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Testing and Verification of Quantum Compilers through Assurance Contracts and Evidence

Furqan Nasir, Muhammad Arif Shah, Iftikhar Alam

arXiv:2610.00255v2cs.SEcs.ET

TL;DR

Quantum compiler assurance needs semantic relations and observations that match the intended use and delivered interface, but assurance methods support different claims and applicability conditions. This survey synthesizes those methods and their evidence, concluding that selection must be conditional and that the reviewed studies do not establish a common effectiveness ranking.

  • Problem

    Compiler assurance must relate intended program meaning to executable artifacts and delivered interpretation, while test and verification claims depend on explicit semantics and observations.

    Source: §1 · pp. 1–2

  • Method

    The survey compares assurance mechanisms through a source-linked matrix that distinguishes formal guarantees, empirical findings, analytical deductions, and proposed practice.

    Source: §1 · p. 2

  • Results

    The evidence supports conditional method selection based on obligations, applicability, and observations, rather than a common effectiveness ranking.

    Source: §6.5 · p. 22, §7.1 · p. 22

  • Takeaways & Limitations

    A well-defined compiler claim must specify its requirement, semantic relation, input conditions, interface boundary, and observations.

    Source: §7.1 · p. 22, §10 · p. 30

    Cross-study inference is constrained by heterogeneity in circuit families, compiler versions, numerical policies, resource settings, and fault definitions.

    Source: §9.3 · p. 30

Abstract

from arXiv · show

Quantum compiler assurance requires a semantic relation that matches the intended use and observations that can expose violations at the delivered interface. This critical integrative survey compares verified transformations, equivalence checking, differential and metamorphic testing, property-based testing, and evidence for assurance across revisions. A source catalogue and focused extraction matrix distinguish formal guarantees, reported empirical findings, analytical deductions, and proposed practice. A recorded coverage update and source-level selection decisions make the review auditable within its declared scope. Four documented failure cases connect conditional applicability, parameter association, termination, and phase conventions to method selection. A worked example involving layout metadata, parameter bindings, and ancillary qubits demonstrates why validating a circuit under a reconstructed interpretation can leave the delivered interface unchecked. An illustrative revision scenario then separates fault detection from change attribution. The resulting guidance specifies applicability, complementary observations, and treatment of inconclusive outcomes. Published bug counts, mutation results, and processing benchmarks support different claims and do not establish a common effectiveness ranking. The proposed regression architecture remains unevaluated as a complete system; its practical value requires controlled comparisons on independently adjudicated compiler-change events.

1 Introduction

Quantum compiler assurance must connect semantic preservation to the delivered artifact and its interpretation, while distinguishing correctness evidence from performance evidence. This survey compares assurance mechanisms and proposes a conditional procedure for choosing evidence, including across revisions.

1 Introduction

  • An assurance claim must specify the requirement and evidence, since semantic validity, executable interpretation, and performance objectives are distinct.Layout, parameter bindings, and result records can affect correct use; a resource trade-off may be intentional.Source: §1 · pp. 1–2
  • Quantum assurance must account for context-sensitive phase, input initialization, measurement choices, parameter domains, and dynamic-circuit records.A phase irrelevant for an isolated operation can become observable under coherent control.Source: §1 · p. 1
  • Verified passes, pairwise equivalence checks, differential and metamorphic tests, property-based tests, and benchmarks support different kinds of claims.Their comparison depends on input quantification, supported features, observed behavior, and evaluated workloads.Source: §1 · p. 2
  • The survey links preservation obligations to evidence at the delivered interface and to interpretation across revisions, rather than claiming that combining testing and verification is new.Prior syntheses address quantum testing, analysis, debugging, empirical methods, and tools [18] [21].Source: §1 · p. 2
  • Its source-linked matrix separates guarantees, empirical findings, analytical implications, and proposed practice, then applies conditional selection to failures and an interface example.The procedure identifies what a method establishes, what additional observation is needed, and when a verdict remains inconclusive; regression implications are proposed practice, not measured effectiveness.Source: §1 · p. 2

2 Review design and evidence assessment

The review examines gate-model compiler assurance through a bounded, source-linked synthesis of mechanisms, obligations, and evidence. Its design records scope and extraction decisions, while acknowledging limits to coverage and cross-study comparison.

2.1 Scope and questions

  • The review covers gate-model compilation assurance, including transformations, interfaces, testing, and revisions, and organizes the synthesis around five research questions.It includes program-level methods when their relations or observations transfer to a compilation boundary; pulse synthesis, hardware characterization, and unrelated application work are outside primary scope.Source: §2.1 · pp. 2–3, §2.2 · p. 3

2.2 Identification and scope control

  • The initial study set came from a planned 2015–2026 SLR, but the full SLR was not completed and its historical counts do not establish a verified selection flow.The pilot named seven seed studies; later searches and coverage checks supplemented discovery, but underlying ranked hit lists and some record-level historical decisions were unavailable.Source: §2.2 · pp. 3–4
  • Dated follow-ups broadened coverage and recorded source-level decisions, while publication families were linked to avoid treating related versions as independent methods.The update added compiler-pipeline, metamorphic-testing, mutation, and scope-only methods; the 102-record catalogue includes related versions and contextual sources, not a census of independent methods.Source: §2.2 · p. 4

2.3 Extraction and comparison

  • The evidence matrix distinguishes 39 detailed scoped extractions from 37 scope-only records among 76 records, and codes evidence type and relevance separately.Extraction captures the assessed object, obligation, oracle, relation, assumptions, cost, evaluation setting, source locator, version, and access depth; screening and extraction were not independently duplicated, and cited experiments were not rerun.Source: §2.3 · pp. 4–5

2.4 Relation to earlier reviews

  • Unlike earlier reviews organized around testing tasks or empirical practice, this survey follows a compiler obligation through relation, applicability, observation, and revision attribution.The comparison with neighboring reviews is presented as overlap rather than evidence that unfeatured topics are absent; Table 1 frames the organizing-unit comparison.Source: §2.4 · pp. 5–6, Table 1 · p. 5

2.5 Assessment limits

  • The synthesis supports conditional relationships among included methods, not field-wide prevalence or a validated effectiveness ranking.Search caps, access restrictions, missing historical record-level logs, and lack of independent duplicate extraction constrain coverage and interpretation.Source: §2.5 · p. 6

3 Operational requirements and quantum semantic boundaries

Compiler assurance must specify what counts as correct, which parts of a compilation result are observed, and how uncertainty is handled. The required semantic comparison depends on the permitted inputs, outputs, measurements, and interface, while fault detection and regression attribution remain distinct.

3.1 A compilation result is more than a circuit

  • A compilation result includes the circuit, interpretation metadata, status, resource measurements, and trace; an oracle sees only its declared projection and returns pass, fail, or inconclusive.Requirements become operational when ownership, applicability domain, acceptance rule, observation, and uncertainty treatment are explicit; incomplete checking leaves an obligation unresolved.Source: §3.1 · pp. 6–7

3.2 Quantum processes and observable distributions

  • Quantum comparisons must match the process and interface: ancilla disposal calls for reduced-process equality, retained measurement records preserve outcome labels, and approximation requires a declared metric and tolerance.Exact probabilities remove sampling uncertainty only for the observed input and measurement domain; noisy execution adds a separate source of difference.Source: §3.2 · pp. 7–8

3.3 Semantic equivalence requires a declared domain

  • For equal-width closed unitary circuits, phase equivalence requires consistent qubit ordering and layout, but ancillas or discarded outputs require embeddings or reduced channels instead.An isolated global phase can become observable under coherent reuse, and added shots in the original measurement basis cannot expose differences invisible to that basis.Source: §3.3 · pp. 8–9, Figure 1 · p. 9

3.4 Observation limits and complementary checks

  • An oracle cannot detect a fault in fields omitted from its observation projection; combining checks narrows acceptance only when both contracts apply.A richer observation can distinguish metadata records unavailable to a gate-only adapter, while added checks bring false-alarm and resource costs that require joint evaluation.Source: §3.4 · p. 9

3.5 Compiler faults and changes in behavior

  • A failure is an observed contract violation, whereas a regression additionally requires a baseline on which the obligation held and evidence connecting deterioration to a change.A useful regression record identifies versions, exposing input and configuration, violated obligation, supporting observation, and unresolved alternatives; one fault can produce many failures.Source: §3.5 · pp. 9–10

4 Semantic verification methods and their boundaries

Semantic verification methods support different claims, bounded by their formal models, representations, domains, and trusted interfaces. The review compares these boundaries across verified transformations, equivalence representations, restricted circuit families, and learning-assisted checking.

4.1 Verified compilers and validation of individual outputs

  • Verified construction proves transformation properties within a formal model, while translation validation checks particular source-output pairs; both depend on faithful semantics and interface representation.Proofs can leave packaging and integration outside the trusted boundary, so proofs and integration tests address complementary obligations.Source: §4.1 · p. 10

4.2 Decision diagrams and algebraic representations

  • Decision-diagram, algebraic, and ZX-based checkers trade representation and instance structure; a heuristic reduction that does not close is inconclusive, not evidence of inequivalence.Reported capacity on a benchmark does not establish general capacity, and controlled mutations or known transformation relationships do not establish detection rates for real compiler changes.Source: §4.2 · p. 11

4.3 Equivalence for parameterized partial and hybrid circuits

  • Parameterized, partial, and hybrid equivalence results apply only under their stated parameter domains, input/output observations, circuit structures, and lifting prerequisites.Finite parameter-free checks establish universal correctness only when a theorem justifies the reduction; selected observations leave other behavior unconstrained, and hybrid lifting must record its assumptions.Source: §4.3 · pp. 12–13

4.4 Learning inside a verifier and learning a verdict

  • Learning may guide a semantic checker’s search without deciding acceptance, but a predicted equivalence label needs separate validation and classifier accuracy is not a proof guarantee.Evaluation depends on training and test distributions; representation growth, simulation cost, and formalization or integration effort remain distinct limits, so maximum qubit counts across workloads are not a common scalability metric.Source: §4.4 · pp. 13–14

5 Testing methods and demonstrated fault evidence

The section compares testing approaches by their observation models and reported findings, while distinguishing what each result can establish. Across methods, failure channels, evaluation settings, and denominators constrain comparisons.

5.1 Differential and metamorphic testing

  • 14,799 transformed programs from six seed algorithms yielded four software crashes and two potential hardware-divergence explanations; the latter were not confirmed compiler defects.MorphQ compared 8,360 program pairs in 48 hours and filed 13 reports, nine confirmed at publication, but the reported bugs were crashes rather than output discrepancies.Source: §5.1 · p. 15
  • QEMI reported 11 crashes and one distribution discrepancy across Qiskit, a Cirq development build, and Q#; agreement on selected inputs is not universal equivalence.QSPE uses statevector validation on selected inputs, which removes shot noise in that setting but does not provide a full-unitary proof.Source: §5.1 · p. 15
  • IterTestQ reported 23 platform issues, 17 confirmed or fixed, across five platforms, combining interface exploration with QCEC checks for selected program pairs.The incremental detection value and reliability of particular combinations still require evaluation on controlled change events; the checker itself also had reported defects.Source: §5.1 · p. 16

5.2 Properties and assertions for targeted generation

  • Crash detection complements rather than replaces semantic miscompilation oracles, while black-box relations and concolic testing require justified preservation properties or scoped compiler observations.Static-analysis warnings can help validate inputs but do not alone show a compiler change caused a regression; concolic coverage concerns modeled decisions, not every compiler contract.Source: §5.2 · pp. 16–17
  • Property-based testing applies a relation across generated inputs, but compiler properties must remain invariant under the transformation and valid for the relevant backend and parameter domain.QuCheck’s inspected preprint evaluation covered five programs at 2 to 10 qubits; additional properties exercise behaviours, while additional shots mainly strengthen evidence for already selected observables.Source: §5.2 · p. 16

5.3 Regression diagnosis and mutation evidence

  • Mutation testing probes whether controlled faults are detected, but surviving mutants may be equivalent, violate assumptions, or miss the observation point.The reported 48% survival used wrong-output and probability oracles with an all-zero input and 100,000-shot simulator setting; it is not a compiler-regression miss rate. Delta debugging supports reproduction and diagnosis, not compiler-level test-selection effectiveness.Source: §5.3 · p. 17
  • Mutant labels can be circular when the compiler under assessment certifies them, and application-level bug corpora require filtering and provenance before use as compiler-regression benchmarks.Of 223 bugs collected from 18 platforms, only 39.9% were quantum-specific, and the dataset spans several component types.Source: §5.3 · p. 17
  • QuteFuzz reported 17 failures across compiler and simulator components; its same-study comparison with QEMI supports conclusions only for those particular settings, not a version-independent method ranking.Table 5 retains source-specific evaluation denominators; the reported settings and limits do not establish a common effectiveness ranking.Source: §5.3 · p. 17, Table 5 · p. 18

6 Target constraints and interpretation of compiled circuits

Compiler assurance must distinguish target-validity and resource objectives from semantic preservation, and interpret delivered metadata and observations under explicit contracts. The reviewed cases and evidence support conditional method selection, not a common effectiveness ranking.

6.1 Circuit quality and compilation performance

  • Compiler output quality spans depth, two-qubit count, connectivity, scheduling duration, and error estimates; performance comparisons require controlled runs and preselected, justified tolerances.Improving one metric can worsen another, so a regression requires a declared objective or monitoring criterion.Source: §6.1 · pp. 18–19

6.2 Metadata and backend contracts

  • Layout, parameter, and result mappings can be wrong even when gates are well formed; validation must use the delivered interpretation or check the records separately.Reconstructing a correct permutation can accept the gates while leaving a corrupted delivered output permutation unchecked; backend snapshots also matter for attributing failures to compiler changes.Source: §6.2 · p. 19

6.3 Reproducibility and provenance

  • Reproducibility records should preserve normalization, seeds, dependencies, backend snapshots, contracts, exclusions, timeouts, and unresolved outcomes; provenance aids reconstruction but does not establish correctness.Structural drift is a monitoring signal, not by itself a semantic defect [27, Secs. IV–VI].Source: §6.3 · pp. 19–20

6.4 Documented cases and their assurance implications

  • Cases A–D expose conditional-merge preconditions, equal-value parameter swaps, shared-crash oracle limits, and phase requirements that change under coherent control.These cases illustrate different assurance decisions, not defect frequency; the shared-crash root-cause account remains a conjecture, and issue closure does not establish a repair.Source: §6.4 · p. 20

6.5 Cross-study findings

  • Across-study evidence supports conditional method selection, but theorem, evaluation, and counterexample evidence differ, and portfolio benefit remains unmeasured.Timeouts and undecidable outcomes are not all incorrect decisions, and related monitoring and repair evidence do not validate the full procedure.Source: §6.5 · pp. 21–22

7 Selecting and combining assurance methods

Method choice should follow the claim, domain, and observations required, with complementary checks tied to independently justified acceptance rules. The worked examples show how delivered metadata and distinguishing inputs affect what a verdict can establish.

7.1 Select the claim before selecting the tool

  • Specify whether the claim concerns a transformation, artifact, program property, or revision before choosing a tool; unsupported cases and restricted test coverage must be reported.If a required obligation remains unresolved when the budget is exhausted, an overall assurance pass is unjustified.Source: §7.1 · pp. 22–23, Table 8 · p. 22

7.2 Combine observations without counting agreement twice

  • Combine checks only when each has its own justified acceptance rule, and evaluate additional detections, overlaps, false alarms, unresolved outcomes, and cost on eligible workloads.Shared parsers or input conversion can undermine apparent independence; removing one observation at a time under comparable budgets helps assess incremental value.Source: §7.2 · p. 23

7.3 Allocate effort after preserving the evidence standard

  • Budgeted testing can charge shared compilation once and report incremental checking and policy costs, while mandatory obligations set minimum acceptance evidence.The proposed architecture is not empirically evaluated in this review.Source: §7.3 · p. 23, Figure 2 · p. 24

7.4 Worked example of layout parameters and ancillary qubits

  • In the constructed layout example, a corrupted delivered permutation changes the decoded result, while a checker substituting the correct swap can accept the gates without checking the API contract.Unequal parameter bindings distinguish the swap witness; ancilla policy, parameter support, delivered mappings, and checker timeouts also bound the assurance claim.Source: §7.4 · pp. 24–25

7.5 Applying the selection procedure to conditional gates and phase

  • Conditional-merge checks must exercise inactive branches, while phase-sensitive reuse requires exact comparison or an interference witness when the contract includes coherent control.A counterexample establishes failure for the stated obligation; calling it a regression also requires a satisfying baseline under the same contract.Source: §7.5 · p. 25

8 Evidence for validation across compiler revisions

Evaluating compiler revisions requires distinguishing event types, restricting selection policies to information available at decision time, and preserving uncertainty in verdicts. The illustrative revision scenario shows how an added observation can support attribution under a stated contract, but supplies no measured detection rate.

8 Evidence for validation across compiler revisions

  • The review finds evidence for parts of a regression workflow, but no common event corpus validates the complete proposed architecture.Monitoring demonstrations do not establish fault-detection recall, and repair-record studies do not evaluate a prospective selection policy.Source: §8 · p. 25

8.1 Distinguish three kinds of fault evidence

  • Forward regression events, repair boundaries, and synthetic mutations answer different evaluation questions; forward comparisons need a matched environment and independently justified contract.A confirmed violation needs a reproducible witness, while unresolved disagreements and unsupported features should retain separate labels.Source: §8.1 · p. 26, Table 9 · p. 26

8.2 Information available at the selection point

  • Selection policies must exclude eventual failures, later repairs, and retrospective labels from earlier decisions, and evaluation partitions must respect chronology and related fault variants.Current observations become available only after their execution cost is incurred; later repairs and labels cannot influence earlier selection.Source: §8.2 · p. 26, Figure 3 · p. 27

8.3 Comparisons and outcomes

  • Fair policy comparisons should fix workloads, targets, eligible oracles, and budgets, then report distinct valid detections, time to first detection, false alarms, and resource use.Timeouts and unsupported features remain separate from equivalence and inequivalence outcomes.Source: §8.3 · p. 27

8.4 Verdict uncertainty and reliability claims

  • Numerical, sampling, and implementation uncertainty require different treatment; sampled tests need prespecified thresholds and error policies, while defect discoveries do not estimate operational reliability.The zero-failure binomial bound applies only to independent identically distributed trials with a perfect failure oracle.Source: §8.4 · pp. 27–28

8.5 Illustrative attribution across compiler revisions

  • With fixed artifacts and environment, the hypothetical revisions yield different labelled outputs under delivered metadata, illustrating an added observation for attribution without measuring detection effectiveness.A single passing test does not prove all-input correctness; identifying an introducing commit requires eligible intermediate revisions and change adjudication.Source: §8.5 · p. 28

9 Research agenda and threats to validity

The agenda targets reliable integration of assurance methods at compiler interfaces and clearer evidence about their complementary value. The review’s reach is constrained by selection, extraction, and cross-study heterogeneity, while its proposed regression architecture remains unevaluated.

9 Research agenda and threats to validity

  • Existing methods address parameterized and dynamic semantics, but reliable integration under actual compiler interfaces remains unresolved.The agenda also distinguishes processing scale from semantic assurance.Source: §9 · p. 28, §9.1 · p. 29

9.1 Open problems in quantum compiler assurance

  • Validation must carry phase, layout, initialization, and ancilla assumptions across representations, preserve classical-record associations with conditional behavior, and specify parameter and approximation rules.Scalable portfolios should report semantic coverage separately from target compliance and compilation performance.Source: §9.1 · pp. 28–29

9.2 Oracle complementarity and transfer

  • Evaluate an additional observation under a fixed budget by reporting unique detections, overlap, false alarms, and unresolved outcomes, separating oracle changes from scheduling changes.The review also calls for chronological validation of cost or risk models and recording shared-artifact dependencies that can couple checker failures.Source: §9.2 · p. 29

9.3 Threats to validity

  • Selective searching, a narrow pilot, and inaccessible material constrain coverage; the review supports analytical relationships among included methods, not prevalence claims.Screening and coding were not independently duplicated, and reported experiments were not rerun.Source: §9.3 · p. 29
  • Heterogeneous settings and related tool lineages limit cross-study inference; the review does not implement or independently validate its proposed regression architecture.Conclusions from compilation and simulation transfer only indirectly to noisy device execution.Source: §9.3 · p. 30

10 Conclusion

Quantum-compiler assurance requires evidence matched to the operational requirement and conditions being assessed. The review distinguishes evidence types and proposes compatible checks, contextualized verdicts, and evaluation on independently attributed compiler changes, without claiming a validated optimal policy.

10 Conclusion

  • A verification or test result supports a well-defined compiler claim only when its domain, assumptions, boundary, observations, and reference relation are explicit.Semantic preservation, executable validity, output interpretation, and performance objectives cannot substitute for one another.Source: §10 · p. 30
  • Published defect totals, mutation experiments, and large-circuit benchmarks measure different forms of evidence and do not establish a common effectiveness ranking.The synthesis does not quantify the benefit of a combined portfolio.Source: §10 · p. 30
  • The proposed practice is to combine checks only when requirements are compatible, preserve verdict context, and assess contributions on independently attributed change events.The guide is not presented as a validated optimal policy.Source: §10 · p. 30

Statements and Declarations

The authors report using generative AI for language and consistency editing and plotting code, while retaining responsibility for the manuscript. They also disclose funding, competing interests, author contributions, and supporting materials.

Declaration of Generative AI and AI-Assisted Technologies in the Manuscript Preparation Process

  • A generative AI assistant supported language editing, prose polishing, draft consistency checks, and plotting code for Figures 1–3.The authors reviewed and edited the content and take responsibility for the published article; AI was not used to fabricate, alter, or select reported data or results.Source: Declaration of Generative AI and… · pp. 30–31
  • The authors report no specific grant and no competing interests, and identify the work as part of Furqan Nasir’s PhD research under Muhammad Arif Shah and Iftikhar Alam’s supervision.Source: Declaration of Generative AI and… · p. 31
  • The review’s supporting information includes its protocol and search updates, source catalogue and extraction, and documented case records; no new compiler benchmark measurements were generated.Source: Declaration of Generative AI and… · p. 31

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