Quantum Readiness Level (QRL) Score

• Quantum Readiness Level (QRL) score is a workflow-aware metric that defines the maturity of hybrid quantum programs by aggregating weighted checklist items and calibration drift measures.
• It systematically maps evidence of robust engineering practices, reproducibility, and classical-quantum integration to a NASA-style readiness ladder for reliable deployments.
• Integrated with normalized quantum utility and audit procedures, QRL facilitates objective benchmarking and guides the advancement of quantum-classical pipelines.

The Quantum Readiness Level (QRL) score is a workflow-aware metric for quantitatively assessing the maturity and auditability of hybrid quantum programs as end-to-end computational pipelines, rather than isolated device or algorithmic evaluations. Conceived within the Hybrid Quantum Program Evaluation Framework (HQPEF), QRL codifies evidence of sound engineering practice, reproducibility, integration of classical baselines, and operational robustness (including calibration drift). It informs the staged advancement of quantum software artifacts from conceptual prototypes to governed, replicable deployments suitable for benchmarking utility and reliability at scale (Osei et al., 23 Nov 2025). The QRL score operates in concert with other HQPEF metrics—most notably the normalized quantum utility (UQ) and pipeline audit procedures—to deliver a reproducible, multi-dimensional readiness certificate for heterogeneous quantum-classical workflows.

1. Formal Definition and Scoring Procedure

The QRL score $QRL(S)$ is constructed as an integer-valued mapping from a raw workflow maturity score $S(c, \delta)$, aggregating a weighted project checklist vector $c \in \{0,1\}^k$, user-prioritized nonnegative weights $w \in \mathbb{R}_+^k$, and a calibration drift measure $\delta$ (in ppm). Specifically,

$S(c, \delta) = \sum_{i=1}^k w_i \, c_i + g(\delta)$

where

$$g(\delta) = \begin{cases} 10 & \text{if } 0 < \delta \leq 10 \ 6 & \text{if } 10 < \delta \leq 100 \ 0 & \text{otherwise} \end{cases}$$

The final QRL level is then determined by: $$QRL(S) = \begin{cases} 1 & S < 10 \ 2 & 10 \leq S < 20 \ 3 & 20 \leq S < 35 \ 4 & 35 \leq S < 50 \ 5 & 50 \leq S < 65 \ 6 & 65 \leq S < 75 \ 7 & 75 \leq S < 85 \ 8 & 85 \leq S < 95 \ 9 & S \geq 95 \end{cases}$$ This stepwise mapping is monotonic in both the programmatic evidence and calibration robustness, directly paralleling NASA-style Technology Readiness Levels (Osei et al., 23 Nov 2025).

2. Metric Intuition, Rationale, and Governance

QRL’s checklist vector $c$ encodes discrete achievements in hybrid quantum workflow development. Typical items (for $k$ up to 10) might include: mathematically sound problem formulation, unambiguous encoding specification in canonical code, demonstrated integration of classical and quantum solver components, reproducible random seed discipline, inclusion of matched-budget classical baselines, comprehensive workflow instrumentation (timing, drift audits), and the definition and fulfillment of service-level objectives (SLOs).

Each item is scored $c_i=1$ upon satisfaction, $c_i=0$ otherwise. Weights $w_i$ are assigned to reflect institutional or project priorities, such as audit traceability, integration depth, or experimental governance. The calibration drift bonus $g(\delta)$ incentivizes long-term device or simulation stability; bonus points are assigned for maintaining low drift over calibration windows.

Thresholding $S$ by $QRL$ yields a nondecreasing readiness ladder: QRL=1–3 correspond to pilot- or concept-stage artifacts; QRL=4–6 denote integrated, reproducible, well-audited prototypes; QRL=7 signals mature research pipelines; QRL=8–9 require formal SLOs, replication, external verification, and governed deployment (Osei et al., 23 Nov 2025).

3. Workflow Integration and Connection to Utility Metrics

Quantum Readiness Level is not an isolated maturity mark; it is structurally interlocked with HQPEF’s broader metrics for utility and performance. The normalized quantum utility (UQ), also termed $S_{norm}(\tau)$, measures comparative solver speed at a fixed output quality threshold $\tau$. Specifically, for two solvers $A,B$ evaluated on identical instance families under a fixed resource budget $B=(t,c,e)$, the quantity

$$S_{norm}(\tau) = \frac{\min\{T_A \mid Q(\theta_A) \geq \tau\}}{\min\{T_B \mid Q(\theta_B) \geq \tau\}}$$

is reported alongside QRL, providing a one-shot glimpse into the practical advantage or cost of moving to quantum techniques relative to classical best practice. By enforcing matched-budget discipline and using QRL to ensure all pipeline stages are comparably instrumented, HQPEF achieves meaningful, reproducible quantum-classical utility comparisons (Osei et al., 23 Nov 2025).

4. Implementation Patterns and Audit Procedures

The QRL score and related metrics are realized via reference Python implementations, with code samples directly provided in HQPEF documentation. Automated QRL calculators accept item vectors, weights, and drift values; audit tooling accumulates per-stage workflow durations and surfaces bottlenecks via mean share analysis. For each run, the stage durations $d^{(r)} \in \mathbb{R}^m$ are converted to mean shares $\bar{s}_i$, and top-$k$ bottleneck stages identified.

Instrumented pipelines (e.g., for QAOA-MaxCut optimization) demonstrate the full QRL workflow: (i) scoring all readiness checklist items, (ii) benchmarking classical and quantum solvers under identical time budgets, and (iii) reporting utility and audit statistics with provenance for reproducibility. All code preserves metadata, random seeds, and resource budgets to guarantee repeatable readiness and utility evaluation (Osei et al., 23 Nov 2025).

5. Practical Interpretation and Use Cases

QRL stage is interpreted as a research pipeline maturity certificate. For instance,

• QRL=7: integrated pipeline with reproducible, matched-budget classical baselines, complete audit instrumentation, and low calibration drift;
• QRL=8–9: corresponds to externally replicable, governed deployments suitable for device benchmarking or production workflows.

In empirical studies, pipelines scoring QRL=7 exhibited mature engineering discipline—suggesting such workflows are suitable for rigorous performance comparisons and algorithmic benchmarking. Progression to higher QRL stages was contingent on formal SLOs, deployment governance, and external replication (Osei et al., 23 Nov 2025).

6. Relationship to Other Hybrid Evaluation Metrics and Optimization Frameworks

QRL addresses workflow readiness; other HQPEF metrics capture static resource usage, optimization, and hybrid interaction. For example, metrics such as wall time ($T_{wall}$), quantum instruction number (QIN), and quantum calculation time ($\tau_Q$) quantify static and dynamic resource usage in hybrid code (Remme et al., 19 May 2025). Optimization practices—constant propagation/folding, instruction reordering, hybrid-dependencies analysis—improve these metrics but ultimately must pass through QRL certification for reproducibility and maturity. Advanced frameworks (e.g., HQPEF-Py, Q-Pragma, Hyrql) integrate QRL scoring as part of pipeline lifecycle management, enabling objective readiness, utility, and audit verdicts for hybrid quantum programs (Osei et al., 23 Nov 2025, Remme et al., 19 May 2025, Gazda et al., 2023, Chardonnet et al., 23 Oct 2025).

7. Guidance for Advancement and Limitations

To advance to higher QRL stages, workflows must satisfy additional checklist items (SLO definitions, replication, audit trails), achieve low drift regimes, and maintain strict reproducibility under matched-budget comparative regimes. Limitations include inability to capture pure device-level physical metrics or hardware error rates, and the necessity for human review of audit/replication evidence beyond checklist fulfillment.

QRL is thus a precise, workflow-centric readiness ladder for hybrid quantum programming. It operationalizes reproducibility, auditability, and integration—necessary for credible progress in quantum algorithm development, benchmarking, and deployment (Osei et al., 23 Nov 2025).