Strategic Governance of Quantum Supply Chains: A Criticality-Based Framework for Risk, Resilience, and Data-Driven Foresight

Strategic Governance of Quantum Supply Chains: A Criticality-Based Framework for Risk, Resilience, and Data-Driven Foresight | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Strategic Governance of Quantum Supply Chains: A Criticality-Based Framework for Risk, Resilience, and Data-Driven Foresight Dongyoun Cho, Mauritz Kop, Min-Ha Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8062873/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Mar, 2026 Read the published version in EPJ Quantum Technology → Version 1 posted 9 You are reading this latest preprint version Abstract Quantum technologies are moving from laboratory research to real-world deployment, but progress rests on narrow, fragile, globally dispersed supply chains. We introduce the Quantum Criticality Index (QCI)—a tri-axial assessment of supply risk, substitutability, and strategic significance—augmented with an artificial neural network (ANN)-based trend-detection module and a scenario-based foresight layer. A case study of molybdenum (Mo), essential for superconducting circuits, single-photon detectors, cryogenic hardware, and other defence-adjacent systems, shows how the QCI pinpoints chokepoints that could hinder hardware trajectories. Building on these diagnostics, we translate risk awareness into action through a governance framework that links the stages of diagnosis, decision, and delivery. By coupling structured indicators with predictive analytics, the QCI provides policymakers and industry with an evidence-based tool that translates diagnostics directly into an operational policy roadmap for allied procurement, intellectual property governance, targeted licensing, and verifiable, sustainable supply-chain assurance. Quantum technologies Supply-chain governance Critical materials Resilience Artificial neural networks (ANN) Quantum Criticality Index (QCI) Export controls ESG Allied technology strategy Figures Figure 1 Figure 2 1. Introduction: Quantum Technologies at a Strategic Crossroads Quantum technologies—encompassing computing, communication, and sensing—are transitioning from laboratory prototypes to pre-commercial deployment. Major governments and corporations now regard quantum capabilities as key determinants of technological competitiveness and national security [1, 2]. Quantum communication offers the potential for globally secure networks; quantum computing may revolutionise optimisation processes, materials discovery, and cryptography; and quantum sensors are poised to transform navigation, subsurface exploration, and specific defence applications. Unlike semiconductors or conventional information and communication technologies (ICT), quantum innovation relies on narrow, specialised supply chains that are poorly characterised and fragile [3]. Numerous critical inputs—such as critical raw materials, components, and equipment—are concentrated within a limited number of jurisdictions or vendors. Early-warning indicators include helium scarcity, which has restricted laboratory operations [4]; export restrictions affecting rare-earth elements and semiconductor-related inputs (e.g., gallium, germanium) that reveal systemic dependencies [5, 6]; and dependence on a small group of dilution-refrigerator suppliers [7, 8]. The dual-use characteristics increase these vulnerabilities. Cryptographic modules, precision sensors, and superconducting qubits serve civilian markets while also providing benefits to military and intelligence applications [9, 10]. Consequently, materials and components essential to these systems attract regulatory scrutiny and may be subject to export controls, sanctions, or weaponisation of interdependence . Several inputs—such as helium-3 (a scarce byproduct of tritium decay) [11, 62], isotopically enriched silicon-28 (required to suppress spin noise) [12, 63], thin-film lithium niobate (TFLN, LiNbO₃) for photonics [64], electronic-grade diamond for quantum memory [65], and superconducting metals like niobium [13] or indium—lack readily available substitutes. This extends to enabling hardware, particularly dilution refrigerators, which face multi-month lead times from a small supplier base (notably Bluefors and Oxford Instruments) [7, 8, 61, 77], thereby elevating tail-risk concerns where a single disruption could halt national initiatives or international deployments. Existing assessments fall short. Government lists of critical raw materials—such as the European Union Critical Raw Materials Act (EU CRMA, 2023) [14] or the United States (U.S.) Critical Minerals Strategy [15]—are essential but tend to be too broad, often failing to capture quantum-specific challenges such as isotopic enrichment, sub-Kelvin refrigeration, or single-photon detection [16, 17]. Additionally, these lists are updated at a slower pace than the rapid advances in the field, leading to mis-prioritisation when particular architectures begin to scale. This paper introduces the Quantum Criticality Index (QCI), a framework for evaluating vulnerabilities in the supply chains of quantum technologies, with a focus on essential raw materials, components, and equipment required for quantum-computing research, development, and manufacturing. The QCI combines supply risk, substitutability, and strategic importance to identify emerging quantum bottlenecks. We enhance static diagnostics with an artificial neural network (ANN)–based foresight layer that detects trend shifts and stress-test scenarios such as demand increases, regulatory changes, and regional shocks. The inquiry addresses three core questions: (i) how a quantum-specific criticality framework can facilitate anticipatory governance of supply chains; (ii) which indicators and methodologies most effectively capture evolving, non-linear risk trajectories; and (iii) how such diagnostics can be operationalised as tools for alliances and regulatory bodies. Our contributions include a tri-axial QCI customised for quantum-technology inputs, an integrated ANN module for early warning and scenario analysis, and a policy roadmap linking QCI outputs to diversification, substitution, circularity, calibrated stockpiles, and standards or control alignment. 2. Background and Motivation 2.1 Quantum Technologies as Strategic Assets Quantum innovation has become a national priority across the U.S., the EU, China, and other regions [ 1 , 2 , 10 ]. Reflecting its transformative and dual-use potential, the United Nations General Assembly proclaimed 2025 as the International Year of Quantum Science and Technology (IYQ), highlighting the field’s global significance for sustainable development, innovation, and international security governance [ 18 ]. Some applications challenge fundamental infrastructures: future quantum computers threaten current public-key cryptography, while advanced sensors could, under certain circumstances, narrow stealth margins relevant to deterrence in undersea or aerial operations. Quantum devices are fragile—often requiring millikelvin environments and highly reliable cryogenic operations [ 19 ], with practical dependencies on specialised dilution-refrigerator systems [ 7 , 8 ]. Consequently, hardware relies on complex, multi-regional supply chains for exotic materials and precision equipment. Governance frameworks remain nascent and struggle to keep pace with technological advancements as deployments approach critical sectors such as secure communications, finance, and defence, increasing bottlenecks and systemic risks [ 20 ]. States are also strengthening their policy toolkits. In the U.S., the Department of the Treasury has finalised and implemented the outbound-investment programme established under Executive Order 14105, “Addressing United States Investments in Certain National Security Technologies and Products in Countries of Concern,” effective 2 January 2025 [ 74 , 76 ]. The order encompasses sectors such as quantum information technologies. Simultaneously, the National Quantum Initiative continues to finance and coordinate domestic Quantum Information Science (QIS) capabilities through its fiscal-year 2025 supplement to the President’s Budget. In Europe, initiatives such as the Quantum Flagship and the 2023 CRMA reinforce strategic autonomy and resilience in critical resources [ 14 ], while the European Commission’s 2025 update to the EU Dual-Use Control List adds further quantum-related items to the export-licensing regime [ 23 ]. The 2025 update also reflects the EU’s alignment with multilateral export-control regimes—namely the Wassenaar Arrangement (WA), the Missile Technology Control Regime (MTCR), the Australia Group (AG), and the Nuclear Suppliers Group (NSG)—as consolidated in 2024. Under the WA, Member States agreed to uniformly control additional dual-use and emerging-technology items, including quantum-related components and equipment, thereby ensuring consistency across national control lists and reinforcing transatlantic policy coherence [ 24 ]. In Asia, China and Japan provide instructive counterpoints. China has consolidated authorities under its Export Control Law (2020) and has progressively tightened controls on strategic inputs and technologies—most recently via Announcement No. 10 [2025], which imposes export controls on items related to tungsten, tellurium, bismuth, molybdenum, and indium [ 25 , 67 , 70 ]. These legal authorities coincide with structural market power, including dominant shares in rare-earth processing [ 68 , 69 ]. Together with expanding catalogues governing restricted technology transfer and security reviews for outbound data/know-how, these measures signal a shift toward domestically anchored supply assurance and greater leverage over dual-use chokepoints. Japan, operating through the Ministry of Economy, Trade and Industry (METI) under the Foreign Exchange and Foreign Trade Act (FEFTA) and aligned with WA commitments, already treats quantum cryptography and related items as licensable exports and is incrementally extending coverage to upstream enablers (e.g., advanced processors, specialised cryogenic equipment, and lithography tooling). These trade and technology-security instruments sit alongside national research and development (R&D) programmes (e.g., the Quantum Strategy and Q-LEAP) and Japan’s economic-security legislation, collectively aiming to balance openness in research with tighter control of high-consequence applications. Despite these advances, fragmented mandates and cross-border supply chains remain barriers to coherent implementation, prompting calls for stronger central coordination and shared risk-indicator frameworks across allied economies. 2.2 Criticality and Supply Risk Frameworks Criticality evaluates resources based on (i) the likelihood of disruption and (ii) the impact on technologies and economies [ 27 , 28 , 29 ]. Building on the methodology established by the U.S. National Research Council (NRC), materials are categorised in a matrix that considers supply risk and technological vulnerability/importance in use (see Fig. 1 ). This framework emphasises the quadrant characterised by high risk and high impact. The indicators used typically include geographic concentration, governance quality, substitutability, and economic or technological significance [ 29 , 30 , 31 ]. The QCI tailors established indicators for quantum-relevant materials and components, combining quantitative and qualitative measures (see Table 1 ). Many indicators align with recognised best practices, such as governance (as measured by the World Bank’s World Governance Indicators, WGI), and substitutability as a key driver of impact [ 27 – 31 ]. Table 1 Selected indicators for quantum-relevant inputs Category Indicator Description Supply-chain risk Political instability / weak governance Fragile institutions or conflict in producer states undermine reliability [ 31 ]. Environmental & social regulation constraints Stringent environmental and social (E&S) rules, licensing delays, community opposition constrain capacity [ 30 ]. High production concentration Output concentrated in few countries/entities reduces resilience [ 29 , 30 ]. Import reliance / limited reserves Net-import dependence and small, concentrated reserves amplify exposure [ 33 ]. By-product or intrinsic limits Recovery as a by-product (e.g., He-3 from tritium decay) caps scalable supply [ 11 , 30 , 33 ]. Technological vulnerability Indispensability to performance Input is function-critical to device efficiency / yield [ 11 , 27 , 32 ]. Absence of viable substitutes No alternative with comparable performance / readiness [ 30 , 32 ]. Sensitivity to controls / sanctions Items likely subject to export controls, sanctions, or list-based restrictions [ 22 , 24 , 57 , 58 ]. Domestic capacity & R&D pipeline Local production / readiness and funded programmes to qualify alternatives [ 1 , 2 , 48 ]. These indicators establish the foundational criteria for evaluating each material’s supply risk and technological vulnerability. Many are derived from recognised best practices in the critical-materials literature. For instance, political stability and governance quality in supplier countries are vital risk factors, frequently quantified through indices such as WGI to gauge supply risk [ 31 ]. Likewise, the absence of viable substitutes and the crucial functional role of a material directly elevate the severity of impact in the event of disruption; within the criticality framework, substitutability is a core determinant of a material’s “importance in use” [ 27 , 28 , 29 , 30 ]. By systematically assessing each quantum-relevant material against these criteria, the proposed QCI identifies the most vulnerable points within quantum-technology supply chains. Notwithstanding their value, traditional criticality frameworks are insufficient when applied to the quantum domain. We identify three primary deficiencies: Quantum blind spots. Several resources crucial for quantum technologies—such as isotopically pure silicon-28, helium-3 gas, and specialised photonic components—are often under-weighted in standard CRM lists because conventional assessments prioritise broad macroeconomic impact over niche, high-leverage inputs for frontier technologies [ 11 , 12 , 32 ]. Static cadence. CRM lists and criticality assessments are updated infrequently and often rely on expert scoring and consensus, which can slow their ability to capture rapid demand shifts or breakthroughs (e.g., a sudden surge in demand for a particular hardware platform) [ 20 , 27 , 28 , 30 ]. Dual-use sensitivity. The strategic importance of quantum-relevant materials extends beyond economic value to encompass geopolitical and military considerations. Contemporary criticality frameworks rarely explicitly incorporate export-control regimes, outbound-investment rules, or security-driven list controls, thereby risking the systematic under-prioritisation of defence-relevant inputs [ 23 , 24 , 57 , 58 ]. Addressing these issues necessitates adapting criticality analysis to the unique characteristics of quantum supply chains. This includes expanding the scope to encompass quantum-specific materials, components, and equipment; enhancing the dynamism of assessments; and incorporating explicit geopolitical and military criteria. Such improvements are essential to better equip stakeholders to anticipate and mitigate supply risks in the quantum sector, thereby fostering a more resilient development pathway for dual-use quantum technologies. 2.3 Emerging Concerns in Quantum Supply Chains Recent developments have revealed significant vulnerabilities within the quantum-technology supply chain, underscoring the urgent need for anticipatory governance. Primary concerns include: materials bottlenecks (e.g., concentrated refining of gallium and germanium; rare-earth processing; geographically narrow niobium supply; the intrinsic scarcity of helium-3) [ 5 , 6 , 11 , 13 ]; equipment dependencies (ultra-low-temperature dilution refrigerators supplied by a short vendor list, notably Bluefors (Finland) and Oxford Instruments (United Kingdom)) [ 7 , 8 ]; geopolitical leverage (e.g., the 2010 rare-earth episode and recent gallium/germanium controls) [ 5 , 6 ]; and talent scarcity (persistent gaps between quantum-skilled roles and available specialists) [ 51 , 52 ]. These concerns argue for systematic prioritisation and early intervention: some risks can be mitigated through recycling, substitution, or redesign, while non-substitutable, dual-use, and geographically concentrated chokepoints in sensitive jurisdictions demand coordinated preventive measures. 2.4 Motivation for a New Framework The convergence of technical fragility, geopolitical contestation, and dual-use regulation renders the quantum ecosystem particularly susceptible to compounding risks. Policymakers increasingly recognise these threats: the EU and the U.S. have highlighted quantum as a strategically important domain—through secure-communication initiatives, alliance strategies, defence science-and-technology priorities, and tightening export-control and outbound-investment regimes [ 1 , 2 , 10 , 19 , 20 , 22 , 23 , 57 , 58 ]. However, existing analytical methods remain insufficient. Conventional critical-mineral or criticality assessments capture elements of the problem but lack a holistic and dynamic perspective tailored to quantum-specific inputs and architectures [ 18 , 19 , 20 , 27 , 28 , 33 ]. No integrated framework continuously evaluates which quantum components are “too critical to fail,” nor how their risk profiles evolve under plausible disruption scenarios. The QCI is proposed to fill this gap. QCI combines recognised critical-materials methodologies with an ANN foresight layer to create a forward-looking instrument explicitly designed for quantum-supply security [ 32 , 37 – 39 ]. Its principal features include: Diagnostics – a data-driven ranking of materials and components based on supply risk and strategic significance, including geopolitical concentration, import dependency, lack of substitutes, and dual-use security relevance [ 27 , 28 , 30 , 31 ]; Foresight – ANNs trained on indicators spanning market demand, technological shifts, and policy changes to simulate demand surges, new export regulations, or geopolitical shocks, providing early warnings when previously benign inputs trend toward high criticality [ 32 , 37 – 39 , 46 , 47 ]; and Policy relevance – translating quantitative diagnostics and foresight outputs into actionable measures such as supply diversification, strategic stockpiling, recycling programmes, substitution R&D, and international coordination mechanisms [ 19 , 20 , 22 , 23 , 24 , 57 , 58 ]. This paper illustrates the utility of the QCI through a case study on molybdenum (Mo)-high-purity metals, which are essential to multiple quantum-hardware and military applications [ 30 , 37 ]. We then derive policy recommendations from the QCI’s findings. By establishing a quantum-specific criticality framework, we aim to enable anticipatory, resilient, and inclusive governance—rather than allowing avoidable supply disruptions to hinder the quantum transition. 3. Methodology 3.1 Quantum Criticality Index (QCI): Tri-Axial Framework The Quantum Criticality Index (QCI) assesses risks associated with procuring raw materials and key components for quantum-technology supply chains. It uses three axes—supply risk, substitutability, and strategic significance—to capture both the probability of disruption and the magnitude of consequences for quantum applications. This framework extends conventional criticality methods with quantum-specific considerations and a blend of static indicators and prospective diagnostic tools [ 27 – 30 , 38 , 43 – 45 ]. Supply Risk. Vulnerability arising from production concentration, import dependence, supplier-country governance stability, reserve sufficiency, by-product dependency, and policy or trade constraints. In markets where one country or a small group controls over half of global output—for example, molybdenum (Mo), where the top producers account for roughly 93% of world supply—even moderate supply constraints or policy changes can trigger acute price spikes or shortages. In the first half of 2025, tighter Mo-concentrate supply—amid production cuts and low inventories—drove up oxide prices despite neutral demand conditions [ 25 , 26 , 37 ]. Substitutability. Feasibility of replacement without severe performance- or cost-penalties. Materials with unique quantum-optical, magnetic, or cryogenic properties, few substitutes, and/or low recycling rates exhibit higher criticality [ 16 , 17 , 30 , 32 ]. Strategic Significance. Importance to critical sectors and dual-use quantum technologies (computing, communications, sensing, and defence). Indicators include presence on national or regional critical-materials lists [ 14 , 33 ], economic footprint and price behaviour [ 36 ], and irreplaceability in vital applications [ 27 , 30 ]. Even with moderate supply risks, a material may be considered critical if its strategic indispensability is high. 3.2 Data Collection and Indicator Design We assembled a comprehensive indicator dataset as the first step of a four-stage workflow (data → modelling → optimisation → validation). Twelve indicators span supply risks, demand trends, geopolitical considerations, and technology significance [ 27 – 30 ]. Each indicator has a definition, primary axis, data source, rationale, and direction of effect. Table 2 Selected indicators for quantum-relevant inputs Indicator Definition Primary Axis Source (examples) Direction Diversity of Supply (DS) Number / dispersion of source countries Supply Risk ITC trade statistics Lower DS → higher risk Supplier Monopoly (MS) Dominance by single / few suppliers Supply Risk ITC Higher MS → higher risk Import Dependency (DI) Share of consumption met by imports Supply Risk UN Comtrade Higher DI → higher risk Demand Growth (DG) Recent demand growth rate Strategic Significance Market reports Higher DG → higher criticality Internal Demand (ID) Domestic demand level Strategic Significance ITC / national statistics Higher ID → higher criticality Political Stability (PS) Governance stability of suppliers Supply Risk WGI (World Bank) Lower stability → higher risk Environmental / Social Regulations (ES) EPI/HDI proxies for regulatory stringency Supply Risk EPI / HDI Stricter rules → higher risk Resource Competition (RC) Market concentration index (e.g., HHI) Supply Risk Industry data Higher RC → higher risk Production Growth (PG) Production trend vs demand Supply Risk USGS Lower PG → higher risk Commodity Price Trend (GSCI) Price-volatility proxy Strategic Significance S&P GSCI More volatile → higher criticality Decision-Flow Model (DFM) Internal criticality flag Supply / Strategic Internal Flagged → higher criticality Wassenaar Arrangement (WA) Export-control classification Supply / Strategic WA list Listed → higher criticality Notes (abbreviations & dimensions). ITC = International Trade Centre [ 55 ]; WGI = Worldwide Governance Indicators (World Bank) [ 31 ]; EPI / HDI = Environmental Performance Index / Human Development Index [ 53 , 54 ]; HHI = Herfindahl-Hirschman Index; USGS = U.S. Geological Survey [ 37 ]; S&P GSCI = S&P Goldman Sachs Commodity Index [ 36 ]; WA = Wassenaar Arrangement [ 24 ]. Typical dimensions: DS/MS/DI/PS/ES/RC/PG are country-level; GSCI/WA are material-level; DFM/ID/DG may be programme- or market-level depending on implementation. Utilising these indicators, we collected data for two exemplar material groups—Mo (high-purity metals) and a representative set of rare earth elements (REEs)—across 216 countries (2023). This yields 12 × 2 × 216 = 5,184 data points, with careful cleaning and consistency checks [ 31 , 37 , 55 ]. 3.3 Data Preprocessing and Normalisation Given heterogeneous units and scales, we apply min–max normalisation to a 0–100 scale: Xₙₒ r ₘ = 100 × (X − Xₘ i ₙ) / (Xₘₐₓ − Xₘ i ₙ). This expresses all indicators on a common scale, preventing large-range features from dominating downstream modelling [ 41 , 42 ]. 3.4 Foresight Module: ANN-Based Predictive Modelling Following the preparation of a clean, normalised dataset, we develop a predictive model to estimate a material’s criticality from input indicators. An ANN captures complex non-linear relationships among multiple features [ 38 ]. The ANN optimises weights and biases to achieve high predictive performance between the inputs and the target criticality score. Key hyperparameters—including the number of layers, activation functions, optimiser, and dataset partitioning—are essential elements in training the model [ 41 , 42 ]. Let x ∈ ℝ¹² denote the 12-indicator input vector. Hidden-layer activations use ReLU; the output is linear. We evaluate predictions using the coefficient of determination: R² = 1 − Σ i (y i − ŷ i )² / Σ i (y i − ȳ)². All model development used Python with TensorFlow (≥ 2.0) and scikit-learn (≥ 0.23) [ 41 , 42 ]. To aid policy interpretability, we compute post-hoc feature attributions (e.g., SHAP) on the trained ANN. 3.5 Weight Optimisation via Particle Swarm Optimisation (PSO) Although the ANN generates a criticality score for any specified set of indicator values, we also explore the inverse problem: identifying combinations of indicator levels that lead to the worst-case (high-criticality) configurations. We employ particle swarm optimisation (PSO) as a metaheuristic search method that complements machine-learning models in determining risk-amplifying configurations [ 43 – 46 ]. For particle \(\:i\) at iteration \(\:k\) : $$\:{\text{x}}_{i}^{(k+1)}={\text{x}}_{i}^{\left(k\right)}+{\text{v}}_{i}^{(k+1)},{\text{v}}_{i}^{(k+1)}=\omega\:{\text{v}}_{i}^{\left(k\right)}+{c}_{1}{r}_{1}({\text{p}}_{i}-{\text{x}}_{i}^{\left(k\right)})+{c}_{2}{r}_{2}({\text{p}}_{g}-{\text{x}}_{i}^{\left(k\right)}).$$ Here \(\:\omega\:\) is inertia (e.g., 0.4–1.4), \(\:{c}_{1},{c}_{2}\) are acceleration coefficients, and \(\:{r}_{1},{r}_{2}\sim\:U\left[\text{0,1}\right]\) . We implement PSO in Python (open-source libraries); no proprietary solver is required. 3.6 Summary and Validation Integrating the components above yields a rigorous, data-driven, forward-looking QCI. A tri-axial structure (supply risk, substitutability, strategic significance) is instantiated via twelve measurable indicators (normalised to 0–100), with an ANN foresight module for early warnings and a PSO layer for stress-tested weighting [ 27 – 30 , 38 , 41 , 42 , 43 – 45 ]. The framework is adaptive: indicators and weights can be updated as new data or policy shocks emerge; models are retrainable. In subsequent sections, we validate the methodology through case studies. As an example, Mo (high-purity metals) is examined to illustrate QCI scoring in practice. We compute Mo’s axis scores, apply the ANN to project criticality under demand growth, and show how PSO-optimised settings produce a final assessment. This identifies known supply vulnerabilities and limited substitutability, flagging Mo as a high-concern material—consistent with recent production trends and China’s 2025 export-licensing measures [ 25 , 37 ]. For policy users, we additionally report (a) a “control-elasticity” sub-index (how marginal changes in licensing/outbound rules shift the QCI score), (b) a component-level supplier-concentration metric (HHI and within-allies share), and (c) an early-warning flag when ANN-predicted trajectories cross pre-set thresholds (e.g., He-3 stockout horizons or DR lead-times). To ensure auditability and avoid performative compliance, we tie these indicators to externally verifiable “crypto-agility” exercises and disclosure checklists—tools outlined in our allied implementation blueprint; and we map regulatory signals to the control-elasticity sub-index through updates to multilateral control lists (Wassenaar Arrangement) and the U.S. outbound-investment program (E.O. 14105), so QCI scores endogenise evolving dual-use friction. [ 66 , 73 , 74 ] 4. Case Study: Molybdenum (Mo) Criticality in Quantum Technologies 4.1 Molybdenum Supply-Chain Risk Molybdenum’s supply chain exhibits substantial concentration and inherent vulnerability. According to the U.S. Geological Survey, global mine output in 2023 was approximately 260,000 metric tons, with China, Chile, Peru, the U.S., and Mexico collectively accounting for about 93% of total production. China remained the largest producer (around 110,000 tons) and continued to face environmental-permitting constraints that limited domestic expansion [ 37 ]. This highly concentrated structure underscores the potential for supply shocks, particularly when coupled with policy or regulatory disruptions. On 4 February 2025, China imposed export-licensing requirements on molybdenum—alongside tungsten and other strategic metals—under Announcement No. 10 [2025] [ 25 ]. Even without an outright ban, these measures pushed global prices higher and raised near-term concerns about shortages, echoing earlier episodes of leverage involving rare earth elements [ 26 ]. Import-dependent economies, therefore, face pronounced exposure to such shocks: abrupt controls can disrupt manufacturing timelines, inflate costs, and force complex materials substitutions. Substitutability remains limited across high-performance applications. As a refractory metal, Mo imparts exceptional high-temperature strength and corrosion resistance to alloys; alternative elements (e.g., vanadium, chromium) only partially replicate these properties. Mo-based alloys are also used in high-temperature structural components, for example, as container materials in molten-salt reactor designs or as a foundry substrate for sapphire crystal growth due to their strength and corrosion resistance. This limited substitutability amplifies supply risk [ 37 ]. 4.2 Vulnerability in Quantum Applications Mo plays quiet but enabling roles across quantum-hardware architectures: Single-photon detectors (SNSPDs) : ultrathin molybdenum-silicide (MoSi) nanowires achieve high system detection efficiency at 1550 nm with low timing jitter at cryogenic temperatures [ 16 ]. Superconducting circuits/resonators : Mo–Re alloys combine mechanical robustness with favourable superconducting properties under strain and magnetic field [ 17 ]. Cryogenic infrastructure : high-purity Mo fasteners and thermal links provide low thermal expansion and minimal magnetic impurities in dilution refrigerators and ultra-high-vacuum systems [ 7 , 8 ]. Although present demand is modest, scalability represents the key vulnerability. As SNSPD arrays, wiring density, and cryogenic fleets expand, speciality Mo forms (e.g., high-purity powders, films, and alloy feedstock) can become rate-limiting. Substitutes (e.g., WSi, NbN, NbTiN) often require redesign and entail performance penalties—lower efficiency, higher loss, or reduced critical current—thereby translating supply risk directly into technical vulnerability, akin to the way helium-3 scarcity constrains low-temperature operations [ 11 ]. 4.3 Comparative Quantum Criticality (vs. REEs) We benchmark Mo using the QCI matrix with (x) supply risk and (y) quantum impact/irreplaceability. Heavy REEs such as ytterbium (Yb) and erbium (Er) occupy the high-risk/high-impact quadrant: they are technologically indispensable (e.g., trapped-ion qubits, optical clocks, C-band amplification, quantum repeaters) and exhibit highly concentrated supply chains. Historically, Mo ranked lower in supply risk due to more diversified mining operations; however, refining and policy leverage are concentrated in a few jurisdictions. Coupled with its enabling role and limited substitutes in quantum components, Mo’s position shifts upward and rightward on the QCI plot—approaching heavy REEs in priority, albeit with a narrower application scope. Source: RQT analysis (2024). 4.4 Molybdenum in the Ecosystem of Chokepoints Mo’s pattern—concentrated supply with limited substitutability under policy shock—recurs across quantum enablers. Cryogenics face multi-month lead times for dilution refrigerators (DRs) despite Bluefors’ U.S. capacity ramp; He-3 stocks are intrinsically rate-limited by tritium decay and DOE processing; TFLN/LNOI has few high-quality wafer suppliers; and a single producer leads the Western supply of electronic-grade diamond. Accordingly, we pair the QCI’s diagnostic signal (this Article) with (i) an allied implementation blueprint for near-term action and (ii) a legislative design for durable, risk-tiered governance—together closing the loop from detection to delivery. [ 61 – 66 , 71 ] 5. Policy and Conclusion: Translating Foresight into Governance To operationalise the QCI’s diagnostic and foresight capabilities, policymakers will need to translate risk alerts into concrete actions. This process begins by establishing QCI-linked stockpile triggers and publishing clear thresholds—such as He-3 reserve floors or DR spare-parts buffers—that activate pre-funded procurement mechanisms when ANN-generated forecasts breach specified risk levels [ 62 ]. Beyond domestic stockpiling, allied industrial coordination is essential, including the formation of allied procurement pools that commit to multi-year “take-or-pay” options for critical hardware (e.g., DRs and cryocoolers) while requiring supplier contingency measures such as second-site manufacturing and in-region spares hubs [ 61 ]. This industrial strategy should be paired with targeted licensing corridors that leverage outbound and inbound screening regimes (e.g., E.O. 14105 and updates to the Wassenaar Arrangement) to prioritise and protect allied capacity for DRs, He-3 handling, thin-film lithium niobate (TFLN, LiNbO₃) wafers, and diamond—while minimising collateral effects on adjacent photonics industries [ 24 , 74 ]. Furthermore, governance will need to extend to the intangible supply chain, given that process know-how (e.g., TFLN wafer etching) frequently constitutes the bottleneck; accordingly, we recommend allied intellectual property (IP) pools or fair, reasonable, and non-discriminatory (FRAND)-style licensing frameworks linked to domestic manufacturing incentives [ 71 ]. Finally, to ensure supply-chain integrity, governance should encompass origin assurance for quantum-grade inputs. We recommend adopting verifiable credentials for origin and processing of key materials—notably He-3, Si-28, diamond, and LiNbO₃—tethered to QCI scores, with non-compliant inputs incurring de-risking penalties in public procurement processes [ 62 – 65 ]. This procurement-led approach also provides a tractable mechanism for integrating the environmental, social, and governance (ESG) pillar. By tying public contracts for new resource extraction or processing to compliance with stringent environmental standards and “just transition” principles, allies can de-risk supply chains without compromising sustainability goals. The urgency of these measures is underscored by industry-reported DR lead times (approximately 6–9 months) and supplier concentration, which together confirm a systemic bottleneck [ 7 , 8 , 61 , 77 ]. Ultimately, operationalising the QCI transforms strategic foresight into anticipatory governance. By linking data-driven diagnostics to enforceable procurement, licensing, and ESG mechanisms, allies can institutionalise resilience within the quantum supply chain rather than reacting to crises ex post. The QCI thus provides not only a technical metric but also a policy framework—one that redefines how emerging technologies are governed through coordinated, evidence-based, and values-driven decision-making. Declarations Ethics Approval and Consent to Participate Not applicable. Consent for Publication Not applicable. Availability of Data and Materials All data generated or analysed during this study are included in this published article. Competing Interests The authors declare that they have no competing interests. Funding This work was supported by the Program on Geopolitics, Technology and Governance . The funding bodies had no role in the design, analysis, or interpretation of data, nor in writing the manuscript. Author Contributions Statement D.C. (Dongyoun Cho) led the manuscript preparation, integration, and submission. D.C. structured the overall argument, harmonised the technical and policy sections, ensured coherence across the manuscript, and served as the corresponding author. M.K. (Mauritz Kop) contributed to the conceptual foundation and legal-policy analysis, particularly regarding technology governance, export controls, and intellectual-property frameworks. M.K. refined the discussion on allied standardisation and regulatory coherence. M.L. (Min-Ha Lee) designed and implemented the methodological components, including the ANN-based foresight model and PSO optimisation, and collected and validated the case-study data. M.L. also contributed to the technical interpretation of QCI indicators. All authors reviewed and approved the final version of the manuscript. Acknowledgements The authors thank the EPJ Quantum Technology editors and reviewers for their constructive comments. The authors express special thanks to Andrew J. Grotto for his support of this work. Declaration on Large Language Model Use: Large Language Models (LLMs) such as ChatGPT were used only as a writing assistant for grammar and language clarity. No AI system contributed to the conceptual, analytical, or interpretative aspects of this work, and thus no authorship attribution is assigned to LLMs. This use has been properly acknowledged in the Methods section. References National Academies of Sciences, Engineering, and, Medicine. Quantum science concepts in enhancing national security: An assessment of applications. Washington (DC): National Academies; 2019. European Commission. Coordinated plan on Quantum Communication Infrastructure (EuroQCI). Brussels: European Commission; 2021. National Research Council. Minerals, critical minerals, and the U.S. economy. Washington (DC): National Academies; 2008. Bains C. The world keeps running out of helium. 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Abingdon (UK): Oxford Instruments; [cited 2025 Oct 15]. Available from: https://nanoscience.oxinst.com/ProteoxFamily Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Mar, 2026 Read the published version in EPJ Quantum Technology → Version 1 posted Editorial decision: Revision requested 23 Dec, 2025 Reviews received at journal 22 Dec, 2025 Reviewers agreed at journal 03 Dec, 2025 Reviews received at journal 22 Nov, 2025 Reviewers agreed at journal 13 Nov, 2025 Reviewers invited by journal 13 Nov, 2025 Editor assigned by journal 10 Nov, 2025 Submission checks completed at journal 09 Nov, 2025 First submitted to journal 08 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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08:13:36","extension":"xml","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":152018,"visible":true,"origin":"","legend":"","description":"","filename":"663458a3e7e34cc697bb00883e8f3b881structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8062873/v1/30c7e6c9f91fd1f4e1030875.xml"},{"id":95669710,"identity":"7c698ce4-8ad2-4198-89dd-54ffac761f54","added_by":"auto","created_at":"2025-11-11 17:13:21","extension":"html","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":171148,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8062873/v1/a594987c20a0d948831a55c5.html"},{"id":95669694,"identity":"8a27ee12-ed5d-45fa-a81d-b9751eec981e","added_by":"auto","created_at":"2025-11-11 17:13:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":70696,"visible":true,"origin":"","legend":"\u003cp\u003eCriticality assessment matrix: supply risk (horizontal) vs. vulnerability/impact (vertical). Adapted from NRC (2008) [27].\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8062873/v1/c27d11bb2de15c1699fc33c0.png"},{"id":95798356,"identity":"9c6629ee-3371-48fa-87ab-8173257719fa","added_by":"auto","created_at":"2025-11-13 08:16:32","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":426597,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eApplying QCI (U.S. case study): REEs vs. Molybdenum (Mo).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8062873/v1/4147cd56db423c098c946f30.png"},{"id":104739503,"identity":"93f4db81-ab80-4f3f-b672-2ec08dc63da5","added_by":"auto","created_at":"2026-03-16 16:08:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1742151,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8062873/v1/973484d6-da30-4563-95fb-f3ca5989d567.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Strategic Governance of Quantum Supply Chains: A Criticality-Based Framework for Risk, Resilience, and Data-Driven Foresight","fulltext":[{"header":"1. Introduction: Quantum Technologies at a Strategic Crossroads","content":"\u003cp\u003eQuantum technologies—encompassing computing, communication, and sensing—are transitioning from laboratory prototypes to pre-commercial deployment. Major governments and corporations now regard quantum capabilities as key determinants of technological competitiveness and national security [1, 2]. Quantum communication offers the potential for globally secure networks; quantum computing may revolutionise optimisation processes, materials discovery, and cryptography; and quantum sensors are poised to transform navigation, subsurface exploration, and specific defence applications.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eUnlike semiconductors or conventional information and communication technologies (ICT), quantum innovation relies on narrow, specialised supply chains that are poorly characterised and fragile [3]. Numerous critical inputs—such as critical raw materials, components, and equipment—are concentrated within a limited number of jurisdictions or vendors. Early-warning indicators include helium scarcity, which has restricted laboratory operations [4]; \u003cstrong\u003eexport restrictions\u003c/strong\u003e affecting rare-earth elements and semiconductor-related inputs (e.g., gallium, germanium) that reveal systemic dependencies [5, 6]; and dependence on a small group of \u003cstrong\u003edilution-refrigerator suppliers\u003c/strong\u003e [7, 8].\u003c/p\u003e\n\u003cp\u003eThe dual-use characteristics increase these vulnerabilities. Cryptographic modules, precision sensors, and superconducting qubits serve civilian markets while also providing benefits to military and intelligence applications [9, 10]. Consequently, materials and components essential to these systems attract regulatory scrutiny and may be subject to \u003cstrong\u003eexport controls, sanctions, or weaponisation of interdependence\u003c/strong\u003e. Several inputs—such as helium-3 (a scarce byproduct of tritium decay) [11, 62], isotopically enriched silicon-28 (required to suppress spin noise) [12, 63], thin-film lithium niobate (TFLN, LiNbO₃) for photonics [64], electronic-grade diamond for quantum memory [65], and superconducting metals like niobium [13] or indium—lack readily available substitutes. This extends to enabling hardware, particularly dilution refrigerators, which face multi-month lead times from a small supplier base (notably Bluefors and Oxford Instruments) [7, 8, 61, 77], thereby elevating tail-risk concerns where a single disruption could halt national initiatives or international deployments.\u003c/p\u003e\n\u003cp\u003eExisting assessments fall short. Government lists of critical raw materials—such as the European Union Critical Raw Materials Act (EU CRMA, 2023) [14] or the United States (U.S.) Critical Minerals Strategy [15]—are essential but tend to be too broad, often failing to capture quantum-specific challenges such as isotopic enrichment, sub-Kelvin refrigeration, or single-photon detection [16, 17]. Additionally, these lists are updated at a slower pace than the rapid advances in the field, leading to mis-prioritisation when particular architectures begin to scale.\u003c/p\u003e\n\u003cp\u003eThis paper introduces the Quantum Criticality Index (QCI), a framework for evaluating vulnerabilities in the supply chains of quantum technologies, with a focus on essential raw materials, components, and equipment required for quantum-computing research, development, and manufacturing. The QCI combines supply risk, substitutability, and strategic importance to identify emerging quantum bottlenecks. We enhance static diagnostics with an artificial neural network (ANN)–based foresight layer that detects trend shifts and stress-test scenarios such as demand increases, regulatory changes, and regional shocks.\u003c/p\u003e\n\u003cp\u003eThe inquiry addresses three core questions: (i) how a quantum-specific criticality framework can facilitate anticipatory governance of supply chains; (ii) which indicators and methodologies most effectively capture evolving, non-linear risk trajectories; and (iii) how such diagnostics can be operationalised as tools for alliances and regulatory bodies. Our contributions include a tri-axial QCI customised for quantum-technology inputs, an integrated ANN module for early warning and scenario analysis, and a policy roadmap linking QCI outputs to diversification, substitution, circularity, calibrated stockpiles, and standards or control alignment.\u003c/p\u003e"},{"header":"2. Background and Motivation","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Quantum Technologies as Strategic Assets\u003c/h2\u003e\u003cp\u003eQuantum innovation has become a national priority across the U.S., the EU, China, and other regions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Reflecting its transformative and dual-use potential, the United Nations General Assembly proclaimed 2025 as the International Year of Quantum Science and Technology (IYQ), highlighting the field\u0026rsquo;s global significance for sustainable development, innovation, and international security governance [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSome applications challenge fundamental infrastructures: future quantum computers threaten current public-key cryptography, while advanced sensors could, under certain circumstances, narrow stealth margins relevant to deterrence in undersea or aerial operations. Quantum devices are fragile\u0026mdash;often requiring millikelvin environments and highly reliable cryogenic operations [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], with practical dependencies on specialised dilution-refrigerator systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Consequently, hardware relies on complex, multi-regional supply chains for exotic materials and precision equipment. Governance frameworks remain nascent and struggle to keep pace with technological advancements as deployments approach critical sectors such as secure communications, finance, and defence, increasing bottlenecks and systemic risks [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eStates are also strengthening their policy toolkits. In the U.S., the Department of the Treasury has finalised and implemented the outbound-investment programme established under Executive Order 14105, \u0026ldquo;Addressing United States Investments in Certain National Security Technologies and Products in Countries of Concern,\u0026rdquo; effective 2 January 2025 [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e]. The order encompasses sectors such as quantum information technologies. Simultaneously, the National Quantum Initiative continues to finance and coordinate domestic Quantum Information Science (QIS) capabilities through its fiscal-year 2025 supplement to the President\u0026rsquo;s Budget.\u003c/p\u003e\u003cp\u003eIn Europe, initiatives such as the Quantum Flagship and the 2023 CRMA reinforce strategic autonomy and resilience in critical resources [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], while the European Commission\u0026rsquo;s 2025 update to the EU Dual-Use Control List adds further quantum-related items to the export-licensing regime [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The 2025 update also reflects the EU\u0026rsquo;s alignment with multilateral export-control regimes\u0026mdash;namely the Wassenaar Arrangement (WA), the Missile Technology Control Regime (MTCR), the Australia Group (AG), and the Nuclear Suppliers Group (NSG)\u0026mdash;as consolidated in 2024. Under the WA, Member States agreed to uniformly control additional dual-use and emerging-technology items, including quantum-related components and equipment, thereby ensuring consistency across national control lists and reinforcing transatlantic policy coherence [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn Asia, China and Japan provide instructive counterpoints. China has consolidated authorities under its Export Control Law (2020) and has progressively tightened controls on strategic inputs and technologies\u0026mdash;most recently via Announcement No. 10 [2025], which imposes export controls on items related to tungsten, tellurium, bismuth, molybdenum, and indium [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e]. These legal authorities coincide with structural market power, including dominant shares in rare-earth processing [\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]. Together with expanding catalogues governing restricted technology transfer and security reviews for outbound data/know-how, these measures signal a shift toward domestically anchored supply assurance and greater leverage over dual-use chokepoints. Japan, operating through the Ministry of Economy, Trade and Industry (METI) under the Foreign Exchange and Foreign Trade Act (FEFTA) and aligned with WA commitments, already treats quantum cryptography and related items as licensable exports and is incrementally extending coverage to upstream enablers (e.g., advanced processors, specialised cryogenic equipment, and lithography tooling). These trade and technology-security instruments sit alongside national research and development (R\u0026amp;D) programmes (e.g., the Quantum Strategy and Q-LEAP) and Japan\u0026rsquo;s economic-security legislation, collectively aiming to balance openness in research with tighter control of high-consequence applications.\u003c/p\u003e\u003cp\u003eDespite these advances, fragmented mandates and cross-border supply chains remain barriers to coherent implementation, prompting calls for stronger central coordination and shared risk-indicator frameworks across allied economies.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Criticality and Supply Risk Frameworks\u003c/h2\u003e\u003cp\u003eCriticality evaluates resources based on (i) the likelihood of disruption and (ii) the impact on technologies and economies [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Building on the methodology established by the U.S. National Research Council (NRC), materials are categorised in a matrix that considers supply risk and technological vulnerability/importance in use (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This framework emphasises the quadrant characterised by high risk and high impact. The indicators used typically include geographic concentration, governance quality, substitutability, and economic or technological significance [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe QCI tailors established indicators for quantum-relevant materials and components, combining quantitative and qualitative measures (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Many indicators align with recognised best practices, such as governance (as measured by the World Bank\u0026rsquo;s World Governance Indicators, WGI), and substitutability as a key driver of impact [\u003cspan additionalcitationids=\"CR28 CR29 CR30\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSelected indicators for quantum-relevant inputs\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCategory\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicator\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003e\u003cb\u003eSupply-chain\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003erisk\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePolitical instability /\u003c/p\u003e\u003cp\u003eweak governance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFragile institutions or conflict in producer states undermine reliability [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEnvironmental \u0026amp; social regulation constraints\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStringent environmental and social (E\u0026amp;S) rules, licensing delays, community opposition constrain capacity [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHigh production concentration\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eOutput concentrated in few countries/entities reduces resilience [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eImport reliance /\u003c/p\u003e\u003cp\u003elimited reserves\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eNet-import dependence and small, concentrated reserves amplify exposure [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBy-product or intrinsic limits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRecovery as a by-product (e.g., He-3 from tritium decay) caps scalable supply [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003e\u003cb\u003eTechnological vulnerability\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndispensability to performance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInput is function-critical to device efficiency / yield [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAbsence of viable substitutes\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eNo alternative with comparable performance / readiness [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSensitivity to controls / sanctions\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eItems likely subject to export controls, sanctions, or list-based restrictions [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDomestic capacity \u0026amp;\u003c/p\u003e\u003cp\u003eR\u0026amp;D pipeline\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLocal production / readiness and funded programmes to qualify alternatives [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThese indicators establish the foundational criteria for evaluating each material\u0026rsquo;s supply risk and technological vulnerability. Many are derived from recognised best practices in the critical-materials literature. For instance, political stability and governance quality in supplier countries are vital risk factors, frequently quantified through indices such as WGI to gauge supply risk [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Likewise, the absence of viable substitutes and the crucial functional role of a material directly elevate the severity of impact in the event of disruption; within the criticality framework, substitutability is a core determinant of a material\u0026rsquo;s \u0026ldquo;importance in use\u0026rdquo; [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. By systematically assessing each quantum-relevant material against these criteria, the proposed QCI identifies the most vulnerable points within quantum-technology supply chains.\u003c/p\u003e\u003cp\u003eNotwithstanding their value, traditional criticality frameworks are insufficient when applied to the quantum domain. We identify three primary deficiencies:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eQuantum blind spots.\u003c/b\u003e Several resources crucial for quantum technologies\u0026mdash;such as isotopically pure silicon-28, helium-3 gas, and specialised photonic components\u0026mdash;are often under-weighted in standard CRM lists because conventional assessments prioritise broad macroeconomic impact over niche, high-leverage inputs for frontier technologies [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eStatic cadence.\u003c/b\u003e CRM lists and criticality assessments are updated infrequently and often rely on expert scoring and consensus, which can slow their ability to capture rapid demand shifts or breakthroughs (e.g., a sudden surge in demand for a particular hardware platform) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eDual-use sensitivity.\u003c/b\u003e The strategic importance of quantum-relevant materials extends beyond economic value to encompass geopolitical and military considerations. Contemporary criticality frameworks rarely explicitly incorporate export-control regimes, outbound-investment rules, or security-driven list controls, thereby risking the systematic under-prioritisation of defence-relevant inputs [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eAddressing these issues necessitates adapting criticality analysis to the unique characteristics of quantum supply chains. This includes expanding the scope to encompass quantum-specific materials, components, and equipment; enhancing the dynamism of assessments; and incorporating explicit geopolitical and military criteria. Such improvements are essential to better equip stakeholders to anticipate and mitigate supply risks in the quantum sector, thereby fostering a more resilient development pathway for dual-use quantum technologies.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Emerging Concerns in Quantum Supply Chains\u003c/h2\u003e\u003cp\u003eRecent developments have revealed significant vulnerabilities within the quantum-technology supply chain, underscoring the urgent need for anticipatory governance. Primary concerns include: materials bottlenecks (e.g., concentrated refining of gallium and germanium; rare-earth processing; geographically narrow niobium supply; the intrinsic scarcity of helium-3) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]; equipment dependencies (ultra-low-temperature dilution refrigerators supplied by a short vendor list, notably Bluefors (Finland) and Oxford Instruments (United Kingdom)) [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]; geopolitical leverage (e.g., the 2010 rare-earth episode and recent gallium/germanium controls) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]; and talent scarcity (persistent gaps between quantum-skilled roles and available specialists) [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThese concerns argue for systematic prioritisation and early intervention: some risks can be mitigated through recycling, substitution, or redesign, while non-substitutable, dual-use, and geographically concentrated chokepoints in sensitive jurisdictions demand coordinated preventive measures.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Motivation for a New Framework\u003c/h2\u003e\u003cp\u003eThe convergence of technical fragility, geopolitical contestation, and dual-use regulation renders the quantum ecosystem particularly susceptible to compounding risks. Policymakers increasingly recognise these threats: the EU and the U.S. have highlighted quantum as a strategically important domain\u0026mdash;through secure-communication initiatives, alliance strategies, defence science-and-technology priorities, and tightening export-control and outbound-investment regimes [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. However, existing analytical methods remain insufficient. Conventional critical-mineral or criticality assessments capture elements of the problem but lack a holistic and dynamic perspective tailored to quantum-specific inputs and architectures [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. No integrated framework continuously evaluates which quantum components are \u0026ldquo;too critical to fail,\u0026rdquo; nor how their risk profiles evolve under plausible disruption scenarios.\u003c/p\u003e\u003cp\u003eThe QCI is proposed to fill this gap. QCI combines recognised critical-materials methodologies with an ANN foresight layer to create a forward-looking instrument explicitly designed for quantum-supply security [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan additionalcitationids=\"CR38\" citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Its principal features include:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eDiagnostics\u003c/b\u003e \u0026ndash; a data-driven ranking of materials and components based on supply risk and strategic significance, including geopolitical concentration, import dependency, lack of substitutes, and dual-use security relevance [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e];\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eForesight\u003c/b\u003e \u0026ndash; ANNs trained on indicators spanning market demand, technological shifts, and policy changes to simulate demand surges, new export regulations, or geopolitical shocks, providing early warnings when previously benign inputs trend toward high criticality [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan additionalcitationids=\"CR38\" citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]; and\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePolicy relevance\u003c/b\u003e \u0026ndash; translating quantitative diagnostics and foresight outputs into actionable measures such as supply diversification, strategic stockpiling, recycling programmes, substitution R\u0026amp;D, and international coordination mechanisms [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis paper illustrates the utility of the QCI through a case study on molybdenum (Mo)-high-purity metals, which are essential to multiple quantum-hardware and military applications [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. We then derive policy recommendations from the QCI\u0026rsquo;s findings. By establishing a quantum-specific criticality framework, we aim to enable anticipatory, resilient, and inclusive governance\u0026mdash;rather than allowing avoidable supply disruptions to hinder the quantum transition.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Methodology","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Quantum Criticality Index (QCI): Tri-Axial Framework\u003c/h2\u003e\u003cp\u003eThe Quantum Criticality Index (QCI) assesses risks associated with procuring raw materials and key components for quantum-technology supply chains. It uses three axes\u0026mdash;supply risk, substitutability, and strategic significance\u0026mdash;to capture both the probability of disruption and the magnitude of consequences for quantum applications. This framework extends conventional criticality methods with quantum-specific considerations and a blend of static indicators and prospective diagnostic tools [\u003cspan additionalcitationids=\"CR28 CR29\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cb\u003eSupply Risk.\u003c/b\u003e Vulnerability arising from production concentration, import dependence, supplier-country governance stability, reserve sufficiency, by-product dependency, and policy or trade constraints. In markets where one country or a small group controls over half of global output\u0026mdash;for example, molybdenum (Mo), where the top producers account for roughly 93% of world supply\u0026mdash;even moderate supply constraints or policy changes can trigger acute price spikes or shortages. In the first half of 2025, tighter Mo-concentrate supply\u0026mdash;amid production cuts and low inventories\u0026mdash;drove up oxide prices despite neutral demand conditions [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cb\u003eSubstitutability.\u003c/b\u003e Feasibility of replacement without severe performance- or cost-penalties. Materials with unique quantum-optical, magnetic, or cryogenic properties, few substitutes, and/or low recycling rates exhibit higher criticality [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cb\u003eStrategic Significance.\u003c/b\u003e Importance to critical sectors and dual-use quantum technologies (computing, communications, sensing, and defence). Indicators include presence on national or regional critical-materials lists [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], economic footprint and price behaviour [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], and irreplaceability in vital applications [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Even with moderate supply risks, a material may be considered critical if its strategic indispensability is high.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Data Collection and Indicator Design\u003c/h2\u003e\u003cp\u003eWe assembled a comprehensive indicator dataset as the first step of a four-stage workflow (data \u0026rarr; modelling \u0026rarr; optimisation \u0026rarr; validation). Twelve indicators span supply risks, demand trends, geopolitical considerations, and technology significance [\u003cspan additionalcitationids=\"CR28 CR29\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Each indicator has a definition, primary axis, data source, rationale, and direction of effect.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSelected indicators for quantum-relevant inputs\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndicator\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDefinition\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePrimary Axis\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSource (examples)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eDirection\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDiversity of Supply (DS)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber / dispersion of source countries\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eITC trade statistics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLower DS \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSupplier Monopoly (MS)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDominance by single / few suppliers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eITC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigher MS \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eImport Dependency (DI)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eShare of consumption met by imports\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUN Comtrade\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigher DI \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDemand Growth (DG)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRecent demand\u003c/p\u003e\u003cp\u003egrowth rate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStrategic Significance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMarket reports\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigher DG \u0026rarr; higher criticality\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInternal Demand (ID)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDomestic demand level\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStrategic Significance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eITC / national statistics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigher ID \u0026rarr; higher criticality\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePolitical Stability (PS)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGovernance stability of suppliers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWGI (World Bank)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLower stability \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnvironmental / Social Regulations (ES)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEPI/HDI proxies for regulatory stringency\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eEPI / HDI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eStricter rules \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResource Competition (RC)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMarket concentration index (e.g., HHI)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIndustry data\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigher RC \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProduction Growth (PG)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProduction trend\u003c/p\u003e\u003cp\u003evs demand\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply Risk\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUSGS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLower PG \u0026rarr; higher risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCommodity Price Trend (GSCI)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePrice-volatility proxy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStrategic Significance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eS\u0026amp;P GSCI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMore volatile \u0026rarr; higher criticality\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDecision-Flow Model (DFM)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eInternal criticality flag\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply / Strategic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eInternal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eFlagged \u0026rarr; higher criticality\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWassenaar Arrangement (WA)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExport-control classification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSupply / Strategic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWA list\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eListed \u0026rarr; higher criticality\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"5\"\u003eNotes (abbreviations \u0026amp; dimensions). ITC\u0026thinsp;=\u0026thinsp;International Trade Centre [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]; WGI\u0026thinsp;=\u0026thinsp;Worldwide Governance Indicators (World Bank) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]; EPI / HDI\u0026thinsp;=\u0026thinsp;Environmental Performance Index / Human Development Index [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]; HHI\u0026thinsp;=\u0026thinsp;Herfindahl-Hirschman Index; USGS\u0026thinsp;=\u0026thinsp;U.S. Geological Survey [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]; S\u0026amp;P GSCI\u0026thinsp;=\u0026thinsp;S\u0026amp;P Goldman Sachs Commodity Index [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]; WA\u0026thinsp;=\u0026thinsp;Wassenaar Arrangement [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Typical dimensions: DS/MS/DI/PS/ES/RC/PG are country-level; GSCI/WA are material-level; DFM/ID/DG may be programme- or market-level depending on implementation.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eUtilising these indicators, we collected data for two exemplar material groups\u0026mdash;Mo (high-purity metals) and a representative set of rare earth elements (REEs)\u0026mdash;across 216 countries (2023). This yields 12 \u0026times; 2 \u0026times; 216\u0026thinsp;=\u0026thinsp;5,184 data points, with careful cleaning and consistency checks [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Data Preprocessing and Normalisation\u003c/h2\u003e\u003cp\u003eGiven heterogeneous units and scales, we apply min\u0026ndash;max normalisation to a 0\u0026ndash;100 scale:\u003c/p\u003e\u003cp\u003e\u003cem\u003eXₙₒ\u003csub\u003er\u003c/sub\u003eₘ = 100 \u0026times; (X\u0026thinsp;\u0026minus;\u0026thinsp;Xₘ\u003csub\u003ei\u003c/sub\u003eₙ) / (Xₘₐₓ \u0026minus; Xₘ\u003csub\u003ei\u003c/sub\u003eₙ).\u003c/em\u003e\u003c/p\u003e\u003cp\u003eThis expresses all indicators on a common scale, preventing large-range features from dominating downstream modelling [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Foresight Module: ANN-Based Predictive Modelling\u003c/h2\u003e\u003cp\u003eFollowing the preparation of a clean, normalised dataset, we develop a predictive model to estimate a material\u0026rsquo;s criticality from input indicators. An ANN captures complex non-linear relationships among multiple features [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The ANN optimises weights and biases to achieve high predictive performance between the inputs and the target criticality score. Key hyperparameters\u0026mdash;including the number of layers, activation functions, optimiser, and dataset partitioning\u0026mdash;are essential elements in training the model [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Let x \u0026isin; ℝ\u0026sup1;\u0026sup2; denote the 12-indicator input vector. Hidden-layer activations use ReLU; the output is linear. We evaluate predictions using the coefficient of determination:\u003c/p\u003e\u003cp\u003e\u003cem\u003eR\u0026sup2; = 1\u0026thinsp;\u0026minus;\u0026thinsp;Σ\u003csub\u003ei\u003c/sub\u003e (y\u003csub\u003ei\u003c/sub\u003e \u0026minus; ŷ\u003csub\u003ei\u003c/sub\u003e)\u0026sup2; / Σ\u003csub\u003ei\u003c/sub\u003e (y\u003csub\u003ei\u003c/sub\u003e \u0026minus; ȳ)\u0026sup2;.\u003c/em\u003e\u003c/p\u003e\u003cp\u003eAll model development used Python with TensorFlow (\u0026ge;\u0026thinsp;2.0) and scikit-learn (\u0026ge;\u0026thinsp;0.23) [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. To aid policy interpretability, we compute post-hoc feature attributions (e.g., SHAP) on the trained ANN.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Weight Optimisation via Particle Swarm Optimisation (PSO)\u003c/h2\u003e\u003cp\u003eAlthough the ANN generates a criticality score for any specified set of indicator values, we also explore the inverse problem: identifying combinations of indicator levels that lead to the worst-case (high-criticality) configurations. We employ particle swarm optimisation (PSO) as a metaheuristic search method that complements machine-learning models in determining risk-amplifying configurations [\u003cspan additionalcitationids=\"CR44 CR45\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. For particle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e at iteration \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\text{x}}_{i}^{(k+1)}={\\text{x}}_{i}^{\\left(k\\right)}+{\\text{v}}_{i}^{(k+1)},{\\text{v}}_{i}^{(k+1)}=\\omega\\:{\\text{v}}_{i}^{\\left(k\\right)}+{c}_{1}{r}_{1}({\\text{p}}_{i}-{\\text{x}}_{i}^{\\left(k\\right)})+{c}_{2}{r}_{2}({\\text{p}}_{g}-{\\text{x}}_{i}^{\\left(k\\right)}).$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eHere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:\\)\u003c/span\u003e\u003c/span\u003e is inertia (e.g., 0.4\u0026ndash;1.4), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{1},{c}_{2}\\)\u003c/span\u003e\u003c/span\u003e are acceleration coefficients, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{r}_{1},{r}_{2}\\sim\\:U\\left[\\text{0,1}\\right]\\)\u003c/span\u003e\u003c/span\u003e. We implement PSO in Python (open-source libraries); no proprietary solver is required.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.6 Summary and Validation\u003c/h2\u003e\u003cp\u003eIntegrating the components above yields a rigorous, data-driven, forward-looking QCI. A tri-axial structure (supply risk, substitutability, strategic significance) is instantiated via twelve measurable indicators (normalised to 0\u0026ndash;100), with an ANN foresight module for early warnings and a PSO layer for stress-tested weighting [\u003cspan additionalcitationids=\"CR28 CR29\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. The framework is adaptive: indicators and weights can be updated as new data or policy shocks emerge; models are retrainable.\u003c/p\u003e\u003cp\u003eIn subsequent sections, we validate the methodology through case studies. As an example, Mo (high-purity metals) is examined to illustrate QCI scoring in practice. We compute Mo\u0026rsquo;s axis scores, apply the ANN to project criticality under demand growth, and show how PSO-optimised settings produce a final assessment. This identifies known supply vulnerabilities and limited substitutability, flagging Mo as a high-concern material\u0026mdash;consistent with recent production trends and China\u0026rsquo;s 2025 export-licensing measures [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. For policy users, we additionally report (a) a \u0026ldquo;control-elasticity\u0026rdquo; sub-index (how marginal changes in licensing/outbound rules shift the QCI score), (b) a component-level supplier-concentration metric (HHI and within-allies share), and (c) an early-warning flag when ANN-predicted trajectories cross pre-set thresholds (e.g., He-3 stockout horizons or DR lead-times). To ensure auditability and avoid performative compliance, we tie these indicators to externally verifiable \u0026ldquo;crypto-agility\u0026rdquo; exercises and disclosure checklists\u0026mdash;tools outlined in our allied implementation blueprint; and we map regulatory signals to the control-elasticity sub-index through updates to multilateral control lists (Wassenaar Arrangement) and the U.S. outbound-investment program (E.O. 14105), so QCI scores endogenise evolving dual-use friction. [\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e, \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Case Study: Molybdenum (Mo) Criticality in Quantum Technologies","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Molybdenum Supply-Chain Risk\u003c/h2\u003e\u003cp\u003eMolybdenum\u0026rsquo;s supply chain exhibits substantial concentration and inherent vulnerability. According to the U.S. Geological Survey, global mine output in 2023 was approximately 260,000 metric tons, with China, Chile, Peru, the U.S., and Mexico collectively accounting for about 93% of total production. China remained the largest producer (around 110,000 tons) and continued to face environmental-permitting constraints that limited domestic expansion [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. This highly concentrated structure underscores the potential for supply shocks, particularly when coupled with policy or regulatory disruptions.\u003c/p\u003e\u003cp\u003eOn 4 February 2025, China imposed export-licensing requirements on molybdenum\u0026mdash;alongside tungsten and other strategic metals\u0026mdash;under Announcement No. 10 [2025] [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Even without an outright ban, these measures pushed global prices higher and raised near-term concerns about shortages, echoing earlier episodes of leverage involving rare earth elements [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Import-dependent economies, therefore, face pronounced exposure to such shocks: abrupt controls can disrupt manufacturing timelines, inflate costs, and force complex materials substitutions.\u003c/p\u003e\u003cp\u003eSubstitutability remains limited across high-performance applications. As a refractory metal, Mo imparts exceptional high-temperature strength and corrosion resistance to alloys; alternative elements (e.g., vanadium, chromium) only partially replicate these properties. Mo-based alloys are also used in high-temperature structural components, for example, as container materials in molten-salt reactor designs or as a foundry substrate for sapphire crystal growth due to their strength and corrosion resistance. This limited substitutability amplifies supply risk [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Vulnerability in Quantum Applications\u003c/h2\u003e\u003cp\u003eMo plays quiet but enabling roles across quantum-hardware architectures:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSingle-photon detectors (SNSPDs)\u003c/b\u003e: ultrathin molybdenum-silicide (MoSi) nanowires achieve high system detection efficiency at 1550 nm with low timing jitter at cryogenic temperatures [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSuperconducting circuits/resonators\u003c/b\u003e: Mo\u0026ndash;Re alloys combine mechanical robustness with favourable superconducting properties under strain and magnetic field [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eCryogenic infrastructure\u003c/b\u003e: high-purity Mo fasteners and thermal links provide low thermal expansion and minimal magnetic impurities in dilution refrigerators and ultra-high-vacuum systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eAlthough present demand is modest, scalability represents the key vulnerability. As SNSPD arrays, wiring density, and cryogenic fleets expand, speciality Mo forms (e.g., high-purity powders, films, and alloy feedstock) can become rate-limiting. Substitutes (e.g., WSi, NbN, NbTiN) often require redesign and entail performance penalties\u0026mdash;lower efficiency, higher loss, or reduced critical current\u0026mdash;thereby translating supply risk directly into technical vulnerability, akin to the way helium-3 scarcity constrains low-temperature operations [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Comparative Quantum Criticality (vs. REEs)\u003c/h2\u003e\u003cp\u003eWe benchmark Mo using the QCI matrix with (x) supply risk and (y) quantum impact/irreplaceability. Heavy REEs such as ytterbium (Yb) and erbium (Er) occupy the high-risk/high-impact quadrant: they are technologically indispensable (e.g., trapped-ion qubits, optical clocks, C-band amplification, quantum repeaters) and exhibit highly concentrated supply chains.\u003c/p\u003e\u003cp\u003eHistorically, Mo ranked lower in supply risk due to more diversified mining operations; however, refining and policy leverage are concentrated in a few jurisdictions. Coupled with its enabling role and limited substitutes in quantum components, Mo\u0026rsquo;s position shifts upward and rightward on the QCI plot\u0026mdash;approaching heavy REEs in priority, albeit with a narrower application scope.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003eSource: RQT analysis (2024).\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Molybdenum in the Ecosystem of Chokepoints\u003c/h2\u003e\u003cp\u003eMo\u0026rsquo;s pattern\u0026mdash;concentrated supply with limited substitutability under policy shock\u0026mdash;recurs across quantum enablers. Cryogenics face multi-month lead times for dilution refrigerators (DRs) despite Bluefors\u0026rsquo; U.S. capacity ramp; He-3 stocks are intrinsically rate-limited by tritium decay and DOE processing; TFLN/LNOI has few high-quality wafer suppliers; and a single producer leads the Western supply of electronic-grade diamond. Accordingly, we pair the QCI\u0026rsquo;s diagnostic signal (this Article) with (i) an allied implementation blueprint for near-term action and (ii) a legislative design for durable, risk-tiered governance\u0026mdash;together closing the loop from detection to delivery. [\u003cspan additionalcitationids=\"CR62 CR63 CR64 CR65\" citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e]\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Policy and Conclusion: Translating Foresight into Governance","content":"\u003cp\u003eTo operationalise the QCI\u0026rsquo;s diagnostic and foresight capabilities, policymakers will need to translate risk alerts into concrete actions. This process begins by establishing QCI-linked stockpile triggers and publishing clear thresholds\u0026mdash;such as He-3 reserve floors or DR spare-parts buffers\u0026mdash;that activate pre-funded procurement mechanisms when ANN-generated forecasts breach specified risk levels [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. Beyond domestic stockpiling, allied industrial coordination is essential, including the formation of allied procurement pools that commit to multi-year \u0026ldquo;take-or-pay\u0026rdquo; options for critical hardware (e.g., DRs and cryocoolers) while requiring supplier contingency measures such as second-site manufacturing and in-region spares hubs [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis industrial strategy should be paired with targeted licensing corridors that leverage outbound and inbound screening regimes (e.g., E.O. 14105 and updates to the Wassenaar Arrangement) to prioritise and protect allied capacity for DRs, He-3 handling, thin-film lithium niobate (TFLN, LiNbO₃) wafers, and diamond\u0026mdash;while minimising collateral effects on adjacent photonics industries [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]. Furthermore, governance will need to extend to the intangible supply chain, given that process know-how (e.g., TFLN wafer etching) frequently constitutes the bottleneck; accordingly, we recommend allied intellectual property (IP) pools or fair, reasonable, and non-discriminatory (FRAND)-style licensing frameworks linked to domestic manufacturing incentives [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFinally, to ensure supply-chain integrity, governance should encompass origin assurance for quantum-grade inputs. We recommend adopting verifiable credentials for origin and processing of key materials\u0026mdash;notably He-3, Si-28, diamond, and LiNbO₃\u0026mdash;tethered to QCI scores, with non-compliant inputs incurring de-risking penalties in public procurement processes [\u003cspan additionalcitationids=\"CR63 CR64\" citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e]. This procurement-led approach also provides a tractable mechanism for integrating the environmental, social, and governance (ESG) pillar. By tying public contracts for new resource extraction or processing to compliance with stringent environmental standards and \u0026ldquo;just transition\u0026rdquo; principles, allies can de-risk supply chains without compromising sustainability goals. The urgency of these measures is underscored by industry-reported DR lead times (approximately 6\u0026ndash;9 months) and supplier concentration, which together confirm a systemic bottleneck [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eUltimately, operationalising the QCI transforms strategic foresight into anticipatory governance. By linking data-driven diagnostics to enforceable procurement, licensing, and ESG mechanisms, allies can institutionalise resilience within the quantum supply chain rather than reacting to crises ex post. The QCI thus provides not only a technical metric but also a policy framework\u0026mdash;one that redefines how emerging technologies are governed through coordinated, evidence-based, and values-driven decision-making.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics Approval and Consent to Participate\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of Data and Materials\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;All data generated or analysed during this study are included in this published article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;This work was supported by the \u003cem\u003eProgram on Geopolitics, Technology and Governance\u003c/em\u003e. The funding bodies had no role in the design, analysis, or interpretation of data, nor in writing the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions Statement\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;D.C. (Dongyoun Cho) led the manuscript preparation, integration, and submission. D.C. structured the overall argument, harmonised the technical and policy sections, ensured coherence across the manuscript, and served as the corresponding author.\u003cbr\u003e\u0026nbsp;M.K. (Mauritz Kop) contributed to the conceptual foundation and legal-policy analysis, particularly regarding technology governance, export controls, and intellectual-property frameworks. M.K. refined the discussion on allied standardisation and regulatory coherence.\u003cbr\u003e\u0026nbsp;M.L. (Min-Ha Lee) designed and implemented the methodological components, including the ANN-based foresight model and PSO optimisation, and collected and validated the case-study data. M.L. also contributed to the technical interpretation of QCI indicators.\u003cbr\u003e\u0026nbsp;All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;The authors thank the EPJ Quantum Technology editors and reviewers for their constructive comments. The authors express special thanks to Andrew J. Grotto for his support of this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration on Large Language Model Use:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Large Language Models (LLMs) such as ChatGPT were used only as a writing assistant for grammar and language clarity. No AI system contributed to the conceptual, analytical, or interpretative aspects of this work, and thus no authorship attribution is assigned to LLMs. This use has been properly acknowledged in the Methods section.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eNational Academies of Sciences, Engineering, and, Medicine. Quantum science concepts in enhancing national security: An assessment of applications. Washington (DC): National Academies; 2019.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEuropean Commission. Coordinated plan on Quantum Communication Infrastructure (EuroQCI). Brussels: European Commission; 2021.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNational Research Council. Minerals, critical minerals, and the U.S. economy. Washington (DC): National Academies; 2008.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBains C. The world keeps running out of helium. 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Available from: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://nanoscience.oxinst.com/ProteoxFamily\u003c/span\u003e\u003cspan address=\"https://nanoscience.oxinst.com/ProteoxFamily\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"epj-quantum-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epjq","sideBox":"Learn more about [EPJ Quantum Technology](http://epjquantumtechnology.springeropen.com)","snPcode":"40507","submissionUrl":"https://submission.nature.com/new-submission/40507/3","title":"EPJ Quantum Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Quantum technologies, Supply-chain governance, Critical materials, Resilience, Artificial neural networks (ANN), Quantum Criticality Index (QCI), Export controls, ESG, Allied technology strategy","lastPublishedDoi":"10.21203/rs.3.rs-8062873/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8062873/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuantum technologies are moving from laboratory research to real-world deployment, but progress rests on narrow, fragile, globally dispersed supply chains. We introduce the Quantum Criticality Index (QCI)\u0026mdash;a tri-axial assessment of supply risk, substitutability, and strategic significance\u0026mdash;augmented with an artificial neural network (ANN)-based trend-detection module and a scenario-based foresight layer. A case study of molybdenum (Mo), essential for superconducting circuits, single-photon detectors, cryogenic hardware, and other defence-adjacent systems, shows how the QCI pinpoints chokepoints that could hinder hardware trajectories. Building on these diagnostics, we translate risk awareness into action through a governance framework that links the stages of diagnosis, decision, and delivery. By coupling structured indicators with predictive analytics, the QCI provides policymakers and industry with an evidence-based tool that translates diagnostics directly into an operational policy roadmap for allied procurement, intellectual property governance, targeted licensing, and verifiable, sustainable supply-chain assurance.\u003c/p\u003e","manuscriptTitle":"Strategic Governance of Quantum Supply Chains: A Criticality-Based Framework for Risk, Resilience, and Data-Driven Foresight","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-11 17:13:16","doi":"10.21203/rs.3.rs-8062873/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-23T12:35:31+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-22T15:05:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"83559900727344557616356254736971935162","date":"2025-12-03T20:49:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-22T15:15:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"272032860215207139243976948395840504681","date":"2025-11-13T13:04:03+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-13T07:25:53+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-10T09:32:31+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-10T04:02:03+00:00","index":"","fulltext":""},{"type":"submitted","content":"EPJ Quantum Technology","date":"2025-11-08T09:10:44+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"epj-quantum-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epjq","sideBox":"Learn more about [EPJ Quantum Technology](http://epjquantumtechnology.springeropen.com)","snPcode":"40507","submissionUrl":"https://submission.nature.com/new-submission/40507/3","title":"EPJ Quantum Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bfc86468-6b89-43e6-b769-255dd319440c","owner":[],"postedDate":"November 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-16T16:04:06+00:00","versionOfRecord":{"articleIdentity":"rs-8062873","link":"https://doi.org/10.1140/epjqt/s40507-026-00486-y","journal":{"identity":"epj-quantum-technology","isVorOnly":false,"title":"EPJ Quantum Technology"},"publishedOn":"2026-03-10 16:00:09","publishedOnDateReadable":"March 10th, 2026"},"versionCreatedAt":"2025-11-11 17:13:16","video":"","vorDoi":"10.1140/epjqt/s40507-026-00486-y","vorDoiUrl":"https://doi.org/10.1140/epjqt/s40507-026-00486-y","workflowStages":[]},"version":"v1","identity":"rs-8062873","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8062873","identity":"rs-8062873","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}