## 1 Introduction

_{0}and a

_{1}are called probability amplitudes and can be complex numbers satisfying the condition \(\left| {{\text{a}}_{0} } \right|^{2} + \left| {{\text{a}}_{1} } \right|^{2} = 1.\) Formally, we can thus think of the state of a qubit as a unit vector in a two-dimensional complex vector space. A superposition allows qubits to be in multiple states simultaneously (DiCarlo et al. 2009).

_{0}= a

_{1}= Sqrt(0.5) will be in state \(\left| 0 \right\rangle\) or \(\left| 1 \right\rangle\) with an equal probability 0.5 when measured.

_{1},…,x

_{n}) of all their inputs x

_{1},…,x

_{n}using a single quantum circuit (in combination with logical quantum gates). This behavior is completely different from classical parallel computing where multiple Boolean circuits can only evaluate parts of the input at the same time. Due to this property, it is possible to run f(.) simultaneously for more than one input allowing us to determine global properties of f(.). This effectively permits an exponentially faster solution of certain problems in comparison to traditional computers. However, one must distinguish between performing such parallel computations and reading out the value of the functions of all inputs. In fact, only one value of f(.) can be retrieved in one iteration since all other values are inaccessible. In contrast to classical bits, we cannot determine the state of a qubit simply by reading. We need to measure and the result depends on the above-mentioned probability amplitudes a

_{0}and a

_{1}that can take on negative or complex values. Thus, in contrast to classical probabilities, probability amplitudes are allowed to be negative which can lead to constructive interference (both are negative or positive) or deconstructive interference (one is positive and one is negative). While quantum computers are faster than traditional computers in performing multiple simulations, they hardly produce one correct answer to a question in a single run. Instead, quantum computing delivers probability distributions that we can understand as a range of results over multiple runs, which is the reason why quantum computers will not entirely replace classical computers. If the input is large or the output is large, e.g., event logs with billions of events in process mining applications, then it is probably infeasible to use quantum computing. However, they provide distinct benefits when solving very specific and complex problems, such as simulation or optimization tasks, where excluding a large fraction of possibilities is timesaving and efficient. It makes sense that the practical application of such quantum algorithms on working and scalable quantum computers offers a wealth of possibilities that human society at the macroscale, and organizations at the microscale, might benefit from (Trabesinger 2017).

## 2 Status of Quantum Computing

## 3 An Agenda for Information Systems Research around Quantum Computing

IS Research traditions | Potential areas of investigation |
---|---|

Behavioral Information Systems Research | Which factors drive the adoption of quantum computing by individuals, groups, and organizations? How should a training agenda be developed that helps IT leaders acquire the necessary knowledge to make informed decisions regarding quantum computing? How important is trust in quantum computing and how can it be increased? Which strategic process models facilitate the integration of quantum devices into organizational structures? How should organizations orchestrate the interaction of quantum computing and classical computing? |

Design Science Research | How can quantum computing facilitate calculations for solving optimization problems? How can the simulation of the behavior of complex systems benefit from quantum computing research? What are the implications of quantum-related speed-ups for machine learning applications? How can quantum computing accelerate and improve the analysis of large datasets? How can new applications and workflows be designed that jointly leverage advances in classical computing, quantum computing and Artificial Intelligence? What are the implications of post-quantum and quantum cryptography for the security of Information Systems? |

Economics of Information Systems Research | How can we assess the business value of quantum computing in different application fields? What is the (monetary) impact of quantum-related innovations on a company’s business model? What are the requirements for a vital ecosystem of startups, technology companies, investors and research institutions and how does this environment foster innovation in quantum computing? What are the economic consequences of quantum computing for the society? How can organizations measure efficiency gains in business process design and product development? How can governments help quantum computing startups grow? Which business problems should be prioritized when allocating resources for quantum computing projects? |