum computing. We propose a quantum neural network with a global structure that reduces the number of unitary matrices required in quantum circuits. This approach resulted in a 97% reduction in training time and up to a 25% improvement in the training completion rate, ultimately achieving a 100% success rate in training while surpassing the error correction performance reported in previous studies. In addition, we demonstrated the enhanced robustness of quantum error correction against internal network noise. Moreover, the fidelity of quantum error correction under internal network noise increased by up to 15% due to the reduced computational load.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.

Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ansätze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a proof-of-concept framework for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.

The growing complexity of quantum programming frameworks has exposed a critical limitation in existing large language model (LLM)-based code assistants: general-purpose models hallucinate PennyLane-specific gate names, misplace device configurations, and produce structurally invalid circuits when faced with specialized quantum coding challenges. We present PennySynth, a retrieval-augmented generation framework that addresses this gap by conditioning LLM inference on a curated knowledge base of 13,389 PennyLane instruction-code pairs, built via a three-stage extraction, verification, and deduplication pipeline over official PennyLane repositories, community GitHub sources, and QHack competition archives. PennySynth introduces a code-aware embedding strategy using st-codesearch-distilroberta-base, trained for natural-language-to-code retrieval, increasing average retrieval cosine similarity from 0.45 to 0.726 compared to a general-purpose baseline. Evaluated across 74 challenges spanning three years of the QHack competition (2022, 2023, 2024), PennySynth achieves 64%, 68%, and 52% pass@5 on QHack 2022, 2023, and 2024, respectively, improving over Claude Sonnet 4.6 without retrieval by +28, +25, and +28 percentage points. We further introduce a quantum-adapted CodeBLEU metric that upweights qml.* token patterns and show that structural code similarity and functional correctness capture distinct aspects of quantum code quality. Controlled ablations reveal that code-aware embeddings are the primary driver of retrieval performance, while dataset expansion and source composition provide additional gains when retrieval quality is sufficiently precise.

Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible decoding strategies, maximum likelihood decoding (MLD) is provably optimal, since it identifies the logical group with largest likelihood by summing over all possible errors within logical class consistent with the observed syndrome. Despite its optimality, MLD is computationally intractable in general (#P-hard), motivating a rich landscape of exact and approximate algorithms. In this topical review, we provide a unified perspective on MLD by surveying recent advances through three complementary lenses: statistical mechanics, tensor networks, and artificial intelligence. From the statistical mechanics viewpoint, the MLD problem maps onto evaluating partition functions of disordered spin models, enabling exact solutions for certain codes and noise models as well as threshold estimation via phase-transition analysis. From the tensor network perspective, approximate contraction of tensor networks on the code's factor graph yields decoders that closely approach MLD accuracy with polynomial computational cost. From the artificial intelligence perspective, neural-network-based decoders, including autoregressive generative models and recurrent transformers, learn to approximate the MLD distribution from data, achieving high accuracy with the parallelism afforded by modern hardware accelerators. We discuss the connections among these three approaches, review their application to both simulated and experimental quantum hardware, and outline open challenges including real-time decoding, scalability to large code distances, and generalization to high-rate quantum low-density parity-check codes.

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R)$regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.

In this paper, we study grant-free, asynchronous control-to-control (C2C) communications in an indoor scenario with a shared wireless channel. Each communication node transmits command units, each consisting of a variable-length low-density parity-check (LDPC)--coded payload preceded by a start sequence and followed by a tail sequence. Due to the asynchronous nature of the access, transmissions from different nodes are not aligned over time. As a result, each receiving controller observes the superposition of multiple command units transmitted by different nodes over a receiver-defined superframe interval. Each node transmits one or more replicas of the same command unit. We propose a receiver architecture in which the detection of command unit boundaries (start/tail sequences) is carried out by a single convolutional neural network (CNN) operating directly on the received signal. We show that, while start-sequence detection must rely only on the received waveform, tail-sequence detection can additionally exploit the soft information produced by the LDPC decoder, together with channel estimates. Finally, once commands units are successfully decoded, successive interference cancellation (SIC) can be applied. Simulation results demonstrate that the receiver we propose achieves reliable packet-boundary identification and a low end-to-end packet loss rate, even under uncoordinated and high-traffic operating conditions.

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy-latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy-latency constraints, considering code distances up to d=9 (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

Edge detection refers to identifying points in a digital image where intensity changes sharply, indicating object boundaries or structural features. Corners are locations where gray-level intensity changes abruptly in multiple directions and are widely used in feature extraction, object tracking, and 3D modeling. In this study, we present a quantum implementation of Sobel-based edge detection and Harris-style corner detection. Two quantum image encoding methods - Flexible Representation of Quantum Images (FRQI) and Quantum Probability Image Encoding (QPIE) - are used to encode the input data and are comparatively analyzed. The proposed approach introduces a quantum gradient computation scheme based on lag-2 differences, enabling the evaluation of gradient-like features in superposition. To improve detection quality and reduce false positives, a classical post-processing step is applied to candidate corner points identified by the quantum circuit. Results show that the proposed quantum circuits produce outputs consistent with classical Sobel and Harris operators. Furthermore, the QPIE-based configuration yields more stable and coherent results than FRQI, especially under limited measurement shots. While gradient computation can be performed efficiently at the circuit level, the overall cost remains dominated by state preparation, measurement, and classical post-processing. All experiments are conducted under noiseless simulation, and performance on NISQ hardware may be affected by noise and measurement limitations. Therefore, this work demonstrates a functional and scalable quantum realization of classical edge and corner detection methods rather than an end-to-end speedup.

Quantum machine learning (QML) provides a promising framework for leveraging quantum-mechanical effects in learning tasks. However, its vulnerability to adversarial perturbations remains a major challenge for practical deployment. In QML systems, small perturbations applied to classical inputs can propagate through the quantum encoding stage and distort the resulting quantum state, thereby degrading model performance. In this work, we propose a defense mechanism that replaces the conventional quantum encoding stage of a QML model with passive steering-based controlled state preparation, which guides the encoded state toward a controlled intermediate state. By tuning the steering strength and the number of steering iterations, the proposed method suppresses the influence of adversarial perturbations while maintaining high clean accuracy and improving adversarial accuracy. Experimental results demonstrate that the passive steering-based defense consistently improves adversarial accuracy across different QML models and datasets under gradient-based adversarial attacks, achieving adversarial accuracy improvements of up to 40.19%.

Quantum error mitigation (QEM) is essential for extracting reliable results from near-term quantum devices, yet practical deployments must balance mitigation strength against runtime overhead under time-varying noise. We introduce \emph{GSC-QEMit}, a telemetry-driven, \textbf{context--forecast--bandit} framework for \emph{adaptive} mitigation that switches between lightweight suppression and heavier intervention as drift evolves. GSC-QEMit composes three coupled modules: (G) a Growing Hierarchical Self-Organizing Map (GHSOM) that clusters streaming telemetry into operating contexts; (S) an uncertainty-aware subsampled Gaussian-process forecaster that predicts short-horizon fidelity degradation; and (C) a cost-aware contextual multi-armed bandit (CMAB) that selects mitigation actions via Thompson sampling with explicit intervention cost. We evaluate GSC-QEMit on benchmark circuit families (GHZ, Quantum Fourier Transform, and Grover search) under nonstationary noise regimes simulated in Qiskit Aer, using an instrumented testbed where action labels correspond to graded mitigation intensity. Across Clifford, non-Clifford, and structured workloads, GSC-QEMit improves average logical fidelity by \textbf{+9.0%} relative to unmitigated execution while reducing unnecessary heavy interventions by reserving them for inferred noise spikes. The resulting policies exhibit a favorable fidelity--cost trade-off and transfer across the evaluated workloads without circuit-specific tuning.

In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.

Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters $T_1$, $T_2$, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an optimal code sequence. We automate this choice by estimating the effective noise channel after each level and selecting the next code accordingly. In particular, we use learning-based methods to tailor small, non-additive encoders when the noise exhibits sufficient structure, then switch to standard codes once the noise is nearly uniform. In simulations, this level-wise adaptation achieves a target logical error rate with far fewer qubits than concatenating stabilizer codes alone--reducing qubit counts by up to two orders of magnitude for strongly structured noise. Therefore, this hybrid, learning-based strategy offers a promising tool for early fault-tolerant quantum computing.

Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings on the toric code under depolarizing noise demonstrate thresholds of 17.9% and 10.95%, nearing the 18.9% and 11.0% maximum likelihood bounds, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.