Computers do arithmetic. Underlying all the amazing applications of computers today is arithmetic, calculated using binary digits or “bits.” The UNIVAC computer of the early 1950s could perform about 465 multiplications per second, much faster than the “human computers” who performed such calculations for the military and other organizations, as highlighted in the movie *Hidden Figures*. Today’s computers are billions of times faster.^{Footnote 1} However, despite these advances, there is an important class of arithmetic problems that remain out of reach for classical computers for the foreseeable future: Large-scale, combinatorics calculations. Combinatorics problems involve the way in which items are arranged. As the number of items grows, the number of possible permutations grows exponentially. The typical objective in combinatorics calculations is to find a specific value, and this exponential growth in the number of permutations makes it increasingly challenging to find that specific value.

Understanding technological change as a drop in the cost of some factor has a long history in the economics and management literatures, for example arithmetic for computers, search for the internet, and prediction for machine learning.^{Footnote 2} In this paper, we argue that—from a management perspective—quantum computing improves combinatorics calculations. We then provide a number of examples of industries in which better combinatorics calculations may be transformative.

To start, it is important to note that a surprising number of practical problems can be viewed as combinatorics problems, including applications in cryptography, chemistry, materials science, finance, and advanced manufacturing. Many of these applications have remained out of reach for classical computers because the number of possible permutations often grows to a point that they could take thousands or millions of years to assess, if each possibility was assessed sequentially.

Combinatorics problems expose the limits of classical computers, and therefore represent the potential for quantum computers. We are not there yet however. Quantum computers do not work at the required scale, and there are major technical issues that remain in the race to scale up today’s quantum hardware. Despite these limitations, considerable progress is being made toward applying present-day quantum hardware to commercial applications. Below, we provide examples of combinatorics problems that companies are already working to solve, driven by advances in quantum computing. We divide these applications into four industry verticals: cybersecurity, materials and pharmaceuticals, banking and finance, and advanced manufacturing. Despite the remaining technical challenges in developing large scale and practical quantum computers, we identify three types of near-term opportunities generated by advances in quantum computing.

First, the development of algorithms for quantum computers has led to advances in our ability to solve large-scale combinatorics problems on already-available classical computers. We have seen a large number of quantum companies, via their work with emerging quantum computing technology, develop “quantum-inspired” algorithms that enable them to solve important practical problems on classical computers.^{Footnote 3} As new algorithms are discovered, the boundary between quantum and classical can shift. Quantum algorithms can inspire insight into new classical solutions. In other words, the rise of quantum-inspired solutions suggests that quantum computing could change the speed of technological advancement for combinatorics problems, even if quantum computers never achieve the scale and reliability needed to dominate other types of computing.

It is not unusual for an emerging technology to push innovation in existing technologies, without displacing the incumbent. This was the case in the TV market, where innovation in LCD screens accelerated after the emergence of commercially viable plasma flat screen televisions. Eventually, innovation in LCD screens outpaced innovation in plasma, so that the emerging technology never really displaced the incumbent.^{Footnote 4}

However, it is unclear whether a similar phenomenon will play out in quantum, particularly since many different models and architectures are still being explored. Current quantum devices are small and noisy, while the holy grail for the technology is to achieve large, highly-controlled, coherent, analog or digital quantum computers.^{Footnote 5} In short, a computer where the rate of component failure is sufficiently low to deliver uninterrupted service. Even for the most complex combinatorics problems, it could be that quantum-inspired classical computers ultimately dominate, or that one or several quantum computer designs ultimately dominate, or that some kind of hybrid approach yields a market leader. For now, however, we know that quantum algorithms have inspired useful innovations in software for classical computers that have generated commercial opportunities.^{Footnote 6}

Second, the threat of the arrival of quantum computers in the near future suggests benefits to investing in certain technologies today—most notably, in cryptography.^{Footnote 7} If a fully functioning sufficiently coherent quantum computer becomes available, many files encrypted using current standards would be more easily decipherable. Therefore, if something needs to remain encrypted for many years, the threat that a quantum computer may be available in a decade or two means that it is worthwhile investing in quantum-safe encryption today.

Third, quantum computers were originally conceived by Richard Feynman to simulate or emulate quantum systems that are difficult to simulate classically on a classical computer.^{Footnote 8} As molecules grow more complex, with more atoms and more electrons in those atoms, the number of possible configurations grows exponentially. This type of chemical engineering requires combinatorics, and so is often not well-suited to classical computers. In other words, materials development and drug discovery are constrained by the combinatorics challenges that arise from simulating new molecules and new applications of molecules. Quantum simulators, which are attainable in near-term devices, should help. While we are still waiting for an example of a new useful molecule that has been discovered through simulation on a quantum computer, complex known molecules have been simulated, demonstrating proof-of-concept.

Both the short-run and long-run opportunities with quantum computing will depend on the particular quantum computing architectures developed. There are many such architectures, each with their strengths, weaknesses, and corresponding technical challenges. This management-focused article will not provide a technical overview. Just as most articles about the impact of other types of information technology on business don’t detail the physics of semiconductors or the underlying mathematics of a Turing machine, we will not detail what quantum computing is, how it works, and how the various architectures differ.^{Footnote 9} Our purpose is then to use examples of companies working with quantum technology to shed light on the types of problems for which these advancements are likely to be most useful, in the near-term and in the long run.