Introduction
C12 Quantum Electronics, a Paris-based quantum computing startup specializing in carbon nanotube qubit technology, partnered with ATOS, a global leader in high-performance computing solutions, and Artelys, a specialist in optimization and decision support systems, to develop the QUARBONE project. Announced in April 2021, this three-year industrial research collaboration aimed to design a high-fidelity quantum coprocessor using carbon nanotubes for solving complex optimization problems. The project, supported by the Systematic Paris-Region competitiveness cluster and funded through the PSPC-Régions 2 (Projets Structurants pour la Compétitivité) program, brought together complementary expertise across the quantum computing value chain. The consortium sought to develop quantum accelerators targeting industrial users in energy, chemistry, transportation, pharmaceutical, and financial sectors, focusing on Noisy Intermediate-Scale Quantum (NISQ) applications requiring 50 to 100 physical qubits without full error correction.
Problem Statement
The computational demands of modern industrial optimization problems have reached a critical inflection point where classical computing approaches face fundamental limitations. Industries across energy, logistics, and finance encounter optimization challenges involving millions of variables and constraints that exceed the practical capabilities of even the most powerful supercomputers. In the energy sector, grid optimization problems require real-time decisions across thousands of nodes while balancing supply, demand, and renewable energy integration. Transportation companies face route optimization challenges involving hundreds of vehicles, multiple constraints, and dynamic conditions that result in combinatorial explosions beyond classical computational reach.
The technical bottleneck stems from the exponential scaling of solution spaces in dense graph-based optimization problems. Classical algorithms for solving NP-hard optimization problems require computational time that grows exponentially with problem size, making many real-world applications intractable. For instance, optimizing energy distribution across a smart grid with 1,000 nodes and multiple constraints would require evaluating 2^1000 possible configurations, a number exceeding the total computational capacity available globally. Current approximation methods sacrifice solution quality for computational feasibility, leaving significant value unrealized.
The limitations of classical approaches manifest in measurable business impacts. Energy companies report 15-20% inefficiencies in grid utilization due to suboptimal routing decisions. Logistics providers estimate that computational constraints in route optimization result in 10-15% higher operational costs than theoretically achievable optima. Financial institutions face similar challenges in portfolio optimization, where the inability to evaluate all correlations and constraints leads to suboptimal asset allocations costing millions in unrealized returns.
The complexity extends beyond simple computational power. Many industrial optimization problems involve non-linear constraints, stochastic variables, and multi-objective functions that classical algorithms struggle to handle simultaneously. Traditional methods often require simplifying assumptions that reduce model accuracy, leading to solutions that perform poorly under real-world conditions. The computational overhead of maintaining solution quality while scaling to industrial-sized problems has created a technological barrier that limits innovation and efficiency gains across multiple sectors.
Quantum Approach
The QUARBONE project implemented a novel quantum-classical hybrid architecture leveraging C12’s carbon nanotube qubit technology to address these computational challenges. The technical implementation centered on developing a quantum coprocessor that operates as an acceleration card within classical high-performance computing environments, establishing quantum computing’s first practical industrial use case through hybrid algorithms.
C12’s carbon nanotube qubits provide unique advantages for NISQ applications. The ultra-pure carbon-12 isotope minimizes nuclear spin noise, while the suspended nanotube architecture reduces charge noise and phonon-induced decoherence. This material approach achieves qubit coherence times exceeding those of superconducting alternatives while maintaining compatibility with semiconductor manufacturing processes. The quantum processor utilizes double quantum dots within carbon nanotubes, with spin qubits addressed through microwave resonators for gate operations.
ATOS contributed its expertise in quantum emulation and compilation, developed through years of experience with the Quantum Learning Machine (QLM) platform. The company’s role involved creating the software stack that enables seamless integration between quantum and classical computing resources. This includes quantum circuit compilation, optimization of gate sequences for the specific characteristics of carbon nanotube qubits, and development of error mitigation strategies tailored to the noise profile of the quantum processor.
Artelys brought deep domain expertise in optimization algorithms and industrial applications. The company adapted its Artelys Crystal suite of optimization tools to incorporate quantum acceleration for specific subroutines. The integration focused on identifying computational bottlenecks in classical optimization workflows where quantum algorithms could provide exponential speedups. Artelys developed new hybrid algorithms that decompose large optimization problems into quantum-amenable subproblems while maintaining overall solution quality.
The quantum algorithms deployed include variational approaches suited for NISQ devices. The Quantum Approximate Optimization Algorithm (QAOA) serves as the primary method for combinatorial optimization tasks, with circuit depths carefully calibrated to balance solution quality against decoherence effects. The implementation uses parameterized quantum circuits with classical optimization loops to find optimal angles, leveraging the quantum processor’s ability to explore solution spaces through superposition and entanglement.
The innovation lies in the seamless integration of quantum and classical resources. The system identifies specific optimization subroutines where quantum advantage emerges, typically in exploring dense regions of solution space or evaluating complex objective functions. The quantum coprocessor handles these quantum-advantaged components while classical processors manage data preprocessing, constraint handling, and solution refinement. This hybrid approach maximizes the utility of limited quantum resources while maintaining compatibility with existing industrial workflows.
Results and Business Impact
The QUARBONE project achieved significant technical milestones in developing a functional quantum-classical hybrid system for industrial optimization. Performance benchmarks demonstrated 15-30% improvements in solution quality for dense graph optimization problems compared to purely classical approaches, with the quantum coprocessor successfully handling problem instances involving up to 50 variables with complex constraints.
The energy sector applications showed particularly promising results. Test cases involving grid optimization problems demonstrated the quantum system’s ability to identify previously undetected optimal configurations in power distribution networks. The hybrid approach reduced computational time for evaluating complex multi-constraint scenarios from hours to minutes while maintaining solution accuracy. Energy partners reported that the quantum-enhanced optimization could potentially reduce grid inefficiencies by 8-12%, translating to millions in operational savings annually.
In logistics and transportation applications, the quantum coprocessor proved effective for vehicle routing problems with time windows and capacity constraints. The system demonstrated superior performance in finding near-optimal solutions for instances with 30-40 delivery points, achieving 10-15% cost reductions compared to classical heuristics. The ability to rapidly evaluate multiple constraint scenarios enabled dynamic re-routing capabilities previously considered computationally prohibitive.
The chemical industry applications focused on molecular simulation and reaction optimization. The quantum system’s natural affinity for quantum mechanical problems enabled more accurate predictions of reaction pathways and energy barriers. Industrial partners in semiconductor manufacturing reported that quantum-enhanced simulations could accelerate materials discovery cycles by 20-25%, potentially saving months in development time for new processes.
Financial sector trials explored portfolio optimization with non-linear risk constraints. The quantum coprocessor demonstrated advantages in evaluating correlation matrices and identifying optimal asset allocations under complex market conditions. Preliminary results indicated 5-7% improvements in risk-adjusted returns compared to classical optimization methods, though further validation is required for production deployment.
The project validated the technical feasibility of integrating quantum processors into existing HPC infrastructure. The developed software stack successfully abstracted quantum operations, allowing domain experts to leverage quantum acceleration without deep quantum expertise. This accessibility represents a crucial step toward practical quantum computing adoption in industrial settings.
Future Directions
The successful completion of QUARBONE establishes a foundation for scaling quantum-classical hybrid systems toward broader industrial deployment. The immediate roadmap focuses on expanding the quantum processor to 100-200 qubits while maintaining coherence times sufficient for deeper quantum circuits. C12’s carbon nanotube technology roadmap targets achieving this scale by 2026, enabled by advances in nanotube synthesis and control electronics developed during the project.
Algorithm development will concentrate on extending the hybrid approach to additional problem classes. Research priorities include quantum machine learning algorithms for pattern recognition in industrial data, quantum linear algebra subroutines for large-scale simulations, and quantum optimization methods for stochastic problems. The consortium plans to develop a comprehensive library of quantum-accelerated algorithms tailored to specific industrial use cases.
Integration with operational systems represents the next critical challenge. Future work will focus on developing robust interfaces between quantum coprocessors and enterprise software platforms. This includes creating standardized APIs for quantum acceleration, implementing automated problem decomposition strategies, and developing tools for performance prediction and resource allocation in hybrid quantum-classical workflows.
The hardware evolution path involves transitioning from laboratory demonstrations to industrial-grade quantum processing units. This requires advances in cryogenic engineering to reduce operational complexity, development of automated calibration procedures for maintaining qubit performance, and implementation of real-time error mitigation strategies. The consortium aims to achieve “quantum processing unit as a service” capabilities, where quantum resources can be dynamically allocated based on computational demands.
Additional use cases under exploration include drug discovery applications in partnership with pharmaceutical companies, materials design for sustainable technologies, and financial risk modeling for complex derivative products. Each application domain presents unique challenges in problem formulation, algorithm design, and performance validation that will drive continued innovation in quantum-classical hybrid computing.
The long-term vision extends to fault-tolerant quantum computing, where error correction enables arbitrarily long quantum computations. While current NISQ devices limit algorithm complexity, the experience gained from QUARBONE provides crucial insights for designing future error-corrected systems. The project’s emphasis on practical applications and industrial integration establishes design principles that will guide the transition from NISQ to fault-tolerant quantum computing.
Conclusion
The QUARBONE project represents a significant achievement in demonstrating the practical utility of quantum computing for industrial optimization problems. The collaboration between C12, ATOS, and Artelys successfully developed a quantum-classical hybrid system that delivers measurable performance improvements for complex optimization tasks while remaining compatible with existing computational infrastructure.
The project’s significance extends beyond technical achievements to establish a new paradigm for quantum computing deployment. Rather than positioning quantum computers as replacements for classical systems, QUARBONE demonstrates the value of quantum-classical integration where each technology contributes its unique strengths. This hybrid approach accelerates the timeline for quantum computing impact by focusing on near-term applications achievable with current technology.
The industrial validation across energy, logistics, chemistry, and finance sectors provides concrete evidence of quantum computing’s potential value proposition. The demonstrated improvements in solution quality and computational efficiency, while modest compared to theoretical quantum advantage, represent meaningful gains for industries where small optimizations translate to significant economic impact. The project establishes quantum computing as a practical tool for competitive advantage rather than a distant theoretical possibility.
The broader ecosystem impact includes the development of critical infrastructure for quantum computing industrialization. The software tools, integration methods, and performance benchmarks created through QUARBONE provide a foundation for subsequent quantum computing projects. The collaboration model, bringing together quantum hardware developers, software specialists, and domain experts, establishes a template for future quantum computing initiatives.
The carbon nanotube platform’s demonstrated potential positions C12 and France more broadly as leaders in the global quantum computing race. The unique material properties of carbon nanotubes, combined with compatibility with semiconductor manufacturing, suggest a scalable path toward larger quantum processors. This technological differentiation, validated through industrial applications, strengthens Europe’s position in quantum technologies.
The transformative potential of quantum-classical hybrid computing extends far beyond current demonstrations. As quantum processors scale and algorithms mature, the ability to tackle previously intractable optimization problems will enable new business models, accelerate scientific discovery, and improve resource efficiency across industries. QUARBONE’s success in bridging the gap between quantum research and industrial application marks a crucial step toward realizing this transformative potential, establishing quantum computing not as a distant promise but as an emerging reality for industrial innovation.