The study’s central conceptual move is deliberately cautious. Rather than claiming that digitalization is inherently green, the authors — T.T. Pham, T.D. Nguyen, H.D. Luu, and colleagues — treat digital transformation as an enabling capability. They construct a five-dimensional Digital Transformation Indicator (DTI) covering digital infrastructure, digital adoption, digital innovation, digital governance, and digital industry development. The index deliberately does not measure environmental performance itself; a province can score high on digital capability while still performing poorly environmentally. What the DTI captures is the capacity to make resource use visible, lower coordination costs, and support the adoption of cleaner technologies when institutions and firms are able to use them.

Building the index required careful handling of Vietnam’s fragmented administrative data. Backbone indicators — such as fixed broadband subscriptions per 100 inhabitants, enterprise broadband adoption, active internet use, ICT-registered enterprise density, e-government readiness, and the digital economy’s share of provincial GDP — were standardized and combined using principal component analysis. The first component explains 63.7 percent of total variance, with loadings ranging from 0.38 to 0.47, and the index passes standard reliability diagnostics including a Kaiser-Meyer-Olkin measure of 0.83 and Cronbach’s alpha of 0.87. Alternative constructions using equal weights and entropy-weighted TOPSIS correlate at 0.971 and 0.924 with the baseline, confirming that no single dimension drives the findings.

The spatial picture that emerges is stark. Hanoi, Ho Chi Minh City, Binh Duong, and Da Nang consistently occupy the upper quartile of digital capability throughout the sample period, while provinces in the Northern Uplands and Central Highlands remain in the lowest. Yet relative rankings are remarkably stable — the rank correlation between 2010 and 2022 DTI values is 0.81 — even as absolute digital levels rise nationwide. Energy efficiency displays a parallel hierarchy, with industrially diversified Red River Delta and Southeast provinces outperforming resource-dependent northwestern and highland regions. Global Moran’s I statistics confirm significant positive spatial autocorrelation in both digital capability (0.341) and energy efficiency (0.287) in 2022.

To move beyond description, the researchers employed two-way fixed-effects panel models and Spatial Durbin Models (SDM), which allow both outcomes and explanatory variables to be spatially interdependent. In the preferred specification with full development controls — including log GDP per capita, industrial structure, human capital, FDI intensity, environmental regulation, and population density — a one-standard-deviation increase in DTI corresponds to a 0.049-unit difference in the energy-efficiency measure. Adding the full control vector attenuates the DTI coefficient by 12.3 percent, from 0.381 to 0.334, indicating that observable development gradients explain part, but not all, of the association. An instrumental-variable specification using distance to pre-2009 fiber-optic trunk lines yields a larger estimate of 0.512, but the authors treat this strictly as directional robustness evidence because the instrument’s exclusion restriction is contestable.

The spillover findings are arguably the most consequential. Under queen-contiguity weights, the SDM decomposition attributes a direct association of 0.312 and a spillover association of 0.187 to DTI, meaning 37.5 percent of the total association is spatially indirect. In plain terms, digital capability in one province is associated with better energy efficiency in neighboring provinces — a pattern consistent with infrastructure corridors, labor mobility, supply chains, and policy learning. Positive spillovers persist, though smaller, under inverse-distance and economic-proximity weight matrices, suggesting the phenomenon is not confined to shared borders. A non-spatial model, the authors note, would systematically understate the resource-sustainability relevance of digital investment.

Mechanism analysis points to innovation capacity as a key transmission channel. Provinces with higher DTI scores show stronger patent activity per capita, and when patent activity is included in the model, the DTI coefficient falls from 0.334 to 0.191. The bootstrapped pathway estimate of 0.144 yields a descriptive ratio of 43.1 percent; using R&D intensity instead produces an analogous figure of 34.7 percent. The authors are careful to label this an innovation-capacity pathway rather than a green-innovation mechanism, because the patent data cover all patents, not specifically environmental ones. These ratios describe mechanism-consistent covariance under sequential assumptions, not causal mediation shares.

Perhaps the most intriguing result is nonlinear. Using Hansen’s threshold regression, the study identifies a critical DTI value of 0.487 — near the 60th percentile of the distribution — above which the association with energy efficiency more than doubles, from 0.187 to 0.412. This is consistent with absorptive-capacity theory: digital capability pays off most when complementary skills, innovation assets, and administrative readiness have accumulated. Provinces such as Vinh Phuc, Khanh Hoa, and Can Tho sit near this benchmark, while Hanoi and Ho Chi Minh City operate well above it. The threshold is explicitly a Vietnam-specific benchmarking point, not a universal policy cutoff, and remains in the 55th to 63rd percentile range across alternative index constructions and outcome measures.

The authors are unusually candid about limitations. Provincial energy consumption is reconstructed from sectoral activity data rather than directly metered, with roughly 7 percent of activity cells requiring imputation; eight provinces with imputation rates above 15 percent were excluded in a sensitivity check, and Green Total Factor Productivity — computed via a Malmquist-Luenberger index treating CO2 as an undesirable output — serves as an alternative outcome with qualitatively consistent results. Placebo tests randomly permuting provincial DTI series place the observed coefficient at the 99.8th percentile of the placebo distribution. Still, the design remains observational, and the authors explicitly decline to claim causal policy effects.

The policy implications are differentiated rather than uniform. For provinces well below the readiness threshold, the evidence favors foundational investments — reliable broadband, basic digital skills, interoperable reporting standards — over advanced applications that cannot substitute for these bases. Provinces near the benchmark are candidates for bundled support combining energy-management systems, data interoperability, and technology-extension services. High-DTI provinces are better positioned to pilot real-time energy dashboards, digital permitting, and cross-agency analytics, ideally with transparent evaluation designs. And because spillovers operate through multiple proximity channels, the study supports harmonized data standards along shared corridors, infrastructure sharing among geographically proximate regions, and benchmarking platforms among economically similar provinces — a nuanced architecture that treats digital transformation not as an environmental end in itself, but as the connective tissue that determines whether green-growth commitments become measurable efficiency gains.

Subject of Research: The association between provincial digital transformation and resource efficiency in Vietnam

Article Title: Digital transformation as environmental implementation capacity: resource-efficiency associations, spatial spillovers, and threshold evidence from Vietnam

Article References: Pham, T., Nguyen, T., Luu, H., Pham, D., Tran, A., Le, K., & Nguyen, M. (2026). Digital transformation as environmental implementation capacity: resource-efficiency associations, spatial spillovers, and threshold evidence from Vietnam. Environmental Challenges, 25, Article 101645. https://doi.org/10.1016/j.envc.2026.101645

Image Credits: AI Generated

DOI: 10.1016/j.envc.2026.101645

Keywords: digital transformation, resource efficiency, energy efficiency, Vietnam, spatial spillovers, threshold effects, environmental implementation capacity, green growth, spatial econometrics, innovation capacity, absorptive capacity, provincial panel data

The work, led by Petr Ptáček together with Paulina Lewandowska and Ryszard Kukulski, both of whom contributed equally, addresses one of the most pressing practical constraints in near-term quantum computing. Devices in the so-called NISQ era, a term coined by John Preskill, operate without full quantum error correction. Every circuit execution is subject to noise, queue times on shared hardware are long, and the cost of running a model scales with the number of shots required per prediction. If quantum machine learning is ever to leave the laboratory and compete with classical methods, reducing the number of circuit evaluations is arguably as important as improving raw accuracy.

The core idea behind the new classifier lies in how it reads out answers from the quantum state. Conventional variational quantum classifiers typically measure the expectation value of an observable, often a Pauli operator, on the output state produced by a parameterized ansatz circuit. This expectation value is then thresholded to assign a class label. The problem is statistical: to estimate an expectation value to a given precision, the circuit must be run repeatedly, and the number of repetitions grows quadratically with the desired precision. The Ostrava team instead draws on the concept of unambiguous state discrimination, in which measurements are designed so that outcomes are either conclusive or explicitly inconclusive, never misleading. By measuring in a way that compares computational basis strings through Hamming distance, the classifier obtains richer, more informative samples from each circuit run.

Hamming distance, the number of bit positions in which two binary strings differ, has a precedent in quantum algorithms for classification. Earlier work on quantum k-nearest-neighbor algorithms used Hamming distance as a similarity metric between encoded data points. The new approach folds that metric into a variational framework: the parameterized circuit transforms and encodes data, and the measurement stage compares the resulting bit strings against reference patterns. Classical post-processing then weighs the conclusive outcomes to produce a classification decision. Because each shot carries more decision-relevant information, far fewer shots are needed per prediction, and the ansatz’s expressivity is exploited more effectively rather than being diluted by coarse averaging.

The theoretical backing matters here. The authors substantiate their experimental results with formal evidence supporting why the approach should perform well, rather than merely reporting empirical wins. This kind of grounding is notable in a field where many proposed quantum machine learning methods have been criticized for lacking provable advantages or for suffering from trainability pathologies such as barren plateaus, the flat regions of the training landscape described by McClean and colleagues in 2018. By tying the measurement scheme to information-theoretic principles and to established discrimination theory, the team provides a rationale for both the accuracy gains and the resource savings.

The empirical testbed was a demanding and socially significant one: the Wisconsin Diagnostic Breast Cancer dataset from the UCI Machine Learning Repository, a standard benchmark in medical classification involving distinguishing malignant from benign tumors based on features derived from digitized images of fine needle aspirate samples. The choice is apt for demonstrating practical relevance, since medical decision support is exactly the kind of domain where classification errors carry real costs and where the efficiency of a model matters if it is ever to run on scarce quantum hardware.

The headline numbers are striking. The unambiguous quantum classifier achieved an average accuracy of 90 percent on the breast cancer dataset, an improvement of 6.9 percentage points over the baseline variational quantum classifier. At the same time, it required eight times fewer circuit executions per prediction. That combination, better accuracy and an eightfold reduction in execution cost, is unusual in quantum machine learning, where improvements in one metric frequently come at the expense of the other. The savings compound across training as well: since model training involves evaluating the objective function many times over many optimization steps, cutting shots per evaluation by a factor of eight can dramatically shorten wall-clock training time and reduce access fees on cloud quantum platforms.

Noise robustness is the second major finding. When noise was injected into the simulations to emulate realistic hardware conditions, the accuracy advantage shrank from 6.9 to approximately 3.1 percentage points, but the eightfold reduction in execution cost persisted. The fact that the method degrades gracefully rather than collapsing is crucial. Many quantum algorithms that look compelling in idealized simulations lose their advantage entirely under realistic noise levels. A classifier that retains a meaningful improvement over its baseline while remaining dramatically cheaper to execute is far more plausible as a candidate for deployment on actual quantum processors, where gate errors, decoherence, and readout imperfections are unavoidable facts of life.

The authors implemented and evaluated their method using the PennyLane framework, the widely used open-source library for hybrid quantum-classical computation, and they have made both the code and the data openly available in a public GitHub repository. The optimizations were handled with classical techniques suited to noisy objective functions, including simultaneous perturbation stochastic approximation, an optimizer originally developed by Spall that estimates gradients from very few function evaluations, a natural pairing with a classifier designed to be frugal with circuit runs.

The broader significance of the study lies in what it suggests about where quantum advantage might first materialize in machine learning. Rather than waiting for large fault-tolerant machines, resource-efficient redesigns of existing algorithms could deliver practical value on today’s hardware. Related efforts in the literature have pursued shot optimization, quantum kernel methods, and data re-uploading schemes, and recent theoretical work on single-shot quantum machine learning has explored how few measurements are truly needed. The Ostrava results sit squarely in this emerging conversation, offering a concrete demonstration that smarter measurement and post-processing can unlock both accuracy and efficiency. If follow-up work confirms these gains on physical quantum processors and across additional datasets, the unambiguous classifier could become a template for building quantum machine learning models that are genuinely competitive, not just conceptually interesting. The research also underscores the value of collaboration between quantum algorithm theorists and application domain experts, a combination that will be essential as the field moves from proof-of-concept demonstrations toward tools that practitioners in medicine, materials science, and beyond can actually rely upon.

Subject of Research: A resource-efficient variational quantum classifier using Hamming distance measurements and classical post-processing

Article Title: Resource-efficient variational quantum classifier

Article References: Resource-efficient variational quantum classifier. (n.d.). https://doi.org/10.1007/s42484-026-00439-9

Image Credits: AI Generated

DOI: 10.1007/s42484-026-00439-9

Keywords: quantum machine learning, variational quantum classifier, Hamming distance, unambiguous state discrimination, NISQ era, breast cancer dataset, circuit evaluations, noise robustness, PennyLane, binary classification, variational circuits, resource efficiency

The research team, led by Moritz Langhorst, modeled the transformation of a plant modeled on publicly reported production data from SSAB’s facility in Oxelösund, Sweden, producing around one million tonnes of liquid steel per year. In the conventional blast furnace-basic oxygen furnace system, the plant consumed roughly 1,325 kilotonnes of iron ore pellets and 579 kilotonnes of coal annually, generating about 1,570 kilotonnes of direct carbon dioxide emissions from iron and steelmaking alone. The rolling mill added another 70 kilotonnes. Crucially, the study also tracked the energy-rich process gases—coke oven gas, blast furnace gas, and basic oxygen furnace gas—that integrated plants routinely recycle as fuel, providing over 1 terawatt-hour per year of surplus energy for power generation and district heating.

When the researchers modeled the shift to the hydrogen-based route, the picture changed dramatically. Direct emissions from iron and steelmaking fell by 94 percent, and total greenhouse gas emissions across the system, including indirect emissions from electricity, dropped by 84 percent under Sweden’s low-carbon electricity mix. When hydrogen combustion replaced natural gas in the rolling mill’s reheating furnaces and heat treatment was electrified, the reduction climbed to 89 percent, cutting emissions intensity from 1.94 to 0.25 tonnes of carbon dioxide equivalent per tonne of plate. That is well below the near-zero emission threshold of 0.33 tonnes proposed by the International Energy Agency for primary steel production. But the transformation came at a steep energy price: electricity demand rose eighteen-fold, from roughly 260 gigawatt-hours to more than 4,600 gigawatt-hours per year, driven overwhelmingly by the alkaline electrolysers producing hydrogen on site.

This electrification shock is the study’s central tension. The additional 4.42 terawatt-hours of annual electricity demand would equal roughly 2.7 percent of Sweden’s entire electricity generation in 2023. In countries with carbon-intensive grids, the climate arithmetic collapses: under the average European electricity mix of 242.3 kilograms of carbon dioxide per megawatt-hour, the emission reduction shrinks from 84 percent to just 30 percent. The authors stress that the promise of hydrogen steelmaking therefore depends entirely on locating production in regions with abundant clean electricity—at least until Europe’s power sector approaches climate neutrality around mid-century. It is a caveat with real-world bite, given that several announced green hydrogen and green steel projects have already been delayed or cancelled across Europe.

The study goes further than previous analyses by treating the steel plant as a single, interconnected organism rather than a collection of independent processes. When the blast furnace disappears, so do the process gases that once fueled the rolling mill, forcing downstream operations to rely on external natural gas, hydrogen, or electricity. This structural coupling means that changes upstream ripple through the entire production chain, and it is precisely where the researchers found unexpected leverage. Material efficiency measures—reducing iron losses in the electric arc furnace, improving casting yields from 96.5 to 98 percent, and raising cutting yields in the rolling mill from roughly 91 to 95 percent—trigger cascading reductions that travel all the way back to the hydrogen demand of the direct reduction plant.

The numbers are compelling. Improving the electric arc furnace iron yield from 89.5 to 95.7 percent, a level typical of scrap-based operation, reduced direct reduced iron demand by nine percent and cut the hydrogen needed for direct reduction by 166 gigawatt-hours per year. Energy efficiency measures worked differently: upgrading electrolyser efficiency from 58.7 percent to a projected 2050 value of 69.94 percent cut the specific electricity demand for hydrogen production by 16 percent, while oxyfuel combustion in the reheating furnace trimmed hydrogen use for that process by 15 percent. Because energy efficiency measures act locally while material efficiency measures propagate upstream through the entire chain, the two strategies proved complementary rather than redundant.

Combined, all modeled efficiency measures reduced the plant’s hydrogen demand by ten percent and its electricity demand by twenty percent—savings of 6.3 kilotonnes of hydrogen and 920 gigawatt-hours of electricity per year. In a world where green hydrogen remains scarce, these percentages matter enormously. The study notes that without efficiency measures, the modeled plant would require up to 63.3 kilotonnes of hydrogen annually, while only about 31 kilotonnes of electrolytic hydrogen were produced across the entire EU, EFTA, and the United Kingdom combined in 2023, out of nearly 8 million tonnes of total hydrogen production that was over 90 percent fossil-based. Every tonne of hydrogen saved through smarter material flows directly expands the number of plants that can realistically decarbonize within the constrained supply expected this decade.

The researchers are careful to acknowledge the limits of their model. It does not include techno-economic assessment, and without carbon pricing or financial support, hydrogen-based direct reduction remains uncompetitive with conventional routes. Yield assumptions for the electric arc furnace fed with direct reduced iron may prove optimistic, since oxide gangue in the DRI limits achievable yields, and electrolyser efficiency projections for 2050 have already been revised downward. Still, the model’s emissions estimate for the reference case closely matched SSAB’s reported 2023 figures, and the qualitative findings proved robust across variations in electricity mix and scrap share. The authors also emphasize that scrap-based electric arc furnace recycling, which would cut electricity demand by over 70 percent compared to hydrogen-based production, remains limited by the availability of low-impurity scrap needed for high-quality flat products.

What emerges from this work is less a prediction than a planning instrument. By quantifying material, energy, and carbon flows across an entire production chain under different decarbonization strategies, prospective plant-level material flow analysis gives steelmakers, grid planners, and policymakers a common physical baseline for site-specific roadmaps. It reveals where emissions migrate as the transition proceeds—the rolling mill’s share of plant emissions jumps from four percent to nearly thirty percent—where hydrogen scarcity will bind hardest, and where operational improvements yield outsized systemic returns. As Europe’s steel industry confronts the largest industrial transformation since the invention of the blast furnace, the message of this study is clear: the technology for near-zero-emission steel exists, but its success will be decided in the details of yields, electrolysers, and every kilowatt-hour in between.

Beyond the headline figures, the study’s methodological choice deserves attention. Material flow analysis has a long pedigree in industrial ecology, where it has been used to map the flows of substances through economies and industrial systems for decades. What distinguishes this application is its prospective character: rather than auditing an existing facility, the framework is designed to simulate structural transformations that have not yet occurred, embedding process-level detail within a plant-wide accounting boundary. This allows the researchers to capture interactions that fall through the cracks of both regional-scale models, which lack operational resolution, and single-process studies, which isolate technologies from their surroundings.

The Swedish setting is not incidental. The country combines an unusually clean electricity grid with pioneering industrial initiatives in hydrogen-based ironmaking, making it a plausible early adopter. Yet even under these favorable conditions, the modeled plant’s electricity appetite rivals that of a mid-sized city, underscoring why grid capacity and electrolyser siting have become central concerns for industrial planners. The finding that the rolling mill’s relative share of plant emissions rises sharply after decarbonization of ironmaking also illustrates a broader principle: as the dominant emission sources are eliminated, previously marginal processes become the next targets, requiring successive waves of intervention rather than a single technological switch.

The distinction between the two families of efficiency measures carries practical implications for how decarbonization investments are sequenced. Material efficiency gains, such as yield improvements, propagate upstream and shrink the entire hydrogen production system needed at the front of the plant, while energy efficiency gains act locally but aggregate into substantial electricity savings. Because hydrogen production dominates the new electricity load, improvements in electrolyser performance translate almost directly into reduced pressure on the power system. For policymakers designing support schemes, the analysis suggests that funding yield optimization and electrolyser development together yields compounding benefits that neither achieves alone, effectively stretching a constrained green hydrogen supply across more tonnes of decarbonized steel.

Subject of Research: Plant-level material flow analysis of the transition from blast furnace steelmaking to hydrogen-based direct reduction and electric arc furnace steelmaking

Article Title: A prospective plant-level material flow analysis to assess systemic efficiency in the transition to hydrogen-based steelmaking

Article References: Langhorst, M., Billy, R. G., Song, X., & Müller, D. B. (2026). A prospective plant-level material flow analysis to assess systemic efficiency in the transition to hydrogen-based steelmaking. Journal of Industrial Ecology. https://doi.org/10.1007/s44498-026-00166-1

Image Credits: AI Generated

DOI: 10.1007/s44498-026-00166-1

Keywords: hydrogen steelmaking, green steel, material flow analysis, decarbonization, electric arc furnace, direct reduced iron, resource efficiency, electrolysis, steel industry emissions, energy efficiency, Sweden, industrial ecology