Quantum Circuit Simulation

Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate. We ask whether a generative model can learn this transformation directly from examples, rather than selecting from a fixed rewrite library or rigid algebraic routines. We present Bridge of $Ψ$'s (BOPS), a generative model based on Schrödinger bridges, using a custom denoiser architecture, that learns a transformation from a source circuit into an equivalent optimized circuit. We train it on data constructed to be hard for existing optimizers, by applying rewrite rules backwards so that each input has a known lower-cost target. On held-out 8 qubits $\times$ 64 depth Clifford+$T$ circuits, BOPS reduces gate count by $2.46\times$ and depth by $2.45\times$ in geometric mean, outperforming all nine baseline optimizers. This constitutes the first generative model bridging quantum circuits and frontier machine learning methods, opening up the quantum compilation stack to learned optimization along multiple axes.

Many signal processing tasks require intensive computations. Quantum computing promises to accelerate certain tasks, but algorithms must be designed around the limitations of quantum mechanics. This paper provides a quantum implementation of finite impulse response (FIR) filters, which are a widely used tool in classical signal processing. The filter can be parallelized and composed as part of larger quantum algorithms, with potential for speedups using quantum amplitude estimation and future fault-tolerant quantum hardware. To accomplish these properties, we introduce a state-space framework wherein sample-based signal processing is performed with unitary quantum circuits. We present the quantum delay gate as the quantum analog of the delay line in discrete-time signal processing. Unitary circuits intrinsically describe lossless systems, but we also implement lowpass and other bounded filters by emulating a projection operator. The FIR filter implementation is tested and demonstrated with a quantum circuit simulator.

Reinforcement learning (RL) can automate quantum architecture search, but its scalability is limited when useful circuit trajectories become rare in the rapidly expanding search space. Existing replay mechanisms reuse observed transitions; the proposed learned model produces additional predicted one step transitions from real state-action seeds. Here we introduce GenQAS, a tensor network-guided RL framework that combines a fixed matrix product state warm-start with prioritized generative replay. A learned local transition model generates synthetic circuit transitions on demand and mixes them with real experience during Double Deep Q-Network updates. Under a random exploration analysis, near ground state circuits occupy a rapidly shrinking region of the accessible state space. We investigate whether real data anchored synthetic replay can improve the effective training signal in this regime. Across chemical Hamiltonian benchmarks from 6 to 12 qubits, GenQAS improves fixed-budget success probability and identifies compact circuits at competitive energy error. At 12 qubits, it improves final success probability by up to $7.0\times$ over passive replay. On a 15-qubit transverse field Ising model, GenQAS increases success probability from $12\%$ to $21\%$. In a noisy 6-qubit BeH$_2$ transfer experiment, generative replay reduces the steps to chemical accuracy by $92.7\%$. These results show that generative replay can mitigate sample starvation in quantum architecture search and support more resource efficient circuit discovery.

As quantum computing progresses from proof-of-principle demonstrations toward practical utility, a significant impediment is the need to augment algorithmic feasibility with system-level optimization across heterogeneous hardware and software stacks. Quantum resource estimation (QRE) plays a central role in this transition, yet existing approaches remain largely compilation-heavy or domain-knowledge-guided symbolic annotations, and tightly coupled to long-term fault-tolerant assumptions, limiting their topical applicability. In this work, we introduce AutoQuREO, an Automated framework for full-stack Quantum Resource Estimation and Optimization. AutoQuREO is built around four core novelties: (i) a flexible, user-defined abstraction of the quantum computing stack; (ii) a modular library of reusable stack components enabling rapid full-stack prototyping; (iii) surrogate modeling of layer-wise resources via algorithmic profiling and neuro-symbolic learning; and (iv) integrated multi-objective optimization that embeds QRE directly into deployment pipelines. Together, these design choices enable AutoQuREO to serve as a digital twin for quantum computing stacks, supporting the tractable exploration of complex design spaces. We demonstrate the capabilities of AutoQuREO through representative co-design case studies, including early-fault-tolerant quantum algorithms, small error correction codes, gate decomposition and variational training of parametric quantum circuits. These examples illustrate how AutoQuREO enables systematic discovery of unexploited resource trade-offs that are computationally intractable or abstruse using existing QRE tools. AutoQuREO is positioned as a general-purpose platform for advancing quantum technology readiness.

Effective implementation of high-level quantum gates is essential for practical quantum computing. To the best of our knowledge, we present the first reported 12-CNOT decomposition of the double qubit excitation operator, improving upon state-of-the-art (SOTA) implementations with 13 CNOTs. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (10), and lowest total circuit depth (16) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits.

Deep parameterized quantum circuits may remain sensitive to a parameter change while the observables retained by a learning model barely respond. We study this separation for a fixed computational-basis measurement. For a pure-state tangent, we compare the quantum Fisher information $F_Q$, the Fisher information $F_{\rm full}$ in the complete bitstring distribution, and the largest variance-normalized response $\mathcal I_{\mathcal A}$ available to a diagonal readout space $\mathcal A$. If the joint state--tangent frame is Haar random, we prove that the two successive information fractions are independent Beta variables whose means are $1/2$ and $r/(2^n-1)$, where $r$ is the centered dimension of the readout. Consequently, even the joint span of all computational-basis Pauli strings through any fixed weight $k$ retain only $O(n^k2^{-n})$ of the full-record information. Exact-statevector experiments across six circuit families show increasing finite-size agreement with this hierarchy in five nonconserving ensembles as the circuit depth grows. A number-conserving family departs strongly from the isotropic prediction even after correcting the support and readout rank, showing that rank alone is insufficient without tangent isotropy.

Classical simulation remains essential for developing and validating quantum algorithms, but its cost grows rapidly with circuit size. Tensor-network contraction can reduce this cost by exploiting circuit structure, although its efficiency depends strongly on the chosen contraction plan. On GPUs, plans with similar theoretical complexity may perform very differently because execution also depends on parallelism, reduction structure, memory traffic, and contraction geometry. We present a learning-to-rank framework for selecting efficient contraction plans before executing them. Each plan is represented by structural features derived directly from its sequence of pairwise contractions, and gradient-boosted rankers are trained from GPU measurements using listwise and pairwise objectives. We evaluate the resulting models on diverse circuit families, using separate in-distribution and circuit-family-shift test sets, and compare them with random and MinFill-based baselines. The learned rankers generally identify better plans, with the listwise model providing the strongest overall decision quality. We also study backend shift by comparing empirical plan orderings on two GPU architectures and evaluating the source-trained models on the second device without retraining. The rankings remain substantially, though not perfectly, stable across GPUs, and the models retain useful decision quality. These results support Learning to Rank as a practical way to reduce contraction-plan search, while showing that performance remains partly backend dependent.

Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $Ω(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{Ω(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.

Quantum software engineering is an emerging research field focusing on efficiently embedding the quantum programming paradigm into existing software ecosystems. A key aspect of this field is the realization of quantum algorithms using gate-based programming and the subsequent low-level optimization of the resulting quantum circuits, a process that is commonly performed by so-called transpilation pipelines. One significant challenge in these pipelines is determining which optimizations to apply to a given circuit. This decision is usually based on fixed default configurations that are uniformly applied to all circuits, frequently resulting in missed opportunities for more aggressive circuit optimization. In this work, we tackle this challenge by applying autotuning with supervised machine learning to develop an automated method for selection of transpiler passes. To train our machine-learning models, we employ feature-model based sampling to generate a representative dataset that examines how different combinations of Qiskit transpiler passes perform across thousands of circuits drawn from the state-of-the-art benchmarking suite MQT Bench. Using these data, we build a predictive model extension for the Qiskit transpilation pipeline that uses a machine learning model to automatically select combinations of transpiler passes aiming to achieve a maximum reduction in two-qubit gates. Our empirical evaluation shows that the combinations selected by our model are never outperformed by Qiskit's optimization levels, achieve on average an additional 19.1$\%$ - 32.4$\%$ reduction in two-qubit gates, and for some circuits finds reductions of up to $95.8\%$ in cases where Qiskit achieves no reduction at all.

Recent work suggests that relational database management systems (RDBMSs) can execute quantum circuit simulation by compiling the simulation into SQL workloads (primarily join-and-aggregate tensor contractions). While early results are promising, they largely focus on a narrow set of highly structured circuits and offer limited support for systematic database research, such as query optimization, physical design, and engine-level evaluation across a broad range of circuits. We present InferQ, a database-oriented benchmark for quantum circuit simulation. InferQ generates general, compositional circuits by assembling subcircuits from a set of circuit templates, emits each simulation task as an RDBMS-ready SQL workload, and extracts circuit and query features (static, graph, SQL, and dynamic) for workload characterization. InferQ also releases a large dataset of 202,975 circuits online, with a web-based viewer to support searching, filtering, and downloading circuits and feature records. In experiments across RDBMS engines (PostgreSQL, SQLite, DuckDB, and Umbra) and the widely used Qiskit Aer simulator, we find that RDBMSs achieve better peak memory usage than Qiskit Aer on more than 50% of the circuits generated by InferQ. Moreover, using InferQ features, lightweight machine learning models (linear and tree-based models) can accurately predict when SQL execution is preferable (with accuracy up to 95.6% for runtime and 97.4% for memory), enabling data-centric simulator selection and opening the door to principled optimization of SQL-based quantum circuit simulation.

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.

As quantum computing continually improves, ensuring the reliability and correctness of quantum libraries has become increasingly critical. To this end, many LLM-based fuzzing approaches towards quantum libraries have been proposed to uncover potential bugs. However, these methods still suffer from limitations such as insufficient flexibility and low efficiency, which hinder the progress of the quantum computing field. To address these challenges, we propose KQFuzz, a novel knowledge-guided fuzzer for quantum libraries. It leverages comprehensive codebase knowledge to ground LLM-based test generation, synergizing this with fitness-guided evaluation and two-level mutations to explore complex execution paths and trigger potential bugs. Firstly, KQFuzz introduces a novel prompting scheme tailored to quantum programs, which strategically incorporates knowledge of the codebase to efficiently generate high-quality quantum seed programs. Moreover, we develop evaluation and mutation strategies to handle the generated seed programs, facilitating efficient fuzzing execution while further enriching the diversity of the resulting test cases. We implement KQFuzz and conduct fuzzing on three popular quantum libraries, including Qiskit, PennyLane, and Cirq. Experimental results demonstrate that our approach significantly outperforms other state-of-the-art methods, with coverage improved by up to 18.44%. During the development of KQFuzz, we discovered 13 bugs, all of which have been confirmed and 12 have already been fixed by the developers.

We introduce a new class of fully-quantum Metropolis walks in which both the proposal and acceptance steps are intrinsically quantum. Unlike standard quantum walks obtained by quantizing classically efficient Markov chains, our algorithm employs Hamiltonian simulation as a quantum-native proposal mechanism, enlarging the class of quantum walks beyond classical counterparts. We target the problem of sampling from the low-temperature Gibbs distribution of classical dense Ising models, within a fixed error in total variation distance. This approach achieves about a cubic polynomial asymptotic advantage over previous quantum-walks, resulting in a total sixth-degree polynomial queries speedup compared to the best classical walk. This shows that speedups beyond the widely assumed quadratic limit are possible within the quantum walk formalism. We perform a complete fault-tolerant compilation of all algorithmic primitives and benchmark against CPU, GPU, and FPGA implementations of the best classical Markov chain. Under identical hardware assumptions, the resulting advantage runtime crossover is reduced from approximately $10^3$ years for conventional quantum walks to less than one day. These results identify fully-quantum Markov chains as a promising route toward practical quantum advantage.

Quantum state preparation is a key component of many quantum algorithms. Performing this step efficiently is essential for realizing practical quantum advantage in quantum chemistry applications. Iterative algorithms like ADAPT-VQE can produce shallow ground-state preparation circuits, but become computationally prohibitive for the larger molecules relevant to materials science and pharmaceutical development. Here, we introduce ADAPT-GQE, a generative AI framework that learns to synthesize ground-state preparation circuits for electronic structure calculations. We first use ADAPT-VQE to generate high-quality reference circuits, which are then used as targets for training models for circuit generation. Once trained, the model can efficiently propose and score circuits, enabling reinforcement learning (RL) to drive circuit generation accuracy beyond the accuracy of the ADAPT-VQE training data. This pipeline achieves order-of-magnitude reductions in circuit generation time relative to ADAPT-VQE while maintaining comparable or improved state-preparation accuracy. We demonstrate ADAPT-GQE on imipramine, a well-established tricyclic antidepressant that serves as a representative, challenging target for computational modelling in drug stability protocols. We execute generated circuits on Quantinuum Helios-1, representing a milestone for AI-generated quantum chemistry circuits on state-of-the-art quantum hardware. These results establish a pathway toward automated quantum circuit synthesis for utility-scale quantum computational chemistry.

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads to trainability issues. In this work, we investigate whether small, classically-emulated quantum circuit components can play a meaningful role within complex models, offering an alternative to purely classical convolutional architectures. To this end, we present a systematic study of the effectiveness of a Hybrid Quantum-inspired Convolutional Neural Network (HQiCNN) compared with a parameter-matched classical Convolutional Neural Network (CNN) that differs only in an intermediate dense neural layer. Both models are evaluated on two real-world medical datasets while systematically varying the different hyperparameters, ensuring a fair model comparison that is both dataset and hyperparameter independent. The results show that no architecture consistently dominates the other: the HQiCNN achieves its largest gains in intermediate-data regimes, whereas the CNN reaches the highest accuracies for the largest training sets in both datasets. Furthermore, removing entanglement produces comparable performance while enabling substantially better scalability of quantum simulations, and richer observable sets become beneficial only when sufficient training data are available. Finally, we propose two SHAP-based explainability tools for comparing the predictions between both models, $|SHAP|$IoU and $EMD_{pos}$ metric, to demonstrate that both architectures consistently attend to anatomically plausible regions. Thus, we provide a comprehensive benchmark showing that, under certain conditions, hybrid quantum-inspired models are an alternative that can offer benefits in practical tasks such as medical image classification.

While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.

Quantum circuit optimization for fault-tolerant computing requires exact functional equivalence while minimizing expensive non-Clifford resources such as T gates. We study this problem using a compact 44.8M-parameter encoder-decoder transformer with structured circuit tokenization, evaluating on parameterized circuits (2-6 qubits) and Clifford+T circuits (3-6 qubits). On parameterized circuits, a hybrid approach -- structure from the transformer, angles from classical optimization -- achieves median fidelity 1.000 on 3-6 qubit circuits. On Clifford+T circuits, where all gates are discrete and no post-processing is possible, the model learns valid syntax and accurate T-Count statistics, yet exact equivalence degrades sharply with target length -- from 88% on circuits with <=9 gates to near zero beyond 26 gates. We trace this failure to autoregressive drift: early-token divergence cascading irrecoverably through left-to-right decoding. Two levers partially mitigate the drift: inference-time strategies that generate multiple candidates and select via equivalence verification raise exact-match rates from 7% to 22.5%, while scaling training data by 2.5x pushes them to 39.5%. Yet the degradation with target length persists -- even with more data, exact equivalence drops from 94% on short circuits to under 4% beyond 26 gates. The contrast between settings is our central finding: when approximate outputs can be rescued by post-processing, the transformer succeeds; when exact discrete correctness is required, autoregressive drift limits reliability, with both inference-time search and data scaling as effective levers while training-side fine-tuning and model-level diversification are not.

Data re-uploading parameterized quantum circuits (DRU-PQCs) are universal function approximators, yet their expressivity produces oscillatory, non-convex loss landscapes that resist gradient-based optimization. We show that the primary optimization bottleneck in DRU-PQCs is not insufficient capacity but a structural failure mode we term Fourier locking (FL): because encoding weights and entangling layers are nonlinearly coupled, random initialization on high-frequency targets collapses the encoding parameters into spurious local minima. Two Fisher diagnostics characterize FL. The input-space quantum Fisher information $F_x$ measures the effective frequency content of the encoded state; the Fisher discriminant ratio of the measured features measures their alignment with the class labels. In two independent 50-seed experiments, the locking is literal: trapped circuits hold $F_x$ frozen for the entire run, while escaping circuits migrate their frequency content (direct training: $r_{pb} = -0.48$; curriculum: $d = 1.34$; both $p < 0.001$). The replicated signature is this spectral mobility, not any endpoint value of $F_x$, and trapped circuits retain a fully non-degenerate parameter-space QFIM ($r_{pb} \approx 0$): the failure is spectral misalignment of a responsive state, not a loss of geometric sensitivity. A frequency-staged homotopy protocol that paces the target frequency ($f: 1.0 \to 3.0$) convexifies the early loss landscape; escaping circuits raise $F_x$ in step with the curriculum, and the escape rate triples (18% vs. 6%). Fourier locking is a frequency-alignment problem, and its remedy is frequency pacing.

Data scarcity and class imbalance are persistent challenges in machine learning that degrade model generalization and introduce predictive bias. We present a hybrid quantum-classical framework for synthetic data generation using a Quantum Circuit Born Machine (QCBM) to address these limitations. The proposed approach exploits quantum mechanical properties -- superposition and entanglement -- within a parameterized variational quantum circuit to model complex probability distributions that are difficult for classical generative methods to capture. Experiments are conducted on two tabular benchmark datasets: the Iris dataset and the Telco Customer Churn dataset. Preprocessing includes normalization and PCA-based dimensionality reduction to enable efficient basis encoding for quantum circuits. The QCBM is trained by minimizing Kullback-Leibler (KL) divergence between real and generated data distributions using a gradient-based parameter-shift optimization rule. Augmenting training data with QCBM-generated synthetic samples at 40-50% of the minority class improves F1-score by approximately 5-15% and minority-class recall by 10-25%. Cross-domain evaluations (Train on Synthetic, Test on Real; and Train on Real, Test on Synthetic) reveal a performance gap of only 3-10%, indicating strong distributional fidelity. Comparative analysis against classical oversampling methods -- SMOTE, Borderline-SMOTE, KMeansSMOTE, and SVM-SMOTE -- shows that QCBM achieves competitive classification performance and produces lower Maximum Mean Discrepancy (MMD) on the Telco dataset, suggesting superior structural similarity in certain imbalanced settings. These findings establish QCBM as a viable complementary tool for data augmentation, particularly for low-dimensional structured tabular data with class imbalance.

An important task in quantum computing is unitary circuit synthesis compatible with physical hardware constraints. This problem has a natural hybrid structure as local single-qubit gates are continuous variables on the Lie group $SU(2)$ while the entangling circuit structure is discrete and hardware-dependent. In this work, we use generative models to perform quantum circuit synthesis incorporating both the natural $SU(2)$ manifold geometry of quantum gates and hardware constraints that determine the overall circuit structure. Our model comprises two components: a circuit skeleton selector that chooses an entangling circuit and a diffusion model that generates quantum gates on the given circuit template by performing diffusion on the curved manifold $\mathrm{SU(2)} \simeq S^3$ itself. We demonstrate this approach with unitary compilation of physically motivated three-qubit Hamiltonian simulation targets such as the Transverse Field Ising Model and the Heisenberg-XXZ Model and show that Lie group diffusion outperforms comparable baselines. The synthesised circuits can also be customised subject to constraints, which we demonstrate by producing circuits with large and small gate rotation angles for the same target unitary evolution. We also investigate the fidelity-complexity frontier of the synthesised gates to demonstrate that the circuit selector learns to select circuits that balance fidelity with complexity rather than collapsing onto the most expansive entangling template. These results demonstrate that Lie group diffusion provides a natural generative framework for hardware-aware quantum circuit synthesis.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading variational algorithm for combinatorial optimization on near term quantum devices. As circuit depth increases, the number of optimization parameters grows, making the search landscape increasingly nonlinear and difficult to optimize. Previous studies have shown that optimal QAOA parameters often lie on a low dimensional manifold that can be approximated using Principal Component Analysis (PCA) at shallow circuit depths. However, the effectiveness of PCA decreases at higher depths because the underlying parameter manifold becomes increasingly nonlinear. In this work, we investigate Kernel Principal Component Analysis (KPCA) with a radial basis function kernel as a nonlinear dimensionality reduction technique for QAOA parameter optimization. The model is trained using 200 graphs from each of 3 graph families, namely Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz, with graph sizes ranging from 7 to 10 nodes. Performance is evaluated on 30 test graphs containing 12 nodes at circuit depths 1, 2, 4, and 8. Experimental results demonstrate that KPCA consistently outperforms PCA at deeper circuit depths across all graph families. At depth 8, KPCA achieves approximation ratios above 0.86, while PCA declines to approximately 0.81 to 0.83. Both methods reduce the number of quantum circuit evaluations by more than 93 percent relative to unrestricted QAOA optimization. These findings suggest that nonlinear kernel methods more effectively capture the structure of the QAOA parameter manifold and provide a practical approach for scaling variational quantum optimization to deeper circuits.

The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.

Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. We observed that fidelity gains came with higher routed two-qubit counts and were concentrated in 5 qubit and 8 qubit circuit families; under the fixed tree action graph, all 10 qubit families favored SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)

Approximate tensor-network simulators enable classical simulation of quantum circuits beyond the reach of exact methods, but selecting optimal approximation parameters -- such as bond dimension thresholds -- remains a costly trial-and-error process. We present a family-aware neural architecture that predicts both the minimum approximation threshold required to achieve target fidelity and the expected wall-clock runtime for quantum circuit simulation, given only the circuit's OpenQASM description and execution context. Our key insight is that quantum circuits from different algorithmic families (e.g., QFT, Grover, VQE) exhibit fundamentally distinct simulation cost profiles due to their differing entanglement structures. We employ family-conditioned residual corrections -- additive, family-specific adjustments atop a shared backbone, drawing on established conditional computation techniques -- enabling the model to capture both universal circuit properties and algorithmic nuances. The architecture incorporates a pretrained family classifier (97.5% accuracy) and domain-informed algorithm fingerprint features derived from gate-composition heuristics. Evaluated on circuits spanning 7--130 qubits across 10 algorithm families, our system achieves 79.5% exact threshold accuracy (91.2% within one rung) and $R^2 = 0.82$ runtime correlation, with inference completing in approximately 50 ms -- replacing trial-and-error simulation runs that may take minutes to hours. Ablation studies confirm that family-aware modeling provides the single largest performance improvement (+3.2 percentage points), validating the hypothesis that algorithm family is a first-class feature for simulation cost prediction.

Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.

We adapt Microsoft's QuantumKatas -- a well-established quantum computing curriculum -- from Q# to Qiskit, the most widely-adopted quantum computing framework, and package it with an evaluation framework for systematic LLM assessment. The resulting benchmark comprises 350 tasks across 26 categories, spanning fundamental gates through advanced algorithms (Grover's, Simon's, Deutsch-Jozsa), error correction, key distribution, and quantum games. Each task includes a natural language prompt, canonical solution, and deterministic test verification via classical circuit simulation. By building on the QuantumKatas' proven pedagogical design rather than creating tasks from scratch, we inherit a principled difficulty progression and comprehensive concept coverage while contributing the framework adaptation, evaluation infrastructure, and empirical analysis. We evaluate 16 LLMs across 7 prompting configurations -- a total of 39,200 model runs -- to demonstrate the benchmark's utility. Three key findings emerge: (1) the benchmark effectively differentiates model capabilities, with best-configuration pass rates ranging from 32.3% to 83.1% and a 26.1 pp average gap between frontier and open-source models; (2) models perform well at implementing known algorithms (SimonsAlgorithm 82.1%, BasicGates 81.6%) but struggle with problem encoding (SolveSATWithGrover 34.4%, DistinguishUnitaries 40.0%); and (3) chain-of-thought prompting shows a modestly bimodal effect -- it is the best strategy for three models (two of them explicitly reasoning-tuned per vendor documentation) but degrades performance for the rest, leaving it mid-pack in aggregate (56.3% mean) behind few-shot-5 (57.8%). We release the benchmark, evaluation framework, and baseline results to support research on LLM capabilities in quantum computing.

We present a novel parameterized 4-qubit Eisert-Wilkens-Lewenstein (EWL) quantum game circuit for recommender systems in quadruple helix innovation ecosystems (academia, industry, government, and civil society). The local strategy operators $U_{i} = R_y(θ_{i})$ for each helix actor are directly tuned by normalized dominance weights extracted from real participant funding data (\texit{ecContribution}) in the European Commission CORDIS Horizon Europe database (project COVend, ID 101045956). The circuit employs a multi-qubit EWL entangler followed by parameterized local rotations, inverse entangler, and full measurement, achieving only 22 gates and circuit depth 11 while scaling as $O(n)$ for $n$-round helix communications. Measurement probabilities after the quantum game serve as recommender scores for disruptive versus sustaining innovation trends. These scores are subsequently mapped into the diagonal Dirac potential of a Dirac-Solow-Swan Hamiltonian, enabling time-evolution simulation of capital accumulation and bifurcation dynamics under disruptive innovation. Numerical experiments on real CORDIS quadruple-helix collaboration networks demonstrate the circuit's NISQ compatibility and its ability to forecast disruptive capital trajectories with high fidelity. The proposed framework bridges quantum game theory, parameterized quantum circuits, and relativistic economic growth models, offering a computationally efficient tool for innovation policy and strategic decision-making in complex socio-economic ecosystems. Complexity analysis and reproducibility are provided through open Qiskit implementations.

We propose a quantum sidecar architecture family for future hybrid AI training and inference. The central idea is not to store an entire Transformer in a small quantum memory, nor to claim one-shot collapse into a fully trained model or an optimal answer. Instead, we identify two physically distinct operating modes for quantum co-processors attached to classical large-model pipelines. The first is a stateful protected-register mode, in which a protected register stores a reusable quantum resource while an ancilla or temporary register performs QND-style readout. The second is a stateless reset-and-reprepare mode, in which each query prepares a task-conditioned quantum circuit, evolves over bounded training or inference control variables, measures candidate signals, resets the qubits, and repeats. We simulate the stateful mode using 2/4/6/8 protected-qubit density-matrix QND-style parity readout with one ancilla and a Qiskit cross-check. For the stateless mode, we include both an abstract candidate-update sampler and a circuit-level QAOA-style statevector sampler over structured candidate landscapes, followed by reset-overhead sensitivity analysis. The resulting framework positions quantum sidecars as bounded signal generators for optimizer-side sampling, adapter or expert selection, retrieval, routing, and reasoning-path proposal. As a speculative outlook, we introduce quantum weight-state sidecars: restricted quantum representations over model-control variables, not direct encodings of complete classical weight tensors.

Accurate salt-body delineation is essential for seismic interpretation because salt structures distort wave propagation, complicate velocity-model building, obscure reservoir geometry, and increase uncertainty in exploration and drilling decisions. Although hybrid quantum-classical models have shown competitive performance on small-scale image-classification tasks, their value for dense, pixel-level geophysical prediction remains largely untested. This work introduces quantum feature gating, a hybrid segmentation architecture that embeds a parameterized quantum circuit (PQC) at feature-fusion points within an encoder-decoder pipeline. A 4-qubit, 2-layer PQC with data re-uploading computes a learned convex combination of lateral and top-down features at each Feature Pyramid Network merge point. A global-average-pooling layer maps encoder features to a fixed 4-dimensional quantum input, decoupling the 72-parameter quantum budget from backbone size and image resolution. The method is evaluated on the 2018 TGS Salt Identification Challenge using 4,000 seismic images at 101 x 101 resolution, across two integration topologies, eight circuit variants, and six encoders with 8M to 118M parameters under five-fold cross-validation. In a controlled EfficientNetV2-L ablation at 256 x 256 resolution, replacing the three Quantum FPN Gates with element-wise addition while holding the encoder, loss schedule, splits, and threshold search fixed reduces mean IoU from 0.9389 to 0.8404, a 9.85 percentage-point gap. Inserting the same circuit as skip-connection attention in a custom U-Net improves IoU by 0.88 points over the SolidUNet baseline, showing that the PQC contribution depends on where and what it gates. These results provide controlled evidence that quantum feature fusion can improve dense seismic segmentation.

Trotter Suzuki product formulas are the standard route to Hamiltonian evolution on noisy intermediate-scale quantum (\NISQ{}) hardware, but their accuracy depends on three coupled choices: term grouping, product-formula order, and time-step allocation. Grouping and order are discrete, which makes direct gradient optimization infeasible and forces existing compilers to rely on static heuristics. We describe P-GONE, a method that combines a conditional diffusion model (D3PM + DDPM), a graph neural network (\GNN{}) encoder, and closed-loop REINFORCE fine-tuning to jointly learn grouping, order, and time-step optimization over a mixed discrete-continuous space. Under fidelity-matched conditions ($F \geq 0.95$), the method achieves circuit depth 86 versus 1673 for Qiskit fourth-order (ungrouped, Suzuki-4), about $19.4\times$ compression, and 141 for Paulihedral (first-order Trotter), about $1.6\times$ compression. At $T=0.90$ the method also beats the Qiskit group-commuting teacher (65 vs 103, $1.6\times$ compression), though at $T=0.95$ the teacher still leads -- a stratified pattern that points toward fidelity-aware fine-tuning. Under a standard depolarizing noise model, the method achieves noisy fidelity roughly $2\times$ the Qiskit fourth-order baseline (0.743 vs 0.380). Ablation shows a clear hierarchy: order learning $>$ time allocation $>$ grouping. Best-of-N sampling ($N=32$ is a practical sweet spot) and CFG guidance give flexible fidelity-depth trade-offs at inference. The method works well on structured Hamiltonians (TFIM, Heisenberg), but random Pauli Hamiltonians fail entirely at $T \geq 0.95$ -- a boundary that defines where the method applies.

Qubit routing is a fundamental problem in quantum compilation, known to be NP-hard. Its dynamic nature makes local routing decisions propagate and compound over time, making global efficient solutions challenging. Existing heuristic methods rely on local rules with limited lookahead, while recent learning-based approaches often treat routing as a generic sequential decision problem without fully exploiting its underlying structure. In this paper, we introduce QAP-Router, framing qubit routing based on a dynamic Quadratic Assignment Problem (QAP) formulation. By modeling logical interactions, or quantum gates, as flow matrices and hardware topology as a distance matrix, our approach captures the interaction-distance coupling in a unified objective, which defines the reward in the reinforcement learning environment. To further exploit this structure, the policy network employs a solution-aware Transformer backbone that encodes the interaction between the flow matrix and the distance matrix into the attention mechanism. We also integrate a lookahead mechanism that blends naturally into the QAP framework, preventing myopic decisions. Extensive experiments on 1,831 real-world quantum circuits from the MQTBench, AgentQ and QUEKO datasets show that our method substantially reduces the CNOT gate count of routed circuits by 15.7%, 30.4% and 12.1%, respectively, relative to existing industry compilers.

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically requires large input-output paired datasets generated by costly high-fidelity PDE solvers. Unsupervised operator learning frameworks alleviate data dependency but remain hindered by computational bottlenecks. To address this, we propose Neural Variational Quantum Linear Solver (NVQLS), the first hybrid quantum-classical operator learning framework leveraging the Legendre--Galerkin weak formulation. We critically resolve the sign ambiguity in VQLS energy minimization, preventing erroneous solution representations. Additionally, we introduce a neural embedding, a novel encoding scheme to map varying forcings and PDE coefficients into parameterized quantum circuit representations. These structural innovations provide theoretical computational complexity advantages under efficient state preparation schemes, while achieving superior accuracy compared to a representative classical baseline. Validations on 1D and 2D parametric PDEs under diverse boundary conditions demonstrate NVQLS's capability to simultaneously process varying inputs, offering a scalable unsupervised approach to quantum-enhanced operator learning.

We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.

In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter $γ$. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

Population pharmacokinetic/pharmacodynamic (PK/PD) modeling traditionally relies on classical ordinary differential equations to simulate drug dynamics. In this work, we reformulate a compartmental PK/PD model as an open quantum system and implement it using quantum circuits developed in PennyLane. Four pharmacological compartments (central, peripheral, effect-site, and response) are encoded using twelve qubits, with inter-compartmental transitions represented through controlled quantum operations that emulate stochastic dynamics. The framework is evaluated on Phase 1 clinical data using a quantum-enhanced stochastic approximation expectation-maximization (SAEM) approach. Compared with the classical implementation, the quantum model achieves substantially improved log-likelihood values, indicating stronger statistical fit while preserving identical parameter estimates, thereby validating numerical consistency and model interpretability. The quantum-based optimization converges faster in terms of iterations, although total runtime is increased due to current simulation overhead. The study demonstrates stable large-scale simulation performance and establishes a hybrid quantum-classical approach that maintains biological fidelity while improving statistical modeling capacity. The dataset and problem statement originate from the Quantum Innovation Challenge 2025, and additional details are provided via the associated link.

Quantum machine learning has emerged as a promising tool for pattern recognition, yet many audio-focused approaches still treat spectrograms as generic images and do not explicitly exploit their time-frequency structure. We propose Q-Patch, a quantum feature map tailored to audio that encodes local time-frequency patches from mel-spectrograms into quantum states using shallow, hardware-efficient circuits with adjacency-aware entanglement. Each selected patch is summarized by a compact four-dimensional acoustic descriptor and mapped to a four-qubit circuit with depth at most three, enabling practical quantum kernel construction under near-term constraints. We evaluate Q-Patch on an audio spoofing detection task using a controlled, balanced protocol and compare it with size-matched classical baselines. Q-Patch improves discrimination between bona fide and spoofed samples, achieving an area under the receiver operating characteristic curve (AUROC) of 0.87, compared with 0.82 for a radial basis function support vector machine (RBF-SVM) trained on the same patch-level features. Kernel-space analysis further reveals a clear class structure, with cross-class similarity around 0.615 and within-class self-similarity of 1.00. Overall, Q-Patch provides a practical framework for incorporating time-frequency-aware representations into quantum kernel learning for audio authenticity assessment in low-resource settings.

High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.

Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimensionality, representing a d-dimensional distribution with k resolution requires dk qubits and an unstructured parameterized circuit would express a unitary in an exponential operator space in the number of qubits, leading to vanishing gradients and poor convergence guarantees even at high depth. Vine copula decompositions are widely used to represent high dimensional distributions classically, showing high quality approximation in many important applications, such as financial modeling. We present Qvine, a vine structured ansatz for quantum circuits, that mirrors the vine decomposition to construct scalable quantum circuits with efficient trainability while achieving similarly high quality approximation for amplitude encoding distributions. For regular vines (R-vines), we show that the circuit depth scales at most quadratic in the dimension of the distribution, while for D-vines, as well as many practical R-vines, the circuit depth scales linear in the dimension. For 3-dimensional and 4-dimensional Gaussians and empirical joint stock price return distributions for selected stocks, our experiments show Qvines achieve high quality loading.

Quantum computing remains in the Noisy Intermediate-Scale Quantum (NISQ) era, where the performance is highly constrained to noise. Addressing the limitation often requires hardware-facing capabilities beyond gate-sequence circuit specification, including mid-circuit measurement and classical feedback for quantum error correction (QEC), precise timing control for dynamical decoupling (DD), and pulse-level waveform access for calibration. OpenQASM-3 was introduced to expose exactly these capabilities, providing a hardware-level programming interface. However, despite the rapid progress of large language models in code generation, there is still no dataset specifically designed to train and evaluate LLMs on OpenQASM-3 programs that involve its advanced hardware-oriented features. To address this gap, we introduce QASM-Eval, the first comprehensive dataset designed to train and evaluate LLMs on OpenQASM-3. Rather than focusing on quantum algorithm design or reasoning, QASM-Eval explicitly targets the language's hardware-facing features. QASM-Eval comprises an expert-verified test set of 100 tasks and a training set of 4,000 tasks, systematically covering classical logic, timing scheduling, pulse control, and complex real-world workflows. To automatically validate generated programs, we check syntax, quantum states and program timeline using an extended verifier. Our evaluation reveals that while state-of-the-art LLMs struggle heavily in OpenQASM-3 coding tasks, targeted fine-tuning on QASM-Eval yields significant gains. QASM-Eval provides a crucial benchmark and training foundation to accelerate the development of reliable LLM assistants for hardware-facing quantum programming in NISQ era. Data and code: https://github.com/fuzhenxiao/QASM-Eval

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.

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever for quantum optimization. We introduce ReaPER$+$, an annealed replay rule that transitions from TD error-driven prioritization early in training to reliability-aware sampling as value estimates mature, achieving $4-32\times$ gains in sample efficiency over fixed PER, ReaPER, and uniform replay while consistently discovering more compact circuits across quantum compilation and QAS benchmarks; validation on LunarLander-v3 confirms the principle is domain-agnostic. Furthermore we eliminate the quantum-classical evaluation bottleneck in curriculum RL by introducing OptCRLQAS which amortizes expensive evaluations over multiple architectural edits, cutting wall-clock time per episode by up to $67.5\%$ on a 12-qubit optimization problem without degrading solution quality. Finally we introduce a lightweight replay-buffer transfer scheme that warm-starts noisy-setting learning by reusing noiseless trajectories, without network-weight transfer or $ε$-greedy pretraining. This reduces steps to chemical accuracy by up to $85-90\%$ and final energy error by up to $90\%$ over from-scratch baselines on 6-, 8-, and 12-qubit molecular tasks. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization.

We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $δ_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $Φ_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes.

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.

Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.

Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs and mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum-classical variational classifier on the next generation firewall telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit flip noise. The implementation is fully reproducible, with time benchmarking and export of best found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.

The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow Matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.

We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with energy'' also expressed as a quadratic function of these states. Traditional quantum mechanics corresponds to a single quadratic constraint of wavefunction normalization with energy expressed as a quadratic form involving the Hamiltonian. When SQM represents states as unitary operators, the stationary problem becomes a quantum inverse problem with multiple applications in physics, machine learning, and artificial intelligence. Any stationary SQM problem is equivalent to a new algebraic problem that we address in this paper. The non-stationary SQM problem considers the evolution of the system itself, involving the same energy'' operator as in the stationary case. Two possible options for the SQM dynamic equation are considered: (1) within the framework of linear maps from higher-order quantum theory, where 2D-type quantum circuits transform one quantum system into another; and (2) in the form of a Gross-Pitaevskii-type nonlinear map. Although no known physical process currently describes such 2D dynamics, this approach naturally bridges direct and inverse quantum mechanics problems, allowing for the development of a new type of computer algorithms. As an immediately available practical application of the theory, we consider using a quantum channel as a classical computational model; this type of computation can be performed on a classical computer.

This paper develops a simulation-based framework for evaluating the energy implications of quantum and classical computing firms competing in a market with limited energy resources. We model providers as differentiated Cournot competitors whose feasible service capacity is induced by technology-specific energy scaling laws: polylogarithmic for quantum algorithms that achieve an equivalent computational target and polynomial for classical emulation. For symmetric groups of quantum and classical firms, the equilibrium reduces to a tractable two-equation system that supports large scenario sweeps over market size, technology mix, and hardware coefficients. We characterize the capacity-constrained Nash equilibrium, prove the existence of a demand scale beyond which quantum service becomes more energy efficient, and report numerical experiments calibrated to trapped-ion and Rydberg platforms. The results identify when quantum energy advantage is only asymptotic and when it becomes operationally relevant.