Industry quantum computing applications

Quantum computing promises to overcome computational limitations with better and faster solutions for optimization, simulation, and machine learning problems. Europe and Germany are in the process of successfully establishing research and funding programs with the objective to advance the technology’s ecosystem and industrialization, thereby ensuring digital sovereignty, security, and competitiveness. Such an ecosystem comprises hardware/software solution providers, system integrators, and users from research institutions, start-ups, and industry. The vision of the Quantum Technology and Application Consortium (QUTAC) is to establish and advance the quantum computing ecosystem, supporting the ambitious goals of the German government and various research programs. QUTAC is comprised of ten members representing different industries, in particular automotive manufacturing, chemical and pharmaceutical production, insurance, and technology. In this paper, we survey the current state of quantum computing in these sectors as well as the aerospace industry and identify the contributions of QUTAC to the ecosystem. We propose an application-centric approach for the industrialization of the technology based on proven business impact. This paper identifies 24 different use cases. By formalizing high-value use cases into well-described reference problems and benchmarks, we will guide technological progress and eventually commercialization. Our results will be beneficial to all ecosystem participants, including suppliers, system integrators, software developers, users, policymakers, funding program managers, and investors.


Introduction
With quantum computers surpassing leading supercomputers in specific computational challenges [1,2], and the availability of noisy intermediate-scale quantum (NISQ)-era quantum computing systems [3][4][5][6] outside of laboratory environments, we have entered 2 QUTAC: quantum application and technology consortium QUTAC aims to raise quantum computing to the level of large-scale industrial applications while preparing our members for a new digital future. We bring together the expertise of Germany's industry to efficiently advance quantum computing towards real-world applications, ensuring Germany's and Europe's digital sovereignty, national security, and competitiveness in a global economy.
QUTAC will move the emerging quantum computing ecosystem forward, supporting the ambitious goals of the German government. It comprises ten companies from four sectors (see Table 1) with the mission to contribute an industry perspective and focus on the development of the German and European quantum ecosystems. QUTAC focuses primarily on the applications of quantum computing. Our members share the need to act due to the potentially disruptive impact of quantum computing on all aspects of our business and value-chains. Collaboration across company borders promises to de-risk fundamental, pre-competitive research. Additionally, quantum computing might allow some members to explore further opportunities in the quantum value-chain, e.g., as a component or software provider. Figure 1 illustrates the focus of QUTAC. The value-chain of QUTAC members comprises complex optimization, machine learning, and simulation challenges that are likely to benefit from advances in quantum computing, providing significant business impact. A wide variety of problems with impact across diverse industries will provide guidance to software and hardware development.
QUTAC's guiding principles are: • Promote the establishment of an economically thriving, independent quantum computing ecosystem in Germany and Europe. • Raise awareness of the potential impact and competitive advantage that quantum technologies can provide across industries, motivating early investment and engagement. • Understand, develop, and test cross-industry applications to identify commercially interesting solutions that can drive the quantum ecosystem forward. • Contribute to the success of the government's ambitious quantum program by providing a perspective from the industry and application angle. QUTAC is organized through working groups that aim to identify commercially attractive solutions for high-impact business problems. QUTAC started with three operational working groups that are structured by the main challenges: "material science", "engineering", and "production & logistics". Members share the need to understand, develop, and evaluate cross-industrial applications on emerging quantum hardware. Such crossindustrial problems include optimizations, machine learning and simulation challenges. QUTAC members present 24 use cases and common challenges in this paper.

Industry applications
While quantum computing will have a significant impact on various industries [12,19], many questions and challenges remain: Which specific problems can be solved? Which of the NISQ quantum devices provide a quantum advantage? How can this advantage be translated into business impact? Here, we present an analysis of high-impact industry quantum applications. The analysis is based on several workshops, a structured survey (answered by 17 experts from 11 companies across 5 industry sectors), and interviews (9 bilateral interviews). The contributing companies have each shared up to three quantum computing use cases.
We identified the following layers: problem domain, problem class, model, algorithms, and quantum systems. To ensure consistency in cross-industry application discussions, we suggest the terminology defined in the following definition box.

Definitions
• Problem Domains: Problem areas of applied mathematics and computer science characterized by similar solution methods aiming to solve computational problems (e.g., Optimization, Simulation, Machine Learning, Cryptography). • Problem Class: A problem class is a set of use cases that share a similar mathematical formulation and the computational complexity class. It can be characterized by the common mathematical and business problem formulation (e.g., Software testing posed as 3-satisfiability problem). • Model: A model is defined as a mathematical formulation describing a system capturing all practically relevant properties. Models are a simplified representation of reality supporting the understanding of its component's interactions and impact on resulting properties as well as predictions on future behavior (e.g., the train and driver recovery problem in a set partitioning problem formulation). • Algorithm: A quantum algorithm is a finite sequence of quantum computer-implementable instructions to perform computations. They are typically used to find a solution or an approximation of a class of mathematically defined problems. • Quantum System: A quantum computing system (short: quantum system) is a system for computation that makes direct use of quantum-mechanical phenomena (e.g., superposition, entanglement) to perform operations on data.

Application overview
General application challenges across the industrial sectors share the common problem domains, in particular optimization, machine learning, and simulation. In the following, we highlight selected challenges from our value-chains. We focus on four areas of value creation: (1) material science, (2) engineering & design, (3) production & logistic, and (4) post-quantum security. Table 3 summarizes the collected use cases.

Material science
Simulating and predicting the behavior of complex, quantum-mechanical systems is critical for new design, such as new types of batteries or pharmaceutical drugs. McKinsey & Company predicts that quantum chemistry will be an early disruptive application of quantum computing [19]. Modeling polymers, solids, molecules at high precision without experimentally synthesizing materials in the lab enables identification of effective molecular structures that satisfy desirable properties such as high energy density or stiffness [20]. Classic examples include drug discovery or the Haber-Bosch process: Industrial production of chemicals such as the catalytic nitrogen fixation of ammonia in the Haber-Bosch process uses up 1% of the world's energy production and is responsible for 1.4% of the carbon-dioxide emission [21]. On a large scale, even relatively small improvements would cause a relevant absolute impact. The global relevance of quantum computing in Material Science is also reflected in our working group. There are various QUTAC material science examples, including prediction of chemical reactivity in the chemical industry (BASF), molecular dynamics for drug discovery (Boehringer Ingelheim, Merck), and battery research (VW).

Engineering & design
Engineering simulations are heavily used across the contributors of this paper, particularly in the manufacturing sector. Such simulations are crucial to decrease efforts for design and testing by reducing the necessity of physical prototypes and laboratories, e.g., wind tunnels in the automotive and aerospace domain. Current in-silico models are limited by the complexity and quality of supported models and the necessary compute time.
Numerical simulations, particularly finite-element-method (FEM)-based, are crucial to simulate complex processes such as aerodynamics, operating strength, structural dynamics, crash & safety, and production concerns [22]. For example, Bosch is investigating QCbased simulation approaches for electric drives.
Furthermore, AIRBUS is exploring the usage of quantum or hybrid quantum-classical approaches for computational fluid dynamics to reduce the computational resources required to analyze the behavior of airflow around the aircraft. Finally, research approaches, such as the usage of surrogate machine-learning-based models for numerical simulations (AIRBUS), are being investigated [23]. Another important problem domain is design optimization. An example is the design of aircraft wingboxes (AIRBUS) [24].
Solutions require various factors to be assessed simultaneously to ensure that structural integrity is maintained. As a result, current processes to address the problem are inefficient and require significant computational resources with long design times. This problem is exacerbated by more advanced and computationally intensive generative design methods that are increasingly explored across industries.

Production & logistics
Optimization and simulation problems are omnipresent in the production & logistics domain across all industries, i.e. manufacturing, chemical & pharmaceutical production, insurance and technology. Examples of common problems are routing, supply chain, production planning, and insurance risk assessment. Real-world problems often involve a large number of variables and constraints to be respected. Classical algorithms, such as simulated annealing, can often only find local optima and provide a non-optimal solution. Quantum optimization approaches, such as quantum annealing, adiabatic or hybrid algorithms (such as the Quantum Approximate Optimization Algorithm (QAOA)) promise to solve problems with large parameter spaces, provide higher quality solutions, and faster solution times. Table 4 maps the use cases to problem classes in the optimization domain. Currently, there is an emphasis on three problem classes: traveling salesman for routing problems, knapsack for many supply chain optimization problems and satisfiability problems (SAT). However, it must be noted that other important problem classes exist, e.g., graph coloring and partitioning, as well as adaptations of the problem class to quantum-feasible models are under development. In [25] it was shown that many of these NP-hard optimization problems can be mapped to an Ising-spin class formulation, making them amenable to quantum annealing and adiabatic algorithms. The traveling salesman problem aims to identify the shortest path between a set of nodes, relevant on multiple scales for inbound, intra-plant and outbound logistics. The knapsack problem is a packing problem aiming to determine the optimal collection of items minimizing the weight of all items and maximizing the value. It has many applications in supply chain management (e.g., truck loading, airplane loading [26], and lot sizing). Further, it is applicable to use cases in finance, e.g., selecting assets for an optimal portfolio. Satisfiability problems aim to identify possible solutions for a set of constraints, e.g., identifying a set of vehicles to produce given option codes and respecting constraints. Sequencing problems select an optimal sequence in which jobs should be executed considering the length of all jobs and available resources. A key objective of industry 4.0 is to increase the customizability and flexibility of production (batch size of 1). Matrix production refers to the usage of flexible product-agnostic production cells that can be combined as needed. However, the increased flexibility also increases demands for selecting the production sequence for a given production cell layout.
QUTAC members expect a medium business impact for most optimization problems. However, the number of optimization problems in our industries is enormous. Further, due to the industrial scale, a method that improves quality or time-to-solution by a few percentage points provides significant benefits.

Reference use cases
While various use cases for quantum computing have been proposed and explored [12,19,27], the findings only provide limited insights for hardware and software solution providers. Thus, hardware and algorithms advances are primarily driving the ecosystem and not applications. As a result, low-level benchmarks methods, e.g., randomized-gate benchmarks [28] and metrics, such as quantum volume [29], are primarily used to evaluate the performance of a quantum system.
We propose establishing a complementary, application-centric evaluation process by using high-impact industry reference use cases for evaluation and benchmark activities [30]. A reference use case comprises a description including an assessment of the business value, an analysis of the problem class, mathematical formulations, quantum and classic reference solution, verification routines, and evaluation metrics.
These reference use cases can be used for performance evaluation of entire QC stacks, allowing the assessment of application-relevant performance parameters. Figure 2 shows how industry reference use cases bridge application requirements and quantum solutions. The reference problems provide the foundation for benchmarks of different parts of the stack, e.g., for micro-benchmarks that characterize certain gate sequencing exhibited by a use case.
Use cases must satisfy the following defining requirements to be amenable as a reference problem: • Business impact: defined as the impact of prospective quantum-induced improvements (e.g., due to improved model quality, better solutions and shorter time-to-solutions) on processes, services or products (e.g., process efficiencies, enabled product and service innovation). • Generality: describes the adaptability of the solution to adjacent problems in other business units, companies and industries. • Access: ensures that problems are openly visible, sufficiently abstracted, formalized and understandable through definitions in unified terminology.

Figure 2
Reference Use Cases Criteria: Reference use cases enable holistic benchmarking involving the entire stack, i.e., quantum system, algorithm • Technical feasibility: determines that a concise formalization and evaluation of the use case on current and future technology can be conducted and well-defined metrics are established (e.g., required computer size, solution quality, maximal solvable problem size, time-to-solution). The QUTAC use case portfolio will serve as the basis for selecting future reference use cases. Particularly, we aim to investigate use cases that (1) have a high business impact, (2) are constrained by classical methods for optimization, simulation, and machine learning, and (3) have promising algorithmic candidates for quantum solutions.
QUTAC's target is to identify at least one reference use case per problem domain. Table 4 gives first indication for suitable reference problems, e.g., traveling salesman problems are relevant in all industries (Vehicle Routing (VW), Robot Production Planning (BMW), Fleet Management (BASF), Transportation Cover (Munich Re)).
The initial QUTAC use case portfolio will be extended to formalized use case descriptions (including data generators, reference implementation and verification routines). We will provide these as open source contribution to the community, encouraging an active engagement on these problems. We postulate that cross-industry benchmarks of reference cases will guide hardware & software providers towards industry use cases.

Discussion
Quantum computing will impact many parts of the value-chains across all industries. Figure 3 illustrates areas of value creation and common problem domains amenable for quantum solutions. The most common problem domain is optimization problems with >50% of all use cases. The majority of the optimization use cases is in the production & logistics challenge. On average, the business impact is given as medium and the time-to-maturity as high. The time-to-maturity for the simulation of quantum-mechanical systems is assessed as medium. Quantum-mechanical simulations are quantum-native problems and make up more than 20% of all use cases across multiple industry sectors, particularly, chemical and pharmaceutical industry and manufacturing. Their potential business impact is assessed as high, as they might enable the acceleration of material discovery for drug discovery and enable new products, particularly batteries. There are only two simulation use cases for engineering process support (e.g., electric drives for Bosch and computational fluid dynamics for AIRBUS). The time-to-maturity of these use cases is estimated to be high.
Artificial intelligence (AI) and machine learning are widely being adopted across industry sectors [31]. QUTAC use cases are surrogate modeling for CFD simulations obtained from fellow author AIRBUS, and reinforcement learning (Siemens). However, AI is broadly applicable to almost all products and parts of the value-chain. For example, BMW lists more than 400 AI use cases in its portfolio. That means that advances in Quantum AI will benefit many use cases [32].

Challenges
While impressive quantum supremacy results have been achieved on technical level [1,2], various challenges remain concerning transferring these results into large-scale industrial applications of quantum computing. In this section, we discuss the result of the QUTAC survey and interviews. Figure 4 illustrates the main challenges in the three focus areas: (1) industry use cases, (2) collaboration, and (3) market incubation.

Industry use cases
There is no proof of value for QC applications yet. The main reason is the early stage of the technology in need of fundamental research breakthroughs to allow for a scale at which business impact is tangible (see Sect. 3). The contributing application experts identified the following challenges: • Business Impact: The contributing companies identified various use cases with medium to high impact through quantum computing. However, often a precise and proven business impact cannot be provided as this business impact critically depends on both technical (e.g., number of qubits) and business details (e.g., the value associated with certain model types). The lack of proven and coherent method for estimating business impact hinders long-term investments both by use case owner and ecosystem partners. • Benchmark: The QC market and ecosystem are highly diverse and dynamic. Existing benchmarks primarily emphasize low-level hardware performance (e.g., gate fidelities and coherence times) and do not accurately reflect application-level performance.
Due to a lack of community-driven application-centered benchmarks, users cannot easily infer the performance they can expect from proposed solutions. By enabling comparisons between quantum solutions, benchmarks can drive improvements on all layers of the QC stack. For example, the ImageNet [33] benchmark lead to breakthroughs in artificial intelligence and drove the creation of specialized hardware. Application benchmarks further help to establish a converged application and hardware roadmap. • Business Integration: Transferring quantum technology solutions to business impact is complex, and in addition to a deep understanding of quantum technology, requires domain and integration expertise. For example, like data-driven use cases, QC solutions rely heavily on available data and models. Results of the quantum solution must then be translated into business outcome, e.g., by integrating them into operational systems or business decisions. In addition to quantum hardware and algorithms, business applications need holistic considerations.

Collaboration
To guide ecosystem activities towards industrializiation and commercialized, marketready products, an environment conducive to innovation is key. Until now, ecosystem development has been held back by traditional, rigid collaboration models in a complex stakeholder landscape, particularly between industry and research institutions. A highly intertwined technology stack and multidimensional governmental funding mechanisms create a complicated ecosystem of institutions and initiatives with many inter-dependencies and overhead. The current state makes partner contracting/sourcing a complex and lengthy process. Funding: Agencies around the globe have been funding basic research in QC for decades (e.g., US [9,10]). In Europe, more than 20 projects are funded as part of the Quantum Technologies Flagship [18].
Germany significantly extended its quantum program, supporting both, foundational research and industrialization of hardware and software [16,17,34] with a budget of two billion Euros over five years. The quantum hubs will focus on different specific qubit technologies (e.g., ion traps or superconducting qubits). Application research is supported, e.g., via a competence network. Further, state-level initiatives in Germany have emerged, including the Munich Quantum Valley [35] and Lower Saxony Quantum Valley [36].
The resulting funding landscape is complex, fragmented and exhibits partially competing and overlapping objectives. As a result the establishment of large-scale industrialization projects will be challenging. Thus, we expect a high number of small initiatives, bearing the risk of redundancy and lack of focus. In this environment, avoiding the decoupling of application-centric industrialization and foundational research is instrumental to advance the technology at this early maturity level.
Horizontal collaboration: Survey respondents noted effective cross-industry collaboration to advance quantum computing as one of the highest-ranked challenges. Crossindustry collaboration is a crucial enabler for (1) creating a shared industry voice towards the ecosystem, (2) establishing high-impact applications that accelerate industrialization, (3) jointly facilitate activities with the emerging ecosystem, and (4) to de-risk long-term investments.
Several consortia on international level have been founded to address these challenges, e.g., QED-C [37] and QuIC [38]. Germany is missing a consortium to advocate for industry needs in growing German QC programs. Additionally, a framework for addressing collaboration challenges is needed, including (1) the lack of a unified terminology and standards (e.g., for use cases, benchmarks and access protocols), (2) the difficulty of sharing proprietary data and information, and (3) the lack of effective strategies to balance openness and corporate interests.
Vertical collaboration: Collaboration of industry and quantum solution providers is crucial to coherently advance applications and hardware by optimizing integration across the entire stack (hardware/software co-design). This requires the integration of industrial domain knowledge with hardware, software, and algorithmic knowledge. Setting up vertical collaborations, especially with international partners, can be challenging and requires careful consideration of IP protection, data security and privacy.

Market incubation
While governments, research institutions and cloud providers began to procure quantum devices, the commercial market is still in its infancy. Industrial applications with proven business impact are instrumental in establishing such markets, creating a virtuous cycle of demand and supply [39]. The contributing experts emphasizes three challenges: Hardware Access: Access to different quantum systems is now possible through cloud service providers [3,5]. However, the availability, scale, and costs limits research and industrialization activities. In many cases, careful consideration of international and data protection law and vendor-specific contracts are required. Further, access is often limited, preventing low-level experiments. High-end, state-of-the-art hardware is often unavailable. As technology advances, we expect this situation to exacerbate. Another challenge is limited access to research test-beds emerging from public projects.
Demand Creation: A virtuous cycle of demand and supply is crucial to establish a new market. Additional to government-driven markets, industrial applications can serve as an important market to initiate such a cycle. In particular, application on NISQ devices useful for industry can drive demand. Market creation is a well-known challenge of deep-tech ecosystems [12], but is particularly pronounced in quantum computing due its long-term nature.
Talent & Education: QC requires both, highly specialized and interdisciplinary skills that bridge different research fields, including engineering, industrialization, and business. Developing talent with knowledge in theoretical and applied computer science (e.g., complexity theory, operations research) and quantum computing (e.g., basics of QC operation and control, error mitigation, quantum algorithms, quantum software development kits, assessment of application-relevant hardware features) in combination with business acumen (e.g., identifying customer needs, knowledge in production and operations processes, their business and technical limitations) is seen as critical. With first applications reaching commercial viability, this situation will exacerbate.

Call for action
To advance quantum computing towards the level of industrial-scale applications, we need to act now. As we observed in other fields, e.g., artificial intelligence, early investments are essential to ensure a competitive advantage in a fast-paced digital economy. QUTAC members identified three fields of action in the focus areas: industry use cases, collaboration and market incubation, and two enablers: talent & education and standards (Fig. 5). A2 Collaboration: European and German funding streams must be aligned to avoid redundancy. Demands and guidance for industry partners must be clearly communicated. Industry users must engage proactively in the consortia, with well-defined value propositions and contributions. Further, international collaboration and cooperation beyond Germany is vital (e.g., through QuIC [38]).
A3 Market Incubation: Commercially-useful quantum applications are vital to create new demands for quantum technologies, initiating the virtuous cycle of demand and supply. The industrialization of quantum computers to industry scale must be the long-term target, enabling profitable business models for all value-chain participants, including start-ups, components suppliers, etc.
The following enablers contribute to all action items in the three focus areas and are prerequisites for their success: E1 Talent & Education: As technology matures, the demand for quantum computing will grow. Both industry and academia must develop critical skills at the intersection of physics, engineering, computer science, and business [40], addressing undergraduate, graduate, post-graduate students, and professionals. A particular focus must be interdisciplinary skills that bridge these fields and combining low-level quantum knowledge with industry domain expertise. E2 Standards: Entry-barriers must be lowered by development of appropriate high-level interfaces and standards (e.g., terminologies, API for accessing infrastructure). Standards are also instrumental for minimizing vendor lock-in. The QUTAC application working group aims to advance the industrial-scale applications of QC (A1). This paper presents an initial set of cross-industry applications of quantum computing, which will provide the foundation for establishing industry reference problems. Based on these reference use cases we will establish benchmarks, which we hope will spark horizontal and vertical collaboration (A2). We actively evaluate engagement models with QuIC and other industry consortia (A2). By collaborating on community standards, e.g., a glossary, access interfaces, high-level business abstraction, we will lower the entry barriers (E2).
We work towards strengthening exchange with German and European funding agencies (A2). We specifically envision collaborative lighthouse projects that increase collaboration across the ecosystems and channel it towards high-value industrial challenges (A1, A2). By providing domain expertise, we contribute critical knowledge while benefiting from the advancements in quantum solutions. At the same time, this will generate demand for industrial quantum solutions -solving the deadlock between users and platform providers.
We postulate that QUTAC's engagement and industrial perspective will enable early markets for quantum computing technologies (A3). Partners are committed to contributing applications, data, technological and business knowledge to the emergent ecosystem (A2). Our results will be beneficial to all ecosystem participants, e.g., suppliers, system integrators, software developers, users, policymakers, funding program managers, and investors. We believe in the long-term business impact of quantum computing. We do not expect immediate value, but are convinced that it is now the time to obtain and share experience with different technologies and advance our business infrastructure to accelerate the adoption of quantum-based methods.