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.

Shor’s algorithm, also known as the integer factorization algorithm, can factorize integers almost exponentially faster than the fastest known classical algorithm. Factorizing integers is very difficult computationally and is therefore also the basis of RSA encryption.

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 the solution x of a linear system (Ax = b), where A is a matrix and b a vector.

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 technologies, such as the solution of D-Wave. 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 deliveries, 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 constraints 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 classical 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 problem. 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. Especially players specializing in portfolio optimization and arbitrage could benefit. 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 profitability. Further, Deutsche Börse (a German company offering marketplace organizing for the trading of shares) already experimented with the applicability of quantum computing for a sensitivity analysis on one of their risk models, a computation that is too expensive to be run on classical computers. 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 procedures 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 cybersecurity. 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. Conversely, it would be easy for a quantum computer to crack data encrypted with classical RSA technology – a phenomenon that may be coined as quantum threat.

The ability of quantum computing to accelerate optimization problems plays a crucial role for narrow AI approaches. Quantum computing 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 computers offer several approaches to solving problems like this, thereby, again, accelerating calculation and allowing for more complex network architectures. They may be applicable to all relevant practices or sub-tasks of artificial intelligence, such as image processing and computer vision or natural language processing, as demonstrated in an experiment by Cambridge Quantum Computing. Having said that, it is important to note that, so far, no near-term machine learning algorithm with provable speedup has been found.

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 represent an almost unsolvable task. In the 1980s, Richard Feynman theoretically substantiated the possibility of a quantum-based computer for simulating molecules. 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 synthesis in the Haber-Bosch process, which today accounts for about 1 to 2 percent of global energy consumption. Better 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.

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 replicate 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 prediction 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 functioning of batteries is deemed to inform today’s electromobility and is already targeted by automotive giants such as VW.

The adoption and diffusion of quantum computing will heavily rely on an emerging ecosystem comprising technology providers, such as IBM, Google, Microsoft, or Amazon 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.

Also, the European Union built their own ecosystem with the “Quantum Flagship”. Companies, providers, research institutions, and governments 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, translating business problems into mathematical and quantum problems, etc.). 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 expensiveness 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, incumbents will need to rely on the capabilities that technology providers, start-ups, consulting firms, or academic institutions may provide, as they might go beyond their domain expertise. As such, prevailing networked businesses and ecosystems need to develop methods and technologies to purposefully connect their way of doing digital business with 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).

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 quantum computing road map.

The proliferation of quantum computing as a generative technology for calculating with an enormous speedup relies on a fundamental 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 . As such, the dematerialization of the physical world in the form of digital data as a digital representation is an essential prerequisite. Only with this prerequisite, one may use quantum computing when calculating the physical world based on its datafied digital representation.

Achieving an adequate digital representation of the respective quantum computing problem requires a mathematical and conceptual understanding to allow for assessing, 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 innovation; for example, it could be interesting for research areas around process mining, such as analyzing and optimizing process configurations or simulating contexts of processes or configurations of processes.

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.

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 decades, the first quantum computers will likely only be available via the cloud for most companies.

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 computing and especially the ability of prime factorization is a threat for current encryption standards and poses huge challenges for the IT organization. Even though new encryption techniques can be used once quantum computers become a real threat to current encryption protocols, past communication and old data can be decrypted retroactively.

Historically, the role of information 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:

First, mathematical and quantum physical skills are needed to translate problems into mathematical formulas.
Second, domain expertise is needed to integrate the business problem within the mathematical formulation.
Third, an intermediary is needed to facilitate between both roles.

Due to the high complexity and high specialization 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 Mathematics) graduates, which may amplify the war for talents in quantum computing. Having said that, companies 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 application is suitable for a quantum computer. However, according to experts, this will be take years.