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Beyond QAOA: A Review of AI and Quantum Computing for Adaptive Combinatorial Optimization

Hoong Chuin LAU

arXiv:2610.11759v1quant-phcs.LGmath.OC

TL;DR

Practical quantum optimization workflows involve learned decisions around the QPU, but evidence is uneven across approaches. This review organizes 119 papers by learned decision and finds stronger evidence for AI-assisted quantum optimization than for quantum computation improving learned optimizers, with no broadly convincing M5 result.

  • Problem

    Quantum optimization workflows involve decisions around formulation, decomposition, execution, and QPU use, while the evidence for how AI affects them and how quantum computation affects learned optimizers is uneven.

    Source: §1 · pp. 2–3

  • Method

    The review organizes the literature by learned optimization decision across AI-for-QO, Q-for-AI, and AI–Quantum Co-Optimization, and grades evidence with an M0–M5 hierarchy.

    Source: §1 · p. 3, §1.1 · p. 3

  • Results

    Evidence favors AI-for-QO over Q-for-AI, and no paradigm has a broadly convincing M5 result.

    Source: §1.1 · pp. 3–4

  • Takeaways & Limitations

    Selective quantum use is an emerging design principle: learned controllers can decline QPU execution when its expected marginal value does not justify its cost.

    Source: §11.2 · p. 25

    The fast-moving literature and heterogeneous reported metrics preclude a quantitative meta-analysis.

    Source: §3.4 · p. 11

Abstract

from arXiv · show

Near-term quantum approaches to combinatorial optimization are limited by qubit counts, circuit fidelity, sampling cost, and the difficulty of encoding constraints, while machine learning is increasingly used to configure and control quantum optimization workflows. We call such workflows adaptive: decisions conventionally fixed in advance, from formulation and penalties to shot budgets, backends, and whether to invoke a quantum processor at all, are made by learned policies that respond to the instance, the progress of the solve, or the hardware. This review examines three paradigms, AI for quantum optimization, quantum for AI-driven optimization, and AI-quantum co-optimization, and organizes the literature by the decision being learned rather than by application. A structured review of 119 papers, 67 coded in detail, shows that the evidence is considerably stronger for AI-assisted quantum optimization than for the reverse direction: learning already reduces quantum evaluations, improves initialization, supports decomposition and penalty control, and mitigates noise, whereas evidence that quantum computation improves learned optimizers remains largely confined to small-scale simulation. Experimental controls are thin: 25 of 57 studies include no classical baseline, the quantum contribution is fully isolated in 10 of 24 studies where an ablation applies, and the median experiment uses 17 qubits. We introduce an M0-M5 evidence hierarchy, from simulation to matched-resource practical advantage, and find no broadly convincing result at the highest level. We argue that scaling is increasingly a systems problem: the question is not only whether a problem fits on a quantum processor, but how classical and quantum resources should be allocated across the optimization process. The review is aimed at researchers in quantum computing, machine learning, and operations research.

1 Introduction

The review treats optimization decisions around the QPU—not just the quantum routine—as learnable, and organizes work by the decision being learned. Its evidence is stronger for AI-assisted quantum optimization than for quantum-enhanced learned optimizers, with no broadly convincing matched-resource practical advantage.

1 Introduction

  • The review classifies work by learned optimization decision and distinguishes AI-for-QO, Q-for-AI, and AI–Quantum Co-Optimization.Adaptive pipelines learn decisions such as formulation, decomposition, execution settings, and whether to invoke a QPU, potentially responding to the instance, solve progress, or hardware state.Source: §1 · pp. 2–3

1.1 Summary of Main Findings

  • AI-for-QO has the strongest hardware-grounded evidence: 7 of 25 coded studies reach at least M2–M3, while 13 of 15 Q-for-AI studies remain at M1–M2.Only 2 of 15 Q-for-AI studies execute on physical hardware.Source: §1.1 · p. 3
  • 25 of 57 core studies lack any classical baseline, and the quantum contribution is fully isolated in just 10 of 24 studies where ablation applies.The median experiment uses 17 qubits, and only 15 of 57 studies report quantum evaluations or QPU calls.Source: §1.1 · p. 4
  • No paradigm has a broadly convincing M5 result; reported resource reductions or gains over quantum baselines are distinct from quantum advantage.The review defines M5 as matched-resource practical advantage.Source: §1 · p. 3, §1.1 · p. 4
  • Scaling constraints include penalty conditioning, slack variables, sparse feasible subspaces, transpiled two-qubit gate counts, and shot budgets—not qubit count alone.These factors often dominate performance on constrained problems.Source: §1.1 · p. 4
  • Recent systems treat selective quantum use as a design principle, letting a learned controller decline execution when expected marginal value does not justify its cost.The review also proposes an M0–M5 evidence hierarchy and benchmarking priorities including strong classical baselines, resource accounting, and cross-problem generalization.Source: §1 · p. 3, §1.1 · p. 4

2 Background

The background explains how optimization problems are encoded and sampled on quantum devices, then introduces quantum and classical learning methods used in hybrid workflows. It emphasizes practical costs, trainability limits, and the evidence needed to claim quantum advantage.

2.1 From Combinatorial Problems to QUBO and Ising Models

  • QUBO provides a canonical unconstrained binary form, so constraints are commonly encoded as penalties or slack variables that can increase the required qubit count.Penalty weights must discourage violations without overwhelming the objective; a standard position-based TSP encoding uses n^2 qubits before further constraint handling.Source: §2.1 · pp. 4–5

2.2 Qubits, Measurement, and Shots

  • Quantum devices return sampled bitstrings, making shots, sampling uncertainty, and transpiled two-qubit gate counts practical resource constraints.Two-qubit gates are typically the dominant source of error on current hardware.Source: §2.2 · p. 5

2.3 Quantum Annealing

  • Quantum annealing interpolates from a mixer Hamiltonian to a problem Hamiltonian, but small spectral gaps require slower anneals and practical runs return distributions of bitstrings.Anneal schedules, embeddings, and chain strength are tunable learning targets.Source: §2.3 · p. 6

2.4 The Quantum Approximate Optimization Algorithm

  • QAOA applies problem and mixer operators in p layers, while a classical optimizer selects its 2p angles using noisy, costly shot-based objective estimates.Greater depth can approximate adiabatic evolution, but also produces deeper, noisier circuits.Source: §2.4 · p. 6, Figure 2 · p. 7

2.5 Parameterized Quantum Circuits as Learning Models

  • Parameterized quantum circuits can encode inputs and produce measured features, scores, or action probabilities, replacing components of classical learned policies.Equivariant circuits preserve corresponding relabeling of graph inputs and outputs.Source: §2.5 · p. 7

2.6 Trainability, Noise, and Quantum Advantage

  • Barren plateaus and hardware noise can flatten training landscapes; quantum advantage requires outperforming the best available classical method under comparable resources.The review therefore distinguishes running on hardware or beating another quantum method from establishing advantage.Source: §2.6 · p. 7

2.7 Learning Methods for the Quantum Reader

  • The learning toolbox spans supervised GNN prediction, Bayesian surrogate search, RL for sequential choices, transfer learning, neural solution construction, and LLM-driven circuit or policy search.These methods take different inputs and produce predictions, configurations, policies, or constructed solutions.Source: §2.7 · p. 8

3 Scope and Review Methodology

The review examines learning across the quantum combinatorial-optimization workflow and evaluates what the literature’s experiments establish. It uses a structured search and coding protocol while noting limits on synthesis and review validity.

3.3 Research Questions

  • Seven research questions organize the review, and their answers are assigned to the pipeline taxonomy, paradigm surveys, problem-family synthesis, evidence assessment, and outlook.The questions cover intervention points, learned objects, benefits, transfer, quantum contribution, evidence strength, and autonomous hybrid optimization.Source: §3 · p. 8, §3.3 · p. 11

3.1 Relationship to Existing Reviews

  • The review analyzes the complete combinatorial-optimization process, asking what is learned, where quantum computation enters, what resources are used, and what experiments establish.Its scope is narrower in application domain but broader in workflow than neighboring reviews.Source: §3.1 · p. 9

3.2 Search, Screening, and Coding

  • The search retained 119 papers in the reference corpus, with 67 forming the evidence core coded in detail.Searches included three broad queries and problem-centered searches; the broad-query counts overlap.Source: §3.2 · p. 10
  • Coding records study methods, learned objects, settings, claimed benefits, strongest supported conclusions, and evidence maturity, alongside four reproducible evidence fields.The fields cover classical baselines, learned baselines, quantum-component ablation, and scale and resource reporting.Source: §3.2 · p. 10

3.4 Threats to Validity and Review Limitations

  • Heterogeneous reported metrics prevent pooled effect estimates, while fast-moving preprints and semantic-search terminology may limit coverage.Maturity levels and evidence fields were assigned by one coder, with AI-assisted first-pass coding checked against papers by the author.Source: §3.4 · pp. 11–12

4 A Pipeline Taxonomy for AI × Quantum Combinatorial Optimization

The review classifies AI–quantum optimization by the pipeline decision being learned, rather than by application. This makes distinctions between single-stage interventions and policies coordinating multiple stages visible.

4 A Pipeline Taxonomy for AI × Quantum Combinatorial Optimization

  • The pipeline runs from the instance through formulation, decomposition, encoding, solver configuration, and hardware execution to repair and reconstruction, with AI able to intervene at each stage.Execution feedback can close the loop; the taxonomy specifies the learned decision, typical AI methods, affected quantum component, and primary metric.Source: §4 · p. 12
  • The taxonomy distinguishes methods learning one stage while others stay fixed, quantum components embedded in learned models, and policies coordinating several stages.The review then reorganizes the literature by problem family.Source: §4 · p. 12

5 AI for Quantum Optimization

AI-for-QO methods learn decisions at individual stages of a quantum optimization pipeline while other stages remain fixed. Across those stages, learning can reduce search costs and support formulation, decomposition, and execution decisions, but does not remove trainability limits.

5 AI for Quantum Optimization

  • AI-for-QO methods learn one pipeline stage while holding the others fixed, covering parameter and query decisions, circuit design, formulation, decomposition, execution, and trainability.The usual comparator is an unassisted quantum routine, such as random initialization or a default schedule.Source: §5 · pp. 12–13

5.1 Parameter Prediction, Transfer, and Amortized Optimization

  • Learning QAOA parameters, transferring them across instances, and amortizing optimization can replace repeated from-scratch searches with prediction and residual fine-tuning.Approximation quality should be considered alongside circuit evaluations and predictor-training cost; learning pays off only beyond a break-even number of instances.Source: §5.1 · pp. 13–14

5.2 Query-Efficient Quantum Optimization

  • Reducing quantum evaluations is the main measurable benefit of query-efficient optimization, making hardware calls and shots primary outcomes rather than implementation details.Reported examples include faster, more stable parameter search and query-efficient optimization on a 127-qubit Ising problem.Source: §5.2 · p. 14

5.3 Circuit and Ansatz Design

  • Quantum architecture search extends learned assistance from parameter tuning to circuit structure, including gates, operator pools, depth, and connectivity.Search acceleration or circuit imitation does not by itself establish discovery of a new quantum algorithm.Source: §5.3 · p. 14

5.4 Formulation, Constraints, and Penalties

  • Constrained problems expose penalty, slack-variable, and feasible-state-density difficulties; formulation choices trade off qubits, coefficients, depth, and sampling difficulty.Adaptive penalty adjustment and learned penalty calibration are among the approaches described.Source: §5.4 · pp. 14–15

5.5 Reduction and Decomposition

  • Decomposition creates bounded quantum subproblems, but scalability also depends on classical coordination and whether its overhead outweighs the benefit.Subproblem size and allocation to the QPU are instance- and hardware-dependent.Source: §5.5 · p. 15

5.6 Noise Mitigation, Hardware Selection, and Solver Selection

  • Learning supports error mitigation, annealing-schedule design, minor embedding, and selection among hardware or solvers as their relative value varies with execution conditions.Learned post-processing has enabled QAOA optimization signals from deep compiled circuits on nonplanar graphs up to 40 qubits.Source: §5.6 · p. 15

5.7 Trainability Limits: Barren Plateaus and Noise

  • Learning can avoid poor initializations, restrict search, or reduce evaluations, but these gains do not show that barren plateaus have been eliminated.Trainability remains something to measure and report; barren plateaus and hardware noise can flatten optimization landscapes.Source: §5.7 · pp. 15–16

6 Quantum for AI-Driven Combinatorial Optimization

Q-for-AI places quantum computation inside a learned model or policy for combinatorial optimization, rather than using it merely to configure a quantum optimizer. The reviewed evidence supports selected architectural properties, but not consistent end-to-end gains over strong classical learned optimizers.

6 Quantum for AI-Driven Combinatorial Optimization

  • A method counts as Q-for-AI only when quantum computation changes the learned model, policy, representation, or inference process used for combinatorial optimization.Ordinary QAOA or VQE directly optimizing a QUBO does not qualify.Source: §6 · p. 16

6.1 Quantum Neural Combinatorial Optimization and Equivariant Policies

  • Quantum neural combinatorial-optimization models explore compact parameterizations and symmetry-aware architectures, but show no consistent end-to-end routing gains over strong classical neural optimizers.The quantum circuit is part of the learned policy, so any benefit must arise from its representation or inductive bias.Source: §6.1 · p. 16

6.2 Hamiltonian-Based Quantum Reinforcement Learning

  • Hamiltonian-based quantum reinforcement-learning models can train better than selected quantum baselines, but simulation experiments do not establish advantage over modern classical learned optimization.Outperforming another quantum ansatz supports a model-design claim, not practical quantum advantage.Source: §6.2 · p. 16

6.3 Quantum Attention, QAP Learning, and Contextual Optimization

  • Quantum attention and contextual learning studies demonstrate architectural substitutions and parameter efficiency in small settings, with no physical-QPU evaluation in the contextual study.Lee and Kwon report fewer trainable parameters than selected classical decision-focused baselines on 16- and 25-variable simulations.Source: §6.3 · pp. 16–17

6.4 Model Generalization Versus System Generalization

  • Model transfer across graph sizes in ideal simulation may degrade with finite-shot sampling, transpilation, and device noise; most Q-for-AI results establish earlier forms of transfer, not hardware or noise transfer.The review distinguishes transfer across instances, sizes, topologies, problem families, noise regimes, and hardware.Source: §6.4 · p. 17

7 AI–Quantum Co-Optimization: From Components to Solver Policies

AI–Quantum Co-Optimization treats solver orchestration as a sequential policy problem, coordinating interacting decisions as instance, search, hardware, and resource state evolve. The reviewed systems support selective quantum invocation, not general quantum superiority.

7 AI–Quantum Co-Optimization: From Components to Solver Policies

  • Co-optimization jointly adapts solver decisions to a changing state, unlike methods that learn one component while holding others fixed.The state includes the instance, search history, execution diagnostics, and remaining budget; the system-level objective accounts for solution gap, time, quantum calls, shots, and constraint violation.Source: §7 · pp. 17–18

7.1 Solver Selection and Resource Routing

  • Solver selection makes quantum computation one conditional option in an algorithm portfolio, selected using instance or execution features.Examples include predicting whether QAOA or a classical method is preferable for MaxCut and extending solver selection across a larger QUBO corpus.Source: §7.1 · p. 18

7.2 Learning Problem Structure and Optimization Dynamics

  • Learned problem structure and optimization controls couple subproblem design to quantum execution choices.Multiplier updates can alter subproblem structure and quantum difficulty, which should in turn inform execution decisions.Source: §7.2 · p. 18

7.3 Selective Quantum Local Search

  • Quantum actions were admissible in only about 16% of reduced repair contexts, and classical repair was better on average even there, though quantum repair helped in some matched-budget regimes.The results support treating quantum repair as a scarce heuristic resource selected by a learned controller.Source: §7.3 · p. 18

7.4 Resource-Aware Automation and Agentic Policy Search

  • Resource-aware automation can route unsuitable configurations away from quantum execution, while AutoQResearch searches conditional solver policies within externally specified spaces and evaluation protocols.AutoQResearch uses a staged scout–promote–confirm procedure; its evidence does not establish autonomous algorithm discovery.Source: §7.4 · pp. 18–19

7.5 Boundary Cases

  • DQAOA-GPT generates circuits for decomposed subproblems, but its decomposition is random rather than jointly learned, so it is classified as AI-assisted circuit synthesis.The review reserves co-optimization for methods that adapt multiple solver decisions jointly or sequentially.Source: §7.5 · p. 19

8 Problem-Centered Synthesis

The problem-centered synthesis compares families by their significance, dominant approaches, bottlenecks, and research opportunities. It finds that validation is often concentrated on small, unconstrained problems, while evidence for constrained problems with operational value is thinner.

8.1 MaxCut and MIS

  • MaxCut enables controlled studies of parameter prediction, transfer, Bayesian optimization, architecture search, and noise mitigation, but misses many feasibility and modeling challenges of constrained optimization.MIS and clique problems bring feasibility, recursion, and compression into focus [35] [73].Source: §8.1 · p. 19

8.2 TSP and VRP

  • Routing formulations require O(n^2) binary variables before capacity, fleet, or time-window constraints, favoring modular methods over monolithic quantum optimization.Prominent approaches emphasize sequential policies, decomposition, learned assignment, local repair, and resource-aware execution [44] [55] [68].Source: §8.2 · p. 19

8.3 Knapsack and MDKP

  • Knapsack models expose inequality-constraint challenges in compact experiments, but fewer qubits do not guarantee lower total computational cost.Relevant comparisons include slack variables, custom penalties, QRAO, qubit-efficient encodings, and learned constraint control [40] [41] [42] [58]; measurement, decoding, or repair may add costs.Source: §8.3 · p. 19

8.4 QAP, Assignment, and Contextual Optimization

  • Assignment supports per-instance variational optimization and amortized prediction across instances, helping separate optimization advantage from learning advantage [61].Source: §8.4 · p. 20

8.5 Scheduling and Resource Allocation

  • Scheduling remains under-represented despite its value for external validity, and its distinct precedence, resource-coupling, and feasibility structure makes it a generalization stress test.The review notes differentiable quantum architecture search for job-shop scheduling [74] and a broader literature with dedicated reviews; evidence across problem families is thinnest for constrained problems with operational value.Source: §8.5 · p. 20

9 Evidence Maturity: What Has Actually Been Demonstrated?

The review grades evidence with an M0–M5 hierarchy and finds the evidence stronger for AI-assisted quantum optimization than for quantum-enhanced learned optimization. It argues that scaling and evaluation depend on the whole hybrid system, not only the quantum routine.

9.1 The Asymmetry of the Literature

  • Seven of 25 AI-for-QO studies reach at least M2–M3; learning reduces QPU evaluations, improves robustness, or lowers execution overhead, but 18 of 25 lack a classical solver comparison.These studies primarily compare learning against unassisted quantum routines, so they show that learning can make quantum optimization cheaper, not that the resulting pipeline is competitive with classical optimization.Source: §9.1 · p. 21
  • Thirteen of 15 Q-for-AI studies remain at M1–M2, and matched-size quantum-layer ablations are rare, leaving evidence stronger for architecture and inductive bias than practical superiority.Only 5 of 15 studies with applicable ablations replace the quantum layer with a matched-size classical layer; only two studies execute on physical hardware.Source: §9.1 · pp. 21–22
  • Co-optimization includes credible examples across solver selection, decomposition, shot allocation, local quantum search, and policy automation, but no paradigm has a broadly convincing M5 result.Half of the coded co-optimization studies include hardware-grounded components.Source: §9.1 · p. 22

9.2 Why the Evidence Stalls: Scaling as a Systems Problem

  • The median study uses 17 qubits, but scaling also faces interacting constraints from circuit depth, shot budgets, feasibility, penalties, latency, repair, and trainability.Qubit-efficient encodings, slack-free penalties, and decomposition can trade smaller quantum width for harder repair, changed objective landscapes, or coordination overhead; real-hardware examples also show noise and sparse feasible states can limit useful sampling [76].Source: §9.2 · pp. 22–23

10.1 Report System-Level Resources

  • Among 57 core studies whose resources could be coded, 19 reported shot or sample budgets, 24 reported no shots, and only 10 reported both quantum evaluations or QPU calls and shot information.Source: §10.1 · p. 23

10.2 Separate Hybrid-System Benefit from Quantum Contribution

  • A hybrid solver's improvement over a baseline does not establish that its quantum component contributes; evaluation should test system benefit and quantum marginal contribution separately.The first does not imply the second.Source: §10.2 · p. 24

10.3 Use Strong Baselines and Matched Decision Budgets

  • Twenty-five of 57 core studies include no classical baseline, while only 10 of 24 applicable studies run a full quantum ablation.The review calls for strong classical competitors, matched decision budgets, and separate ablations of learned and quantum components; 9 studies run partial ablations and 5 run none.Source: §10.3 · p. 24

10.4 Account for Amortization and Generalization

  • When models are reused, papers should report the break-even instance count where estimable and specify whether generalization tests cross instances, sizes, topologies, problem families, noise regimes, or hardware.The break-even number is denoted N ⋆ in Equation (8).Source: §10.4 · p. 24

11 Open Problems and Outlook

The open problems turn gaps in evidence into questions about learned formulations, selective QPU use, generalization, problem diversity, shared benchmarks, and trustworthy agentic search. The outlook describes a shift toward policies that select solvers and resources based on the current search state.

11.1 Learning Formulations, Not Only Parameters

  • A learned controller could select formulation jointly with circuit parameters, testing whether it improves feasible-sample rate and optimality gap at fixed qubit and shot budgets over tuning a fixed formulation.The proposed evidence is cross-problem testing followed by hardware validation, with an ablation that freezes the formulation.Source: §11.1 · p. 25

11.2 Learning When Not to Use a QPU

  • Most pipelines send every eligible subproblem to the QPU, although only a few systems let controllers decline quantum execution and the clearest evidence comes from one study.The proposed test compares a learned invocation policy against always-classical and always-quantum variants under matched total budgets, reporting selection frequency and marginal contribution.Source: §11.2 · p. 25

11.3 Closing the Gap Between Model and System Generalization

  • Thirteen of 15 Q-for-AI studies remain at M1–M2, while transfer demonstrated in ideal simulation can degrade under finite shots, transpilation, and noise.The open test is whether symmetry-aware quantum policies retain parameter savings on hardware and outperform matched classical neural optimizers, with training costs and break-even point reported.Source: §11.3 · pp. 25–26

11.4 Moving Beyond MaxCut

  • Much controlled evidence concerns unconstrained MaxCut, while routing, assignment, scheduling, and knapsack involve sparse feasibility, repair, or stochasticity.Cross-problem studies should report feasibility alongside solution quality to test generality across constraint structures.Source: §11.4 · p. 26

11.5 Shared Environments for Evaluating Orchestration

  • No screened study reaches M5, and the review identifies the lack of shared environments for comparing hybrid policies with strong classical solvers under matched resources as one reason.Proposed environments would cover multiple problem families, solvers, quantum algorithms and backends, and explicit budgets, with results following the reporting checklist.Source: §11.5 · p. 26

11.6 Trustworthy Agentic Experimentation

  • Agentic solver search can overfit its evaluation harness, so trustworthy results require held-out instances, explicit search budgets, replay, independent confirmation, provenance, and ablations.The proposed evidence is gains that persist on held-out instances and in independent replications, with search budget reported.Source: §11.6 · p. 26

11.7 Outlook

  • Early work explored mixers, encodings [39], qubit-efficient relaxations [4] [40], and slack-free penalties [41]; hardware limits motivated decomposition and learned preprocessing [76] [38] [43], followed by state-conditioned controls and policy search [70] [66] [71] [72].The central question becomes which formulation, subproblem, solver, and resource to use at each search point; the open problems seek evidence at M4 and M5 rather than M1 and M2.Source: §11.7 · p. 27

12 Conclusion

The conclusion describes unequal maturity across AI-for-QO, Q-for-AI, and co-optimization, and argues that near-term progress depends on system-level decisions about when quantum execution is worthwhile.

12 Conclusion

  • AI-for-QO has credible evidence across several pipeline components, while Q-for-AI remains exploratory and rarely shows practical superiority over strong classical learned optimization.Co-optimization is beginning to connect solver selection, decomposition, shot allocation, local quantum search, hardware-aware control, and policy search.Source: §12 · p. 27
  • The evidence remains shallow, and near-term systems should favor selective QPU use over routing every eligible subproblem to quantum hardware.The review frames progress as identifying subproblems and execution regimes where quantum computation's marginal value exceeds its added cost.Source: §12 · p. 27

Data Availability

  • The accompanying spreadsheet provides coding for all 119 papers and full evidence coding for the 67-paper evidence core, with counts and maturity levels reproducible from its entries.Its Evidence Coding sheet records evidence fields and supporting passages; its Counts sheet computes reported counts.Source: Data Availability · pp. 27–28

A Evidence-Matrix Coding Scheme

The evidence matrix records descriptive fields for the core studies and applies fixed-category evidence fields to every non-survey core study, enabling reported counts to be recomputed.

A Evidence-Matrix Coding Scheme

  • The coding scheme has descriptive Tier 1 fields and fixed-category Tier 2 fields, which are coded for every non-survey core study.For Tier 2, “not reported” means the paper was read and the information was absent; “not checked” means the full text was unavailable, and unchecked studies are excluded from that field's denominator.Source: A Evidence-Matrix Coding Scheme · p. 32, Table 7 · p. 32
  • The matrix records what is learned, training regime, test or generalization regime, and problem size, including whether tests cross instances, sizes, topologies, problems, noise, or hardware.Learned objects include parameters, circuit structure, penalties, decomposition, shot budget, backend, solver choice, repair action, and conditional solver policy.Source: A Evidence-Matrix Coding Scheme · p. 33
  • Outcome fields record solution quality, feasibility, runtime or cost, claimed benefit, evidence-supported conclusion, and the strongest directly supported M0–M5 maturity level.The maturity scale runs from conceptual evidence and ideal simulation through generalization, hardware validation, end-to-end hardware-grounded workflow, and matched-resource practical advantage.Source: A Evidence-Matrix Coding Scheme · p. 33
  • Baseline fields distinguish classical non-learned competitors from classical learned baselines and record whether AI or quantum contributions are isolated by ablation.A quantum ablation asks whether the quantum component is replaced with a classical counterpart and compared; partial ablations lack matched size or budget or cover only some experiments.Source: A Evidence-Matrix Coding Scheme · pp. 33–34
  • Resource and execution fields capture qubit counts, device class, shots, quantum evaluations, runtime or cost, and evidence under noise, calibration variation, compilation, or physical hardware.The scheme also records code, data, seeds, hyperparameters, and implementation details when available.Source: A Evidence-Matrix Coding Scheme · p. 34
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