Electronic Markets https://doi.org/10.1007/s12525-022-00570-y FUNDAMENTALS Quantum computing Roman Rietsche1 · Christian Dremel2 · Samuel Bosch3 · Léa Steinacker4 · Miriam Meckel5 · Jan‑Marco Leimeister1 Received: 8 January 2022 / Accepted: 27 June 2022 © The Author(s) 2022 Abstract Quantum computing promises to be the next disruptive technology, with numerous possible applications and implications for organizations and markets. Quantum computers exploit principles of quantum mechanics, such as superposition and entanglement, to represent data and perform operations on them. Both of these principles enable quantum computers to solve very specific, complex problems significantly faster than standard computers. Against this backdrop, this fundamental gives a brief overview of the three layers of a quantum computer: hardware, system software, and application layer. Furthermore, we introduce potential application areas of quantum computing and possible research directions for the field of information systems. Keywords Quantum computing · Quantum physics · Cloud computing · Emerging technology · Information systems JEL Classification O14 · O32 Introduction Quantum computing promises to be the next disruptive tech‑ nology, with numerous possible applications and implica‑ tions for organizations and markets. A recently published report by McKinsey estimates the global market value of quantum computing to be at USD 1 trillion by 2035, mainly in the financial, chemical, pharmaceutical, and automotive sectors (Hazan et al., 2020). Today, the world’s largest tech‑ nology companies, such as Google, IBM, Microsoft, Ama‑ zon, and Alibaba, are already investing billions in research and development of their quantum computing and provide partial access to these quantum computers to the public via cloud infrastructures. However, not only industry players invest but also governments, for example, China is investing USD 10 billion in a national quantum computing laboratory, the U.S. government provided USD 1 billion, and the EU has a budget of overall more than EUR 1 billion (Castelvecchi, 2018; Deicker & Yasiejko, 2018). Quantum computers exploit principles of quantum mechanics, such as superposition and entanglement, to rep‑ resent data and perform operations on them (Ding & Chong, 2020). Both of these principles enable quantum computers to solve very specific, complex problems significantly faster than standard computers. Additionally, interference plays Responsible Editor: Rainer Alt 1 Institute of Information Management, University of St. Gallen, Müller‑Friedberg‑Strasse 8, 9000 St.Gallen, Switzerland Roman Rietsche roman.rietsche@unisg.ch 2 Norwegian University of Science and Technology, Høgskoleringen 1, 7491 Trondheim, Norway Samuel Bosch sbosch@mit.edu 3 Léa Steinacker lea.steinacker@unisg.ch Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Ave., MA 02139 Cambridge, United States of America 4 Miriam Meckel miriam.meckel@unisg.ch University of St.Gallen, Müller‑Friedberg‑Strasse 8, 9000 St.Gallen, Switzerland 5 Institute for Media and Communications Managment, University of St.Gallen, Müller‑Friedberg‑Srasse 8, 9000 St.Gallen, Switzerland * Christian Dremel christian.dremel@ntnu.no Jan‑Marco Leimeister janmarco.leimeister@unisg.ch 13 Vol.:(0123456789) R. Rietsche et al. an important role specifically when reading information from the quantum computer (Aaronson, 2008). Quantum computers can calculate and test extensive combinations of hypotheses simultaneously instead of sequentially (S.‑S. Li et al., 2001). Furthermore, some quantum algorithms can be designed in a way that they can solve problems in much fewer steps than their classical counterparts (their complex‑ ity is lower). For this reason, quantum computing could rep‑ resent a significant breakthrough in modern IT in the next few years and might initiate the transition to the "5th indus‑ trial revolution" (Hadda & Schinasi‑Halet, 2019). First experiments show promising results, such as the one done by Google in 2019 in which the company claims to have achieved so‑called quantum supremacy (IBM “quantum advantage”) (Arute et al., 2019). In an artificial experiment, they were able to demonstrate that a programmable quan‑ tum device could solve a problem that a classical computer could not solve in a feasible amount of time. However, the task solved by Google ‘s quantum computer was custom tailored to the specific quantum hardware used and has no real‑world applications. Nevertheless, it was an important proof of concept. Furthermore, in 2020, Chinese scientists claimed to have built a quantum computer that is able to perform specific computations approximately 100 trillion times faster than the world‘s most advanced supercomputer (Zhong et al., 2020). Given its current state of development, experts antici‑ pate that quantum computing could provide unprecedented advantages, especially in the areas of optimization, artificial intelligence, and simulation (Langione et al., 2019; Ménard et al., 2020). It is likely that simulations of molecules (for chemical and pharmaceutical industries) will be among the first real‑world applications of quantum computers. This is because molecules directly follow the laws of quantum mechanics, so using quantum computers is the most natural way of simulating them. Other industries that could soon benefit include the financial sector, transportation and logis‑ tics, the global energy and materials sector but also areas such as meteorology or cybersecurity (Gerbert & Ruess, 2018; Langione et al., 2019; Ménard et al., 2020). However, to date, quantum computing has extensive unsolved chal‑ lenges in physics and computer science, ranging from hard‑ ware architectures and data management to application soft‑ ware and algorithms, which requires fundamental research in all these areas and beyond (Almudever et al., 2017). To inform information systems (IS) research, this Fun‑ damental provides the fundamental concepts of quantum computing and depicts research opportunities. Therefore, we provide in our second section a brief overview of a quantum computer system and its three layers of a quantum com‑ puter: hardware, system software, and application layer. The third section introduces potential application areas of quan‑ tum computing.1 Building upon these and the introduced 13 conceptual layer view on quantum computing, we relate to each layer by detailing potential research opportunities in the context of electronic markets. A whole new ecosystem around quantum computing technology itself is emerging already, provoking questions around the change of (1) busi‑ ness models and process innovation, (2) challenges for IT organizations, or (3) sourcing from start‑ups, full‑stack providers such as Google, IBM, Microsoft, or Alibaba or individual development. Quantum computing system In 1980, Paul Benioff envisioned the concept of a quantum touring machine, i.e., the theoretical concept of a quantum computer (Benioff, 1980). In 1982, Richard Feynman pro‑ posed the first practical application of a quantum computer: efficient simulations of quantum systems (Feynman, 1982). In general, a quantum computer can be defined as a universal computing device that stores information in objects called quantum bits (or qubits) and transforms them by exploiting very specific properties from quantum mechanics (Ding & Chong, 2020). The quantum computer performs quantum computing, which is a type of computation that collects the different states of qubits, such as superposition, interference, and entanglement, to perform calculations (Grumbling & Horowitz, 2019). Importantly, quantum computers are not intended to become general purpose computers that oper‑ ate by themselves. They will be highly specialized devices that can solve specific tasks much faster than classical com‑ puting. Operating quantum computers will most certainly require a classical computer for loading input/output data, retrieving results from computations as well as controlling the quantum computer’s electronic and internal processes. Thus, quantum computers and classical computers form a quantum computing system that enables quantum comput‑ ers to perform quantum computing. To depict the differ‑ ent layers of a quantum computing system, we adopt the model of Ding and Chong (2020) for three reasons. First, it allows us to analytically distinguish the key components of a quantum component system to illustrate the fundamental mechanisms and elements. Second, it builds on an analytics distinction of hardware, system software, and application, which is mirrored in conceptual views on computing archi‑ tectures, e.g., cloud computing (Infrastructure‑as‑a‑Service, 1 The Fundamentals article is built on the extent body of knowledge on quantum computing. For our literature review we broadly searched for the term “quantum computing” in libraries, such as EBSCO, Sci‑ enceDirect, IEEE, or the AIS eLibrary in computer science and IS research. Both the application areas as well as the research opportuni‑ ties are informed by the prevailing themes of 21 conducted interviews with technology and academic experts from well‑established Fortune 500 companies and prestigious academic institutions. Quantum computing Fig. 1 Showing a classical com‑ puter (von Neumann architec‑ ture) and a quantum computer forming a quantum computing system (adapted from Ding and Chong (2020)) Quantum Computing System von Neumann Architecture Application Layer Quantum Algorithms Input Devices ALU Register Output Devices Systems Software Layer Quantum Domain Specific Language, Error Correction, Noise Mitigation Hardware Layer Quantum Computer Control Unit Classical Computers Central Processing Unit (CPU) Quantum Hardware System Controller Memory Unit Qubits Fig. 2 Classical bit and qubit (Superposition) Platform‑as‑a‑Service, and Software‑as‑a‑Service) or the layered modular architecture of digital technologies (Yoo et al., 2010). Third, our expert informants distinguished between similar layers as well in their interview statements to explain the state of the art, the challenges for today’s organizations, and the functioning of quantum computing systems. Figure 1 shows a quantum computing system con‑ sisting of a van Neumann architecture for classical comput‑ ing and a quantum computer with its three layers architec‑ ture, which we will explain accordingly. Hardware layer One fundamental difference between classical and quantum computers is how information is stored. Whereas classical computers use bits, which can have the value of either zero or one, to store information, quantum computers use quantum bits (or qubits), which can hold any linear combination of zero and one simultaneously (Steane, 1998). Qubits leverage the advantage of the properties of quantum mechanics and in particular the effect of superposition (visualization see Fig. 2). Superposition Loosely speaking, a qubit is described by its probability of being either zero or one and not by the distinct value of zero or one. Thus, a qubit can have the probability of being 60% zero and 40% one. Importantly, only at the point of measuring the state of the qubit, it “collapses” to the single classical defined value of either zero or one (Bosch, 2020; Ding & Chong, 2020). The property of superposition has the advantage that a quantum computer with just four qubits is able to represent 16 four‑digit numbers simultane‑ ously. With each further qubit, the number of representable states doubles whereas a classical computer, with a sequence of four bits, can only represent a single four‑digit number. The real advantage of quantum computing relies on the fact that one can perform an exponential amount of calcu‑ lations at the same time. Even though at the end of every program it is possible to read only the solution to one cal‑ culation, it is possible to develop a quantum algorithm that makes it very likely that the final result is precisely the one that one is looking for. For example, we might be trying to find out if there exists any possible rarely occurring turbu‑ lence that could cause a plane to crash. Instead of simulating 13 R. Rietsche et al. billions of combinations of air conditions on a classical com‑ puter and checking their individual results, we could simply test almost all possible air conditions at once on a quantum computer and read out only the result that causes the plane to crash. Quantum annealing takes advantage of the fact that physical systems strive towards the state with the lowest energy, e.g., hot things cool down over time or objects roll downhill. As such, in quantum annealing the energetically most favora‑ ble state then corresponds to the solution of the optimiza‑ tion problem (Albash & Lidar, 2018). Using the property of superposition, the quantum annealer is able to calculate all potential solutions at the same time, which speeds up the calculation process drastically in comparison to classical computers (Shin et al., 2014). Quantum annealing is most suitable for optimization problems or probabilistic sampling and is used by companies such as D‑Wave. However, to date, it is unclear whether the quantum annealing technique will ever achieve significant quantum speedup (Albash & Lidar, 2018). Entanglement Not only qubits are unique to quantum computing. Entanglement is also a property of quantum mechanics. Entanglement is when the state of one qubit is dependent on the state of another qubit (Steane, 1998). Thus, when two qubits are entangled, making any kind of flip or rotation on one of the qubits would result in the same change happening to the other qubit (Einstein et al., 1935; Schrödinger, 1935). Furthermore, when the state of either one of the two qubits is measured, the state of both qubits collapses to either one or zero (depending on their prob‑ abilities). This is even the case when the qubits are far away from each other. Thus, the advantage of entanglement is that when a qubit influences the other qubits around it, all are working in tandem to arrive at a solution. Therefore, qubits can be correlated in a way that is not possible for bits in traditional computers. This opens up new possibilities and gives the quantum computer the ability to process infor‑ mation in a fundamentally different way than a classical computer (Mooney et al., 2019). One example is superdense coding, which is the process of transporting two classical bits of information using one entangled qubit (A. Harrow et al., 2004). This process is especially interesting for secure quantum key distribution (Bennett & Brassard, 2014). This is a secure communication method that implements a cryp‑ tographic protocol relying on quantum entanglement and other quantum phenomena. It enables two parties to produce a shared random secret key (entangled qubit) known only to them, which can then be used to encrypt and decrypt mes‑ sages (Scarani et al., 2009). Based on the fundamentals of quantum mechanics, we now discuss the approaches to physically represent and manipulate qubits. Broadly speaking, the approaches can be split into two main categories: a) analog quantum com‑ puting and b) digital gate‑based quantum computing (Ding & Chong, 2020). System software layer Analog quantum computing In analog quantum computing, the quantum state is smoothly changed by quantum opera‑ tions such that the information encoded in the final system corresponds to the desired answer with high probability. One example of analog quantum computing is adiabatic quantum computers (Albash & Lidar, 2018), which refer to the idea of building a type of universal quantum computing. A special form of adiabatic quantum computers is quantum annealing, which is a framework that incorporates algorithms and hard‑ ware designed to solve computational problems via quantum evolution towards the ground states (Vinci & Lidar, 2017). The system software layer builds on top of the hardware layer and orchestrates the system’s processes to leverage the potentials of the qubits (superposition and entanglement). This layer has to cope with challenges of the thermodynami‑ cally unstable quantum states. It actively reduces thermal noise within and around the quantum system and performs error correction procedures. In quantum computing there are many potential sources that can cause noise. For example, quantum computers and especially digital gate‑based ones are highly sensitive to changes in the environment, such as vibration, temperature 13 Digital gate-based quantum computing In digital gate‑ based quantum computing, the information encoded in qubits is manipulated through digital gates. In comparison to the analog approach in which you sample the natural evo‑ lution of quantum states to find the optimal state of low energy, in digital gate‑based quantum computers the evolu‑ tion of the quantum states is manipulated in terms of activity and controlled to find the optimal solution (Ding & Chong, 2020). Thus, the state of qubits is actively manipulated and therefore provides the advantage of being much more flex‑ ible, and it can be used to solve large classes of problems, in contrast to quantum annealing. Digital gate‑based quantum computing is conceptually very similar to classical computa‑ tion (Grumbling & Horowitz, 2019). A classical algorithm is run on a computer as a series of instructions (gates such as AND, OR, NOT, …). They manipulate individual or pairs of classical bits and flip them between zero and one states according to a set of rules. Quantum gates operate directly on one or multiple qubits by rotating and shifting them between different superpositions of the zero and one states as well as different entangled states. Companies using digi‑ tal gate‑based quantum computing are, for example, IBM, Google and Rigetti. Quantum computing fluctuations, etc. Noise can also be caused by imprecise control of the quantum hardware or manufacturing defects (Ding & Chong, 2020). Most quantum computers even require their chips to be cooled down to a hundredth of a degree above absolute zero temperature to operate. Thus, since noise cannot be avoided, the first era of quantum computers is also called noisy Intermediate‑Scale Quan‑ tum Computer (NISQ, Preskill, 2018). This abbreviation implies that current quantum hardware using dozens of qubits has error rates that are too high, which need to be improved before we can build useful quantum computers with hundreds, or even thousands, of usable qubits. Noise in the environment can lead to qubit decoherence which is environmental influences causing quantum states to randomly change (Grumbling & Horowitz, 2019). This is problematic, as a single error in a calculation usually causes the result to be incorrect, unless the error is cor‑ rected during the calculation. Since it is impossible to prevent every kind of noise, error correction is important. Ongoing research on quantum error correction seeks to achieve system‑level fault tolerance. Quantum error cor‑ rection differentiates between physical and logical qubits. Logical qubits are represented by a group of physical qubits, which are needed for error correction. Physical qubits work together on correcting errors on individual physical qubits. A group of physical qubits is less likely to cause an error in a calculation than just one physical qubit. Unfortunately, error‑correcting mechanisms can cause errors themselves. Depending on the error‑correcting mechanism, the relation is typically five to nine physical qubits to achieve one almost error‑free logical qubit (Mari‑ nescu & Marinescu, 2012; Shor, 1995). One way to do this is by representing every qubit with groups of several physical qubits that, loosely speaking, work together on correcting errors on individual physi‑ cal qubits. A perfect physical qubit can work as a logi‑ cal qubit, as it requires no error correction. Today, the biggest challenge is scaling up to thousands of qubits. Even though the computational space that can be used for calculations doubles (Ding & Chong, 2020) with the addition of every individual qubit, this advantage pres‑ ently cannot be exploited in its full capacity due to high error rates. One prominent example for trying to increase the number of qubits is IBM, which states that it wants to achieve over 1,000 qubits by 2023, while currently there are machines with 60–100 available (Gambetta, 2020). Application layer One of the main challenges of today’s quantum computers is the unsolved problem of efficient quantum memory (Cili‑ berto et al., 2018). There exist several theoretical proposals for building quantum random access memory (QRAM). Even though it may be experimentally difficult to build (just as the quantum computer itself), recent publications demonstrated several possible paths of doing so (Hann et al., 2019; Park et al., 2019). Thus, currently exists no efficient way to store states of qubits in a memory for a long time for other calcu‑ lations. Therefore, data needs to be loaded from a classical computer to the targeted quantum computer, and after per‑ forming the calculation states need to be read (measured) by the classical computer before the qubits lose their informa‑ tion. Due to the no cloning theorem, we are also not able to make copies of quantum states and use them for calculations. The only way to load a quantum state from quantum memory into a quantum program is by applying a SWAP operation, and thereby removing it from the memory. When a quantum state is measured, it collapses to either one or zero. Therefore, we have no way of finding out what state a certain qubit is in. The only way we can approximately find out what state a qubit is in is if we have multiple copies of the same qubit and measure them all. In some cases, read‑ ing the classical data may dominate the cost of quantum algo‑ rithms so that it cannot speed up the whole algorithm at the macro level. Reading out the data exactly may be infeasible, which cannot meet the computing needs in some tasks. This is especially the case for methods that need large data sets, such as machine learning and artificial intelligence. Finding a useful algorithm for quantum computers is mostly about constructing it in such a way that the prob‑ ability of measuring the desired outcome is maximized. Even though the output of the quantum computer may be an exponentially large number of solutions, we are usually just interested in a small subset of these solutions. Finding them without having to run the whole algorithm many times is the art of quantum algorithm construction. Here are three of the most important quantum algorithms. • Grover’s algorithm is also known as the quantum search algorithm. Grover’s algorithm is used for searching an unstructured database or an unordered list. Classically, for finding a particular item in a database of size N, we need to go through, on average, N/2 items to find the right one. Using Grover’s algorithm, we can do this in only √N steps, on average. For a large N, this can be remarkably faster. This is called a quadratic speedup (Grover, 1996). • Shor’s algorithm, also known as the integer factoriza‑ tion algorithm, can factorize integers almost exponen‑ tially faster than the fastest known classical algorithm. Factorizing integers is very difficult computationally and is therefore also the basis of RSA encryption (Shor, 1994). • HHL (Harrow Hassidim Lloyd) is also known as the quantum algorithm for linear systems of equations. The algorithm can estimate the result of a function of 13 R. Rietsche et al. the solution x of a linear system (Ax = b), where A is a matrix and b a vector (A. W. Harrow et al., 2009). Application areas of quantum computing Thanks to the enormous progress in hardware, more and more established commercial companies are investing in quantum technology. Examples include Boehringer Ingel‑ heim, who recently announced a research partnership with Google (Boehringer‑ingelheim, 2021), and Daimler, who announced progress in the field of materials research (Motta et al., 2020), or chemistry giants like BASF who aim to stay at the forefront of chemistry research and busi‑ ness (Hartmann & Deppe, 2021). Quantum computing has three essential capabilities to address today’s compu‑ tational problems that current computers are not or only partially capable of and that bear benefits for companies: 1) search and graph, 2) algebraic and 3) simulation (Hoff‑ mann, 2021; Li et al., 2020). These capabilities determine the potential applications of this technology in numerous industries, such as finance, chemistry and pharma, manu‑ facturing, energy, or cybersecurity (Gerbert & Ruess, 2018; Langione et al., 2019; Ménard et al., 2020). Table 1 pro‑ vides a summary of the problem types, approaches and potential use cases. Search and graph The fact that a qubit can theoretically represent an infinite number of states allows for solving complex combinatorial optimization problems, which is currently one of the major application areas for current quantum computing technolo‑ gies, such as the solution of D‑Wave (Johnson et al., 2011). Combinatorial optimization is the process of finding one or more optimal solutions to a problem. Examples of such problems include supply chain optimization, optimizing public transportation schedules and routes, package deliver‑ ies, etc. These solutions are searched for in a discrete (finite) but very large configuration space (i.e., a set of states). The set of possible solutions can be defined with several con‑ straints and the goal is to optimize the objective function with the best solution. Since the problem spaces in certain complex problems are very large, it is extremely difficult to find the optimal or even a single good solution to these problems with classi‑ cal computers in a reasonable time frame or with sufficient accuracy. Such combinatorial optimization problems often pose a great challenge for the private as well as the public sector. While they are often simple to describe, they turn out to be very difficult to solve. Combinatorial optimization problems may be divided into order, assignment, grouping, and selection problems, and within these classes, subclasses exist, such as the knapsack or the traveling salesman prob‑ lem. In addition to the property that there can be a lot of qualitatively different solutions for a problem, no known algorithm exists that can easily compute these problems directly. Searching very large problem spaces requires an enormous amount of computing capacity and time. Respectively, quantum computers are expected to play a decisive role in the financial services industry. Espe‑ cially players specializing in portfolio optimization and arbitrage could benefit (Egger et al., 2020). From a very large pool of existing financial instruments, a subset should be selected so that a certain portfolio volume is achieved, while at the same time a large number of factors must be taken into account to minimize risk and achieve profitabil‑ ity (Chakrabarti et al., 2021). Further, Deutsche Börse (a German company offering marketplace organizing for the trading of shares) already experimented with the applicabil‑ ity of quantum computing for a sensitivity analysis on one of their risk models, a computation that is too expensive Table 1 Overview quantum computing problem types, approaches, and potential use‑cases Problem type Approach Search and graph Finding one or more optimal solution(s) to a complex problem. Often the problems involve a large number of possible parameter combinations. Algebraic Calculating complex network architectures and the weights for machine learning and artificial intelligence. This involves transforming and calculating large matrices. Simulation Calculating how states of a system change through manipu‑ lating parameters to analyze the behavior of complex systems. 13 Example use‑cases ‑ Find optimal parameter configuration to optimize portfolio in the finance industry ‑ Search for possible routes to optimize traffic flow in trans‑ portation ‑ Factorize prime numbers to break encryption in secure com‑ munication ‑ Transform matrices to find objects in images in computer vision ‑ Find patterns in texts to understand semantics in natural language processing ‑ Simulate states of molecules and their changes to understand chemical reactions in pharma industry ‑ Simulate the behavior of materials to find more efficient materials in battery industry Quantum computing to be run on classical computers (Braun et al., 2021). Due to its suitability to solve optimization problems, another application of quantum computing is the optimization of flow, e.g., of traffic or goods. Collaborating with D‑Wave Systems, VW has already shown in a pilot project how to optimize a simplified traffic flow in the city of Lisbon by leveraging quantum annealing technologies (Neukart et al., 2017; Yarkoni et al., 2019) – a project that started in late 2016 with a proof‑of‑concept project. It investigated the readiness of quantum computing by building a traffic‑flow optimization program that used GPS coordinates of 418 taxis in Beijing to resolve traffic congestion. Moreover, quantum computers are superior to classical computers regarding certain prime factorization proce‑ dures that play an important role in the secure encryption of data. A popular example for this is the aforementioned Shor (1994) algorithm that factors a number into its prime factors, a process used often in cryptography and cyberse‑ curity. A dataset encrypted with quantum technology would be impossible to decrypt with classical computer technology, or at least not in time periods relevant to human users. Con‑ versely, it would be easy for a quantum computer to crack data encrypted with classical RSA technology – a phenom‑ enon that may be coined as quantum threat (Mone, 2020). Algebraic The ability of quantum computing to accelerate optimiza‑ tion problems plays a crucial role for narrow AI approaches (Gao et al., 2018; Langione et al., 2019). Quantum com‑ puting can help to calculate complex network architectures and weights for machine learning and artificial intelligence. Quantum computing shows its advantage in transforming and calculating large metrices. For example, in the context of supervised learning, the model aims to minimize the error between the prediction of the model itself compared to the input and adequate output or label given. Quantum comput‑ ers offer several approaches to solving problems like this, thereby, again, accelerating calculation and allowing for more complex network architectures (DeBenedictis, 2018). They may be applicable to all relevant practices or sub‑tasks of artificial intelligence, such as image processing and com‑ puter vision (Dendukuri & Luu, 2018) or natural language processing, as demonstrated in an experiment by Cambridge Quantum Computing (Lorenz et al., 2021). Having said that, it is important to note that, so far, no near‑term machine learning algorithm with provable speedup has been found. Simulation A quantum computer has a fundamental advantage over classical computers: It can simulate other quantum systems (e.g., a nitrogen molecule) much more efficiently than any computer system available today. For classical computers, even molecules with comparatively low complexity repre‑ sent an almost unsolvable task. In the 1980s, Richard Fey‑ nman theoretically substantiated the possibility of a quan‑ tum‑based computer for simulating molecules (Feynman, 1982). Since then, researchers have attempted to transfer the quantum system of a molecule into another quantum system, i.e., into the quantum computer, in order to simulate it. One new hope in the application of quantum computers is the simulation of more efficient catalysts for ammonia syn‑ thesis in the Haber–Bosch process, which today accounts for about 1 to 2 percent of global energy consumption. Bet‑ ter catalysts could reduce energy consumption and thus also help slow global warming. Even quantum computers without full error correction may already be better suited for this application than simulations on classical computers (Budde & Volz, 2019). Furthermore, the development of active ingredients and drugs is often a lengthy and very cost‑intensive process. This is due in particular to the fact that a large number of substances have to be tested on a trial‑and‑error basis in the real world. Yet, building on the same principles of quantum physics, quantum computing may be able to virtually repli‑ cate the behaviors such that simulation‑based research may sooner or later replace this cost‑intensive process. For instance, BASF, pursuing its high requirements for the accuracy of quantum chemical calculations, investigated, in collaboration with the company HQS, the applicability of quantum computing. Specifically, they aimed to understand the quantum mechanical calculation of the energy course of chemical reactions, as this actually allows for the pre‑ diction of the probable course (i.e., how does the reaction proceed, which products, by‑products, etc., are formed, how can I accelerate the reaction with the help of catalysts, etc.) of chemical reactions. This application of needed methods reaches the limits of conventional computing methods (Kühn et al., 2019). In addition, material research on the function‑ ing of batteries is deemed to inform today’s electromobility and is already targeted by automotive giants such as VW (Neukart, 2021; Ziegler & Leonhardt, 2019). Link to the field of information systems Even though there are high investments in quantum com‑ puting, most expert estimations still place the widespread industrial application of quantum computing at least five to ten years in the future. Its exact manifestations in many critical areas remain unclear. Thus, it is the task of today’s research community to creatively conjure up and explore the full potential and the socio‑technological consequences of quantum computing. Therefore, based on analyzing exist‑ ing literature and the conducted interviews with 21 leading 13 R. Rietsche et al. Table 2 Further areas of research and potential research questions Further research and development Potential research questions Quantum computing ecosystems as a new networked business ‑ Does the access to quantum computing need to be regulated? ‑ Does quantum computing need new sourcing strategies? ‑ How does the emerging quantum computing ecosystem act as a spoke compo‑ nent to other industries and ecosystems? ‑ Which transformation may result from the emergence of a quantum computing networked business? Digital understanding as a foundation for quantum comput- ‑ What approaches could be used or developed to analyze business problems and ing use cases and ecosystems therefore leverage the potential of quantum computing? How can these prob‑ lems be described mathematically? ‑ What are possible design principles of artifacts to describe use cases? ‑ How will quantum computing impact the modeling of a social and economic reality as a transformation from binary to multidimensional quantum states? Quantum computing as a challenge for IT organizations and ‑ What are possible security approaches to protect legacy IT with old encryption IT service providers standards considering the quantum threat? ‑ Can quantum computers and artificial intelligence be used for real‑time threat and anomaly detection? ‑ How can quantum computers be used to simulate possible intrusions and cyber‑ attacks for calculating risk–cost evaluations? Quantum computing skills ‑ How could information systems act in a mediating role for adopting quantum computing technologies? ‑ Should quantum computing be included in the information systems curriculum? ‑ How can future information systems managers be trained to be aware of the disruptive potential of quantum computing? ‑ How can management leverage the potentials of available techniques, approaches, and platforms around quantum computing? ‑ How can gaps of knowledge and access to infrastructures be mitigated? experts in industry and research, we propose the following four initial directions for research on quantum computing in information systems (for a summary, see Table 2): 1) quan‑ tum computing ecosystems as a new networked business, 2) digital understanding as a foundation for use cases and eco‑ systems, 3) quantum computing as a challenge for IT organi‑ zations and IT service providers, and 4) skills needed to lev‑ erage quantum computing in the quantum computing field. All of these directions try to consider the fact that quan‑ tum computing despite its disruptive potential will initially be an extension of computing capabilities for established electronic markets, ecosystems, and its participants (see Fig. 3), while new ecosystem participants are already estab‑ lishing themselves (e.g., IonQ or Rigetti). We further try to focus on established research areas and the focus of our research community. Quantum computing ecosystems as a new networked business The adoption and diffusion of quantum computing will heavily rely on an emerging ecosystem comprising technol‑ ogy providers, such as IBM, Google, Microsoft, or Ama‑ zon Web Services, start‑ups with specific playgrounds such as 1Qbit or IonQ as well as consulting firms and academic institutions to support customers in adopting and building applications using quantum computing technologies (Carrel‑ Billiard et al., 2021; IBM, 2019). Also, the European Union 13 built their own ecosystem with the “Quantum Flagship”.2 Companies, providers, research institutions, and govern‑ ments ultimately need to engage in such an ecosystem to allow for getting hold of capabilities that transcend their own organizational boundaries or even their entire industry (e.g., building their own computing infrastructures, trans‑ lating business problems into mathematical and quantum problems, etc.) (Carrel‑Billiard et al., 2021). Due to this emerging new organizing logic and structure for quantum computing, key aspects need to be considered when pursuing information systems research in this context. First, the entrance barrier to quantum computation is expected to be very high due to multiple limitations such as the necessity of knowledge in quantum physics, the expen‑ siveness of building quantum computers and the shortage of experts in the labor market. As such, they may enforce divides and limit access. Steps should be taken to reduce a possible quantum divide. Second and consequently, incum‑ bents will need to rely on the capabilities that technology providers, start‑ups, consulting firms, or academic institu‑ tions may provide, as they might go beyond their domain expertise. As such, prevailing networked businesses and eco‑ systems need to develop methods and technologies to pur‑ posefully connect their way of doing digital business with 2 https://qt.eu/ Quantum computing Fig. 3 Quantum computing system and relevant point of contacts for established eco‑ systems the emerging quantum computing ecosystem players in the different layers, namely the hardware layer (e.g., Amazon Web Services, IBM, and Google), the system layer (e.g., IonQ and Rigetti), and the application layer (e.g., Cambridge Quantum Computing or 1QBit) (IBM, 2019). Today, the playground is already diverse, with fuzzy boundaries leading to the need for design‑science‑oriented guidance for incumbents to assess their own business and technology maturity. For instance, IonQ and Rigetti are positioned on both the hardware and the system software layer. Additionally, for companies it is important to mediate the engagement with different players as part of their quan‑ tum computing road map. Thus, possible research questions might include the following: Does the access to quantum computing need to be regulated? Does quantum comput‑ ing need new sourcing strategies? How does the emerging quantum computing ecosystem act as a spoke component to other industries and ecosystems? Which transformation may result from the emergence of a quantum computing net‑ worked business? Digital understanding and representation as a foundation for quantum computing use cases and ecosystems The prolif‑ eration of quantum computing as a generative technology for calculating with an enormous speedup relies on a fundamen‑ tal premise: The problem which will be solved by a quantum computing approach needs to be replicated in the form of digital data on which basis a calculation becomes possible in the first place. Emerging technologies such as machine learning already challenge today’s organizations. The main reason is that it is complicated to digitally represent business practices and economic behavior to allow for analysis. This phenomenon may be summarized as datafication (Lycett, 2013). As such, the dematerialization of the physical world in the form of digital data as a digital representation is an essential prerequisite (Recker et al., 2021). Only with this prerequisite, one may use quantum computing when cal‑ culating the physical world based on its datafied digital representation. Achieving an adequate digital representation of the respective quantum computing problem requires a math‑ ematical and conceptual understanding to allow for assess‑ ing, understanding, and realizing the value of quantum computing aside from other computing approaches (e.g., high performance computing). Furthermore, quantum computing may also serve as an enabler for process inno‑ vation; for example, it could be interesting for research areas around process mining (Mendling et al., 2020), such as analyzing and optimizing process configurations or simulating contexts of processes or configurations of pro‑ cesses (vom Brocke et al., 2021). Therefore, research on use case analysis and in particular on methods of how to find, describe, and analyze use cases systematically and at scale are highly relevant. Possible research questions could include the following: What approaches could be used or developed to analyze business problems and therefore lev‑ erage the potential of quantum computing? How can these problems be described mathematically? What are possible design principles of artifacts to describe use cases? How will QC impact the modeling of a social and economic reality as a transformation from binary to multidimensional quantum states? 13 R. Rietsche et al. Quantum computing as a challenge for IT organizations and IT service providers IT competencies are increasingly built up in business units using commercial IT services without having the IT department in the loop. Quantum computing drives this change even further, since for the next few dec‑ ades, the first quantum computers will likely only be avail‑ able via the cloud for most companies (Carrel‑Billiard et al., 2021). IT departments are therefore under pressure in terms of how to manage quantum computer usage in companies, especially with regards to transmitting the respective data which is needed for quantum‑computing‑based calculations. This is of particular interest, since data preparation including data input and output might be the bottleneck for quantum computing in the long run. Furthermore, quantum comput‑ ing and especially the ability of prime factorization is a threat for current encryption standards and poses huge chal‑ lenges for the IT organization. Even though new encryption techniques can be used once quantum computers become a real threat to current encryption protocols, past communica‑ tion and old data can be decrypted retroactively. Future research questions could include the following: What are possible security approaches to protect legacy IT with old encryption standards? Can quantum computers and AI be used for real‑time threat and anomaly detection? How can quantum computers be used to simulate possible intru‑ sions and cyberattacks for calculating risk–cost evaluations? The latter is of special interest due to the hyper‑connectivity of digital services, which poses an enormous vulnerability for an infrastructural attack. Quantum computing skills Historically, the role of informa‑ tion systems has been to bridge the gap between informatics and business. In the age of quantum computing, this role is becoming more important than ever before. In order to leverage the potential of quantum computing, at least three roles are required (Carrel‑Billiard et al., 2021; Hughes et al., 2022): First, mathematical and quantum physical skills are needed to translate problems into mathematical formulas. Second, domain expertise is needed to integrate the busi‑ ness problem within the mathematical formulation. Third, an intermediary is needed to facilitate between both roles (Gartner, 2019). Due to the high complexity and high spe‑ cialization of the job types (e.g., error correction specialist, quantum algorithm developer), the entrance barrier to the field of quantum computing is significantly higher than for regular "coding". Additionally, for years there has been a shortage of STEM (Science Technology Engineering Math‑ ematics) graduates, which may amplify the war for talents in quantum computing (OECD, 2021). Having said that, com‑ panies such as IBM, Google, or research institutions such as ETH, are working on developing programming languages and compilers in which a device will decide if the applica‑ tion is suitable for a quantum computer. However, according 13 to experts, this will take years. Future research questions could include the following: How could information sys‑ tems act in a mediating role for adopting quantum computing technologies? Should quantum computing be included in the information systems curriculum? Since quantum computing knowledge is important on a strategic level, how can future information systems managers be trained to be aware of its potential? How can management leverage the potentials of available techniques, approaches and platforms around quan‑ tum computing? How can gaps of knowledge and access to infrastructures be mitigated? Conclusion In this Fundamentals article, we provide an overview of the constituting concepts of quantum computing. Against this backdrop, this fundamental gives a brief overview of the three layers of a quantum computer: hardware, system soft‑ ware, and application layer. On this basis and our access to leading experts in quantum computing, we propose several focus areas for studying the socio‑technical implications of quantum computing for the emergence of new ecosystems or their extensions as well as for ecosystem participants themselves. The disruptive nature of quantum computing will lead to various changes in all socio‑technical components of organi‑ zations and in IS‑related ecosystems. As such, we expect a large impact on the IS discipline in academia, practice, and teaching. At the same time, we are aware that quantum computing is in its infancy, both as a field of research for IS research as well as in its development towards an estab‑ lished and well‑understood computing approach. Against this backdrop, we hope to inform and inspire research on the socio‑technical peculiarities of quantum computing on the ecosystem level or level of electronic markets (e.g., quantum computing ecosystems as a new networked business), the organizational level (e.g., the role of IT organizations and service provider for establishing quantum computing), the individual level (e.g., quantum computing skills) as well as on the crucial role of data (i.e., digital understanding and representation of economic behavior) to allow for quantum computing calculations. Acknowledgements We would also like to thank all the interviewees for their help and especially Rajiv Krishnakumar for his support in revising this article. Open Access This article is licensed under a Creative Commons Attri‑ bution 4.0 International License, which permits use, sharing, adapta‑ tion, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated Quantum computing otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Aaronson, S. (2008). THE LIMITS OF Quantum. Scientific American, 298(3), 62–69. http://www.jstor.org/stable/26000518. Accessed 3 June 2021 Albash, T., & Lidar, D. A. (2018). Adiabatic quantum computation. Reviews of Modern Physics, 90(1), 015002‑1‑0150026–4. https:// doi.org/10.1103/RevModPhys.90.015002 Almudever, C. G., Lao, L., Fu, X., Khammassi, N., Ashraf, I., Iorga, D., Varsamopoulos, S., Eichler, C., Wallraff, A., Geck, L., Kruth, A., Knoch, J., Bluhm, H., & Bertels, K. (2017). The engineering challenges in quantum computing, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2017, 836–845. https:// doi.org/10.23919/DATE.2017.7927104 Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo, S., Brandao, F. G. S. L., Buell, D. A., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Collins, R., Courtney, W., Dunsworth, A., Farhi, E., Foxen, B., & Martinis, J. M. (2019). Quantum supremacy using a programmable superconducting processor. Nature, 574(7779), 505–510. https://doi.org/10.1038/ s41586‑019‑1666‑5 Benioff, P. (1980). The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as repre‑ sented by Turing machines. Journal of Statistical Physics, 22(5), 563–591. https://doi.org/10.1007/BF01011339 Bennett, C. H., & Brassard, G. (2014). Quantum cryptography: Public key distribution and coin tossing. Theoretical Computer Science, 560, 7–11. https://doi.org/10.1016/j.tcs.2014.05.025 Boehringer‑Ingelheim. (2021). Partnership in quantum computing for Pharma R&D | Press. https://www.boehr inger‑ingelheim.com/ press‑release/partnering‑google‑quantum‑computing. Accessed 3 June 2021 Bosch, S. (2020). Quantum algorithms for linear algebra and optimization [Master Thesis, École polytechnique fédérale de Lausanne]. Library catalog. https://www.academia.edu/43923193/Quantum_ Algor ithms_ for_ Linear_ Algeb ra_ and_ Optim izati on? source= swp_share. Accessed 3 June 2021 Braun, M. C., Decker, T., Hegemann, N., Kerstan, S. F., & Schäfer, C. (2021). A quantum algorithm for the sensitivity analysis of business risks. http://arxiv.org/pdf/2103.05475v1. Accessed 3 June 2021 Budde, F., & Volz, D. (2019). The next big thing? Quantum computing’s potential impact on chemicals. https://www.mckinsey.com/ industries/chemicals/our‑insights/the‑next‑big‑thing‑quantum‑ computings‑potential‑impact‑on‑chemicals. Accessed 3 June 2021 Carrel‑Billiard, M., Treat, D., Dukatz, C., & Ramesh, S. (2021). Accenture get ready for the quantum impact. https://www.accenture. com/_acnmedia/PDF‑144/Accenture‑Get‑Ready‑for‑the‑Quant um‑Impact.pdf. Accessed 3 June 2021 Chakrabarti, S., Krishnakumar, R., Mazzola, G., Stamatopoulos, N., Woerner, S., & Zeng, W. J. (2021). A threshold for quantum advantage in derivative pricing. Quantum, 5, 463–504. https:// doi.org/10.22331/q‑2021‑06‑01‑463 Ciliberto, C., Herbster, M., Ialongo, A. D., Pontil, M., Rocchetto, A., Severini, S., & Wossnig, L. (2018). Quantum machine learning: A classical perspective. Proceedings Mathematical, Physical, and Engineering Sciences, 474(2209), 20170551. https:// doi. org/10.1098/rspa.2017.0551 DeBenedictis, E. P. (2018). A future with quantum machine learn‑ ing. Computer, 51(2), 68–71. https://doi.org/10.1109/MC.2018. 1451646 Dendukuri, A., & Luu, K. (2018). Image processing in quantum computers. http://arxiv.org/pdf/1812.11042v3. Accessed 3 June 2021 Ding, Y., & Chong, F. T. (2020). Quantum computer systems: Research for noisy intermediate-scale quantum computers. Synthesis lectures on computer architecture. Morgan &Clay‑ pool. https://doi.org/10.2200/S01014ED1V01Y202005CAC051 Egger, D. J., Gambella, C., Marecek, J., McFaddin, S., Mevissen, M., Raymond, R., Simonetto, A., Woerner, S., & Yndurain, E. (2020). Quantum computing for finance: State‑of‑the‑art and future prospects. IEEE Transactions on Quantum Engineering, 1, 1–24. https://doi.org/10.1109/TQE.2020.3030314 Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum‑ mechanical description of physical reality be considered com‑ plete? Physical Review, 47(10), 777–780. https:// doi. org/ 10. 1103/PhysRev.47.777 Feynman, R. P. (1982). Simulating physics with computers. International Journal of Theoretical Physics, 21(6–7), 467–488. https://doi.org/10.1007/BF02650179 Gambetta, J. (2020). IBM’s Roadmap for scaling quantum technology. https://www.ibm.com/blogs/research/2020/09/ibm‑quant um‑roadmap/. Accessed 3 June 2021 Gao, X., Zhang, Z.‑Y., & Duan, L.‑M. (2018). A quantum machine learning algorithm based on generative models. Science Advances, 4(12), eaat9004. https:// doi. org/ 10. 1126/ sciadv. aat9004 Gartner. (2019). The CIO's guide to quantum computing. https:// www. gartn er. com/ smart erwit hgart ner/ the‑ cios‑ guide‑ to‑ quant um‑computing. Accessed 3 June 2021 Gerbert, P., & Ruess, F. (2018). The next decade in quantum computing and how to play. https://www.bcg.com/publications/2018/ next‑ decade‑ quant um‑ compu ting‑ how‑ play. Accessed 3 June 2021 Grover, L. K. (1996). A fast quantum mechanical algorithm for data‑ base search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, pp. 212–219. https://doi. org/10.1145/237814.237866 Grumbling, E., & Horowitz, M. (2019). Quantum computing: Progress and prospects (2019). National Academies Press. https://doi.org/ 10.17226/25196 Hadda, M., & Schinasi‑Halet, G. (2019). Quantum computing: A technology of the future already present. https://www.pwc.fr/fr/assets/ files/pdf/2019/11/en‑france‑pwc‑point‑of‑view‑quantum‑compu ting‑2019.pdf. Accessed 3 June 2021 Hann, C. T., Zou, C.‑L., Zhang, Y., Chu, Y., Schoelkopf, R. J., Girvin, S. M., & Jiang, L. (2019). Hardware‑efficient quantum random access memory with hybrid quantum acoustic systems. Physical Review Letters, 123(25), 250501. https://doi.org/10.1103/PhysR evLett.123.250501 Harrow, A., Hayden, P., & Leung, D. (2004). Superdense coding of quantum states. Physical Review Letters, 92(18), 187901. https:// doi.org/10.1103/PhysRevLett.92.187901 Harrow, A. W., Hassidim, A., & Lloyd, S. (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15), 150502. Hartmann, M. J., & Deppe, F. (2021). Erste Demonstration von Quantenüberlegenheit. https://doi.org/10.1002/piuz.202001587 Hazan, E., Ménard, A., Patel, M., & Ostojic, I. (2020). The next tech revolution: quantum computing. https://www.mckinsey.com/fr/~/ media/McKinsey/Locations/Europe%20and%20Middle%20East/ France/ Our% 20Ins ights/ The% 20next% 20tech% 20revoluti on% 20Quantum%20Computing/Quantum‑Computing.ashx. Accessed 3 June 2021 13 R. Rietsche et al. Hoffmann, M. (2021). The quantum speedup will allow completely new applications. Digitale Welt, 5(2), 10–12. https://doi.org/10. 1007/s42354‑021‑0329‑5 Hughes, C., Finke, D., German, D.‑A., Merzbacher, C., Vora, P. M., & Lewandowski, H. J. (2022). Assessing the needs of the quantum industry. IEEE Transactions on Education, 1–10. https://doi.org/ 10.1109/TE.2022.3153841 IBM. (2019). Building your quantum capability: The case for joining an “ecosystem". https://www.ibm.com/thought‑leadership/insti tute‑business‑value/report/quantumeco. Accessed 3 June 2021 Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., Chapple, E. M., Enderud, C., Hilton, J. P., Karimi, K., Ladizin‑ sky, E., Ladizinsky, N., Oh, T., Perminov, I., Rich, C., & Rose, G. (2011). Quantum annealing with manufactured spins. Nature, 473(7346), 194–198. https://doi.org/10.1038/nature10012 Kühn, M., Zanker, S., Deglmann, P., Marthaler, M., & Weiß, H. (2019). Accuracy and resource estimations for quantum chemistry on a near‑term quantum computer. Journal of Chemical Theory and Computation, 15(9), 4764–4780. https://doi.org/10.1021/acs.jctc. 9b00236 Langione, M., Tillemann‑Dick, C., Kumar, A [Amit], & Taneja, V. (2019). Where will quantum computers create value—and when? https://www.bcg.com/publications/2019/quantum‑computers‑cre‑ ate‑value‑when. Accessed 3 June 2021 Li, S.‑S., Long, G.‑L., Bai, F.‑S., Feng, S.‑L., & Zheng, H.‑Z. (2001). Quantum computing. Proceedings of the National Academy of Sciences of the United States of America, 98(21), 11847–11848. https://doi.org/10.1073/pnas.191373698 Li, Y [Yangyang], Tian, M., Liu, G., Peng, C., & Jiao, L. (2020). Quan‑ tum optimization and quantum learning: A Survey. IEEE Access, 8, 23568–23593. https://doi.org/10.1109/ACCESS.2020.2970105 Lorenz, R., Pearson, A., Meichanetzidis, K., Kartsaklis, D., & Coecke, B. (2021). QNLP in practice: Running compositional models of meaning on a quantum computer. http://arxiv.org/pdf/ 2102.12846v1. Accessed 3 June 2021 Lycett, M. (2013). ‘Datafication’: Making sense of (big) data in a complex world. European Journal of Information Systems, 22(4), 381–386. https://doi.org/10.1057/ejis.2013.10 Marinescu, D. C., & Marinescu, G. M. (2012). Quantum error‑correct‑ ing codes. In Classical and Quantum Information (pp. 455–562). Elsevier. https://doi.org/10.1016/B978‑0‑12‑383874‑2.00005‑9 Ménard, A., Ostojic, I., Patel, M., & Volz, D. (2020). A game plan for quantum computing. https://www.mckinsey.com/business‑funct ions/ mckin sey‑ digit al/ our‑ insig hts/a‑ game‑ plan‑ for‑ quant um‑ computing. Accessed 3 June 2021 Mendling, J., Pentland, B. T., & Recker, J. (2020). Building a com‑ plementary agenda for business process management and digital innovation. European Journal of Information Systems, 29(3), 208–219. https://doi.org/10.1080/0960085X.2020.1755207 Mone, G. (2020). The quantum threat. Communications of the ACM, 63(7), 12–14. https://doi.org/10.1145/3398388 Mooney, G. J., Hill, C. D., & Hollenberg, L. C. L. (2019). Entangle‑ ment in a 20‑qubit superconducting quantum computer. Scientific Reports, 9(1), 13465. https://doi.org/10.1038/s41598‑019‑49805‑7 Motta, M., Gujarati, T. P., Rice, J. E., Kumar, A [Ashutosh], Mas‑ teran, C., Latone, J. A., Lee, E., Valeev, E. F., & Takeshita, T. Y. (2020). Quantum simulation of electronic structure with a transcorrelated Hamiltonian: Improved accuracy with a smaller footprint on the quantum computer. Physical Chemistry Chemical 13 Physics: PCCP, 22(42), 24270–24281. https://doi.org/10.1039/ d0cp04106h Neukart, F. (2021). Quantencomputing in der Automobilindus‑ trie. Digitale Welt, 5(2), 34–37. https:// doi. org/ 10. 1007/ s42354‑021‑0334‑8 Neukart, F., Compostella, G., Seidel, C., von Dollen, D., Yarkoni, S., & Parney, B. (2017). Traffic flow optimization using a quantum annealer. Frontiers in ICT, 4, 29. https://doi.org/10.3389/fict.2017. 00029 OECD. (2021). Significant shortages exist in ICT and other STEM related knowledge domains. In OECD Economic Surveys: Portugal. OECD Economic Surveys: Portugal 2021. OECD. https:// doi.org/10.1787/f1155a36‑en Park, D. K., Petruccione, F., & Rhee, J.‑K.K. (2019). Circuit‑ based quantum random access memory for classical data. Scientific Reports, 9(1), 3949. https:// doi. org/ 10. 1038/ s41598‑019‑40439‑3 Recker, J., Lukyanenko, R., Jabbari, M., Samuel, B., & Castellanos, A. (2021). From representation to mediation: A new agenda for conceptual modeling research in a digital world. MIS Quarterly, 45(1a), 269–300. https://doi.org/10.25300/MISQ/2021/ 16027 Scarani, V., Bechmann‑Pasquinucci, H., Cerf, N. J., Dušek, M., Lüt‑ kenhaus, N., & Peev, M. (2009). The security of practical quantum key distribution. Reviews of Modern Physics, 81(3), 1301–1350. https://doi.org/10.1103/RevModPhys.81.1301 Schrödinger, E. (1935). Discussion of probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society, 31(4), 555–563. https://doi.org/10.1017/ S0305004100013554 Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science. IEEE Computer Society, 124–134. https://doi.org/10.1109/SFCS.1994.365700 Shor, P. W. (1995). Scheme for reducing decoherence in quantum com‑ puter memory. Physical Review a, 52(4), R2493. https://doi.org/ 10.1103/PhysRevA.52.R2493 Steane, A. (1998). Quantum computing. Reports on Progress in Physics, 61(2), 117–173. https://doi.org/10.1088/0034‑4885/61/2/002 vom Brocke, J., Baier, M.‑S., Schmiedel, T., Stelzl, K., Röglinger, M., & Wehking, C. (2021). Context‑aware business process man‑ agement. Business & Information Systems Engineering, 63(5), 533–550. https://doi.org/10.1007/s12599‑021‑00685‑0 Yarkoni, S., Leib, M., Skolik, A., Streif, M., Neukart, F., & von Dollen, D. (2019). Volkswagen and quantum computing: An industrial perspective. Digitale Welt, 3(2), 34–37. https://doi.org/10.1007/ s42354‑019‑0166‑y Zhong, H.‑S., Wang, H., Deng, Y.‑H., Chen, M.‑C., Peng, L.‑C., Luo, Y.‑H., Qin, J., Wu, D., Ding, X., Hu, Y., Hu, P., Yang, X.‑Y., Zhang, W.‑J., Li, H., Li, Y [Yuxuan], Jiang, X., Gan, L., Yang, G., You, L., Wang, Z., Li, L., Liu, N.‑L., Lu, C.‑Y., & Pan, J.‑W. (2020). Quantum computational advantage using photons. Science (New York, N.Y.), 370(6523), 1460–1463. https://doi.org/10.1126/ science.abe8770 Ziegler, M., & Leonhardt, T. (2019). Quantum computing. Applied now. Digitale Welt, 3(2), 50–52. https:// doi. org/ 10. 1007/ s42354‑019‑0170‑2 Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.