Quantum advantage claims in chemical dynamics are difficult to evaluate when critical assumptions---model reductions, discretizations, Hamiltonian access models, numerical precision, and validation practices---are implicit.Focusing on discretized diabatic nonadiabatic Hamiltonians $H_{\mathrm{dia}}({Q}) = T_Q\otimes \mathbb{I}_N + V_{\mathrm{dia}}({Q})$, we propose a unified theoretical and methodological framework that standardizes:(i) qubit register encodings and physical-subspace embeddings including a leakage diagnostic when dimensions are not powers of two;(ii) Hamiltonian access models, i.e., explicit decompositions versus sparse-oracle access with fixed-point value semantics;(iii) instance-parameterized resource envelopes for Hamiltonian simulation and observable estimation;(iv) an additive error-budget ledger separating modeling/truncation error from oracle precision, unitary simulation error, estimation error, leakage, and hardware noise; and(v) a benchmark problem family $\mathcal{P}_{\mathrm{nonad\,chem}}$ together with prototype instance ladders and a reporting checklist for matched classical--quantum comparisons.To support reproducibility without requiring software dependencies, we further specify a lightweight intermediate representation (IR) as a proposed data standard for nonadiabatic benchmark instances, including units, conventions, discretizations, embeddings, access declarations, and precision metadata.This paper is intentionally free of numerical results and implementation claims; it is a proposed baseline intended to make future algorithmic and experimental studies comparable and reviewable.
Quantum advantage claims in chemical dynamics are difficult to evaluate when critical assumptions---model reductions, discretizations, Hamiltonian access models, numerical precision, and validation practices---are implicit.Focusing on discretized diabatic nonadiabatic Hamiltonians Hdia(Q)=TQ⊗IN+Vdia(Q), we propose a unified theoretical and methodological framework that standardizes:(i) qubit register encodings and physical-subspace embeddings including a leakage diagnostic when dimensions are not powers of two;(ii) Hamiltonian access models, i.e., explicit decompositions versus sparse-oracle access with fixed-point value semantics;(iii) instance-parameterized resource envelopes for Hamiltonian simulation and observable estimation;(iv) an additive error-budget ledger separating modeling/truncation error from oracle precision, unitary simulation error, estimation error, leakage, and hardware noise; and(v) a benchmark problem family Pnonadchem together with prototype instance ladders and a reporting checklist for matched classical--quantum comparisons.To support reproducibility without requiring software dependencies, we further specify a lightweight intermediate representation (IR) as a proposed data standard for nonadiabatic benchmark instances, including units, conventions, discretizations, embeddings, access declarations, and precision metadata.This paper is intentionally free of numerical results and implementation claims; it is a proposed baseline intended to make future algorithmic and experimental studies comparable and reviewable.
Quantum computation is an attractive front for many problems that are intractable for computers today. One such problem is nonadiabatic quantum molecular dynamics, where quantized internal states coupling to parameterized modes result in a Hamiltonian resistant to oracle-based models and spectral decomposition. This dissertation applies diabatic Hamiltonian operators directly to the computational basis as first-quantized split-operator propagators, validated with dynamic observables including absorption and recurrence spectra, scattering cross-sections, population dynamics, and quantum scars. Circuits are derived and specified, with focused circuit optimization in multi-mode and multi-channel extensions, including multivariate potential energy terms and graph theoretic optimization from molecular symmetry. Resource estimation shows circuit depth advantage against QROM-loading architectures on a fault-tolerant scale, and a quantitative comparison against quantum signal processing variants confirms that a Trotter-based architecture retains a scalable T-gate advantage. Expanding beyond electronic states demonstrates that duality between finite basis and discrete variable representations permits congruent structural decompositions into quantum circuits, expanding the use of multi-channel dynamics far beyond chemistry.
Abstract Quantum machine learning (QML) has attracted growing interest because quantum states and circuits may provide new representational primitives for learning, yet progress remains constrained by noisy intermediate-scale quantum (NISQ) hardware and heterogeneous evaluation practices. This article presents a critical review of recent QML architectures and representative empirical and theoretical studies, with emphasis on work published since 2022 alongside selected seminal references. To improve comparability, “quantum advantage” is assessed in three distinct senses: computational scaling under stated input-access assumptions, empirical predictive performance in the benchmark setting considered, and resource efficiency at a fixed budget accounting for both classical compute and quantum execution, including shot costs. Organized by architecture family and application domain, the review analyzes how baseline strength, hyperparameter optimization, preprocessing, and budget reporting shape conclusions. Overall, quantum feature maps and kernels, as well as variational (often hybrid) pipelines, can be competitive on selected small- to medium-scale benchmarks, but robust end-to-end evidence for a general practical advantage remains limited. Reported gains are often sensitive to budget matching and may be dominated by measurement overheads, dataset and preprocessing effects, and training instabilities. The review concludes that credible progress requires standardized benchmarking, transparent end-to-end resource accounting, and hardware-centered evaluations that test scalability and robustness beyond toy regimes.
Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire applications, have been proposed over the years. Objective comparisons are further hampered in practice as different variations of the same metric are used, and the data disclosed together with a reported metric value is often not sufficient to reproduce the measurements. In this poster, we present our recent article, where we address these challenges by providing a review of metrics and benchmarks for quantum computers [1], including 1) a comprehensive collection of benchmarks allowing holistic comparisons of quantum computers, 2) a consistent format of the definitions across all metrics including a transparent description of the methodology and of the main assumptions and limitations, and 3) a reproducible approach by linking the metrics to open-source software used to evaluate them . We identify five areas where international standardization working groups could be established, namely: i) the identification and agreement on the categories of metrics that comprehensively benchmark device performance; ii) the identification and agreement on a set of well-established metrics that together comprehensively benchmark performance; iii) the identification of metrics specific to hardware platforms, including non-gate-based quantum computers; iv) inter-laboratory comparison studies to develop best practice guides for measurement methodology; and v) agreement on what data and software should be reported together with a metric value to ensure trust, transparency and reproducibility. We provide potential routes to advancing these areas. We expect that this work will accelerate the progress of quantum computing hardware towards quantum advantage. [1] D. Lall et al., A Review and Collection of Metrics and Benchmarks for Quantum Computers: Definitions, Methodologies and Software, arXiv:2502.06717.
The integration of quantum computing and artificial intelligence (AI) constitutes a bidirectional synergy that is reshaping both disciplines. This review investigates the reciprocal relationship in which AI addresses foundational challenges in quantum computing, while quantum computing offers the potential to advance machine learning beyond classical constraints. Recent advancements exemplify this interaction: Google DeepMind’s AlphaQubit neural network decoder has achieved state-of-the-art quantum error correction, improving performance by 6% over tensor networks and 30% over correlated matching methods. Additionally, quantum neural networks have demonstrated exponential improvements in sample complexity for specific learning tasks. This review systematically examines the current landscape of quantum-AI integration across three primary dimensions. First, it addresses AI-enhanced quantum systems, such as transformer-based error correction, reinforcement learning for circuit optimization, and AI-driven hardware calibration. Second, it explores quantum-accelerated machine learning algorithms, including variational quantum neural networks, quantum generative adversarial networks, and quantum reinforcement learning. Third, it evaluates industry deployments in sectors such as life sciences, financial services, climate modeling, and pharmaceutical development. Notable examples include IonQ’s quantum chemistry simulations, which achieved 40% efficiency improvements in carbon capture material design; St. Jude’s identification of KRAS protein inhibitors using quantum machine learning with experimental validation; and JP Morgan Chase’s implementation of quantum portfolio optimization. The analysis indicates that the field has advanced from preliminary demonstrations to production-grade applications, especially in drug discovery and molecular simulation, where quantum computing offers measurable benefits. Nevertheless, several challenges remain, including barren plateaus in variational algorithms, scalability constraints in current noisy intermediate-scale quantum (NISQ) devices, requirements for real-time decoding speed, and the necessity for fault-tolerant quantum computing (FTQC) systems. IBM’s 2029 roadmap, which targets 200 logical qubits capable of executing 100 million gates, together with progress in high-rate quantum low-density parity-check codes, outlines a trajectory toward practical fault tolerance. This review makes two principal research contributions: Comprehensive Evaluation Framework for Quantum Advantage Assessment: We establish the first systematic, integrated methodology for determining quantum computing feasibility that combines problem characterization, resource estimation, quantum advantage assessment, and quantum algorithm paradigm selection. This framework consolidates criteria scattered across academic literature and industry practice into a unified decision-making tool applicable across chemistry, optimization, machine learning, and simulation domains. The framework addresses a critical industry need: enabling non-expert practitioners (chemists, financial analysts, materials scientists) to objectively assess quantum computing suitability without requiring deep quantum expertise. Novel Quantum Resource Optimization Algorithms: We present three concrete algorithmic contributions advancing quantum-AI integration: • Data Encoding Efficiency Algorithm that automatically selects optimal qubit encoding strategies (amplitude vs. angle encoding) minimizing total quantum resource consumption • Error Budget Optimization Algorithm that iteratively determines optimal quantum error correction code distance balancing logical error rate targets against physical qubit overhead • Real-time Hardware Specification Aggregation from multiple quantum cloud platforms (IBM Quantum, Amazon Braket, Google, IonQ) enabling dynamic feasibility assessment as hardware capabilities evolve Combined, these contributions establish quantum computing advantage assessment as a rigorous, data-driven discipline rather than ad-hoc expert judgment. The framework enables strategic quantum computing investment decisions, accelerates problem identification for early quantum utility, and provides a reference methodology for standardizing quantum advantage evaluation across academia and industry. This review synthesizes insights from recent academic literature, industry implementations, and expert perspectives to deliver a comprehensive assessment of quantum-AI synergies grounded in this evaluation framework. The mathematical foundations, ranging from quantum Fourier transforms to Gaussian processes, are examined. Best practices for researchers and practitioners are also outlined. The findings suggest that, although universal quantum advantage has not yet been realized, domain-specific quantum-AI applications in chemistry, optimization, and sensing are achieving practical utility in 2024-2025. This development marks a significant transition from theoretical potential to commercial realization, informed by rigorous evaluation methodologies.
A robust definition of quantum runtime is essential for assessing the performance of quantum algorithms and claims of quantum advantage. While for most classical hardware the total runtime is well approximated by computation plus a weakly varying constant, on current quantum hardware a clean experimental separation between "pure computation" and "overhead" is often not justified. Consequently, conventional quantum runtime analyses excluding substantial system-level overheads can lead to biased performance assessments. In this work we introduce experimentally grounded, end-to-end definitions of quantum runtime for digital and analogue quantum computers, together with a methodology for selecting strong classical baselines for quantum-classical runtime comparisons. Within this framework, we evaluate recent claims of quantum advantage in annealing and gate-based algorithms. We examine three representative case studies. First, we revisit annealing for approximate QUBO problems PRL 134, 160601 (2025), which employs a well-motivated time-to-ε metric but effectively uses annealing time as a proxy for runtime. Second, we analyze a restricted implementation of Simon's problem PRX 15, 021082 (2025), where the favorable scaling in oracle calls is undisputed; however, we show that the estimated runtime of the quantum experiment is approximately two orders of magnitude slower than a tuned classical baseline at the tested sizes. Finally, we find that the runtime advantage of the BF-DCQO hybrid algorithm arXiv:2505.08663 is not observed under more comprehensive benchmarking. Therefore, on current NISQ hardware, runtime-based quantum advantage has not yet been demonstrated under experimentally grounded performance metrics, and credible claims require careful time accounting, appropriate performance measures, and properly chosen classical reference implementations, as discussed in this work.
Abstract Quantum optimization has become a leading application for near-term quantumcomputing, and yet many publications compare algorithms against idealizedassumptions and small toy benchmarks. This limits the interpretability, reproducibility,and practical relevance of reported performance gains, particularlyin the noisy intermediate-scale quantum (NISQ) era. In this work, we presenta systematic literature review that investigate quantum optimization beyondtoy benchmarks. Following established SLR protocols, we analyze the literaturealong multiple methodological dimensions, including algorithmic approach,benchmark realism, encoding strategies, hybrid quantum-classical workflows,hardware and noise modeling, evaluation metrics, and reporting practices. Weintroduce a unified taxonomy that captures the interaction between problemformulation, encoding overhead, noise-aware execution, and hybrid optimizationloops. In addition, we propose a reproducibility checklist and scoring rubric toassess reporting completeness and experimental rigor across studies. Instead ofdeveloping new quantum optimization algorithms or making theoretical quantumadvantage claims, the main contribution of this work is that it providesa methodological analysis on benchmarking realism and encoding or evaluationpractices as well as reproducibility rigor in NISQ-era quantum optimization studies.Our review uncovers a continued chasm between algorithmic innovation andevaluation maturity, with the number of publications and diversity of methodsgrowing without corresponding growth in standardized benchmarks, strongclassical baselines, noise-consistent evaluation, or reproducibility.