# The Business Case for Quantum Computing

## Quantum computers may deliver an economic advantage to business, even on tasks that classical computers can perform.

Imagine that a pharmaceutical company was able to cut the research time for innovative drugs by an order of magnitude. It could expand its development pipeline, hit fewer dead ends, and bring cures and treatments to market much faster, to the benefit of millions of people around the world.

Or imagine that a logistics company could dynamically manage the routes for its fleet of thousands of trucks. It could not only take a mind-numbing range of variables into account and adjust quickly as opportunities or constraints arose; it could also get fresher products to store shelves faster and prevent tons of carbon emissions every year.

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Quantum computing has the potential to transform these and many more visions into reality — which is why technology companies, private investors, and governments are investing billions of dollars in supporting ecosystems of quantum startups.1 Much of the quantum research community is focused on showing *quantum advantage*, which means that a quantum computer can perform a calculation, no matter how arbitrary, that is impossible on a classical, or binary, computer. (See “A Quantum Glossary.”) Running a calculation thousands of times faster could create enormous economic value if the calculation itself is useful to some stakeholder in the market.

However, the expense of building quantum hardware, coupled with the steady improvement of classical computers, means that the commercial relevance of quantum computing won’t be apparent unless researchers and investors shift their focus to the pursuit of what we call *quantum economic advantage*. A business achieves a quantum economic advantage when a quantum computer provides a commercially relevant solution, even if only moderately faster than a classical computer could, or when a quantum computer provides viable solutions that differ from what a classical computer yields.

### Why Quantum Economic Advantage Matters

In a dramatic first, a team at Google led by John Martinis made headlines around the world in 2019 when their quantum machine appeared to complete a calculation (cross-entropy benchmarking) in seconds that would take tens of thousands of years on a classical computer.2 Other companies have made similar claims of quantum advantage, including researchers from quantum computing startup Xanadu, which recently completed a well-defined task (Gaussian boson sampling) in under a second that would have taken the best classical supercomputer over 9,000 years.3

Hundreds of articles and many of the top minds in the field have focused on showing these kinds of quantum advantage.4 Their demonstrations represent important milestones in the development of quantum computers. But because they typically involve esoteric computations that might not be relevant to the kinds of problems many businesses need to solve, managers might assume that the technology isn’t yet useful and economically viable for businesses. We contend that quantum technology need not provide a quantum advantage to be economically useful, as long as it can still provide different or timelier outputs than its classical counterparts. Any quantum speedup provides an opportunity for quantum economic advantage. (See “Landscape of Quantum Economic Advantage.”)

While quantum advantage will be directly useful in some cases, many of the most important uses of quantum computers will arise from providing cost-effectiveness and speed rather than from performing a calculation that is impossible on a classical computer. In other words, a quantum economic advantage may exist without a quantum advantage.5

Quantum speedups create an appetite for solutions to business challenges where the ability to solve complex problems extremely quickly would confer a powerful competitive advantage. Considerable effort in quantum computing is dedicated to searching for potential speedups for business problems, although evidence for a robust quantum speedup for commercially relevant problems has been elusive. Nonetheless, identifying and realizing such commercial potential provides a crucial incentive to build quantum computers and significantly influences their design.

Classical computing remains a valuable tool for solving complex problems; the pioneering work of AlexNet (deep learning) and AlphaFold (protein structure) are two examples that have high commercial value. Quantum computing might be the better tool to solve a business problem if it provides the solution more quickly than a classical competitor. Running the same calculation on both quantum and classical computers may also provide two different answers, either of which might be better. When the commercial stakes are high enough, having both classical and quantum solutions can be useful, meaning the quantum solutions might still be commercially valuable.

The question of when existing or forthcoming improved quantum computers will generate substantial commercial opportunities is therefore of immediate interest, long before clear-cut quantum advantage will become obvious in future fault-tolerant machines.6

### Opening Valuable Commercial Frontiers

Identifying the commercial potential of a quantum computer does not require an understanding of the quantum physics that undergird the technology. Instead, the focus should be on what quantum computers can do better, faster, or perhaps differently than classical computers and on the stakeholders who will see those outcomes as valuable. The visions from the pharmaceutical and logistics sectors that we shared at the start of this article illustrate the transformative effects that quantum computing could have. The examples we highlight below show the high value that quantum computing can already unlock within existing workflows.

**Make better investment decisions faster.** The finance industry faces many optimization problems. Finding the optimal trading trajectory, for example, involves determining the best trading strategy for an investment portfolio over a specific period. Portfolio optimization is a valuable problem to solve, given that over $100 trillion in assets are under management globally.7 Even small improvements in optimization techniques are valuable because of the absolute level of assets invested.

In some cases, determining the optimal investment strategy requires a search through all possible trading trajectories. That effort grows exponentially more challenging as the number of possible securities in the portfolio and the number of opportunities to change the portfolio increase. Recent work has attempted to tackle a portfolio optimization problem that has 10¹,³⁰⁰ possible trading strategies — a quantity far in excess of the number of atoms in the visible universe (10⁸⁰).8

Quantum machines may be able to help.9 Researchers at the quantum software company Multiverse Computing compared a handful of different methods for solving the optimal trading trajectory problem. Only two of the six optimization methods provided a solution for the most complex version of the problem assessed, and the classical solution took almost 700 times longer to generate than the quantum solution. The quantum tools also yielded a different solution — one with higher profits but lower risk-adjusted returns — than the one suggested by strictly classical techniques.

These outcomes are not an example of quantum advantage, because it remains possible that an exhaustive assessment of all possible approaches to solving this problem might generate solutions that are the same as or better than the quantum approaches the researchers at Multiverse used. But it may nevertheless represent an example of quantum economic advantage, because generating a solution quickly is valuable. (See “Gaining an Edge When Time Is Money.”)

Determining which of the two solutions is better — quantum or classical — remains a challenge. While financial market stakeholders currently don’t have access to fully fault-tolerant quantum computers, they also typically don’t have easy access to the classical supercomputers that are used to benchmark quantum advantage. Thus, comparing current quantum approaches to classical optimizers that are sold commercially still provides a valuable benchmark for the efficacy of a quantum approach. The best classical supercomputers might still generate a similar or superior solution in a timely manner — that is, in a time span that is less than one human lifetime.

**Solve seemingly unsolvable business trade-offs.** Almost any business problem that involves complex trade-offs — from day-to-day planning to long-term strategic decisions — could be well suited for quantum computers. Think of retailers that are assessing where to place certain products in their stores to maximize revenue, or educators trying to assess which questions to ask and in which order to maximize learning. These trade-off challenges are known as *combinatorial optimization problems*. The creation of the best-tasting recipe at a restaurant is also a combinatorial optimization, as are the logistics challenges we described at the beginning of this article. Even modest improvements can have a major impact on a company’s profitability.

Business leaders often rely on human intuition to solve these optimization problems. As businesses grow, they may come to rely on computing power to identify the best solutions. For the most complex of these problems, even today’s most powerful computers can provide only an approximation. Quantum computers could, however, perform a search through all possible combinations of arrangements or sequences to find the best solution, providing a moderate speedup over comparable classical searches.10

Almost any business problem that involves complex trade-offs could be well suited for quantum computers.

That’s where they can have a wide range of applications in almost any business sector. For instance, identifying the reasons for machine failure when failure rates are low is a challenging combinatorial optimization problem in advanced manufacturing.11 Finding the cause of failure quickly is important, because downtime can be costly. If quantum computing can speed up the process of determining why a manufacturing process failed, it could be valuable even in settings where classical approaches could eventually find the same reason for failure.

**Discover better materials.** The timeliness and quality of quantum computing solutions should also improve the efficiency of R&D processes that lead to new materials and medicines, because they reduce the cost and quicken the pace of discovery relative to classical techniques.

In materials design, computers already aim to simulate the complex behavior of constituent atoms and molecules and reliably predict the structure-property relationships of molecules. In typical applications, however, classical computers face significant limits on the size of molecules they can simulate. Even simulations involving the smallest molecules are computationally intensive, and the addition of even one atom or electron can make a classical simulation drastically slower. This renders many avenues of computer-aided design unavailable for the larger molecules that are of interest to the pharmaceutical, chemical, and materials industries.

Greater computing speed confers the ability to simulate larger and more complex molecules in a practically useful time frame, and quantum computers are poised to make a significant impact in this area.12 They are believed to be able to provide speedups for the calculations required to predict the electronic structure of atoms and molecules, although the precise nature of these speedups is currently a matter of intense debate within the scientific community.13

### The Enduring Value of Quantum Advantage

Recent claims of quantum advantage may have no commercial application — and thus no quantum *economic* advantage — but they are nonetheless important because they establish the possibility that quantum computers can perform certain tasks that classical computers cannot.

The application of Shor’s algorithm is perhaps the most frequently referenced example of how quantum advantage might affect society. American mathematician Peter Shor, who recently won science’s most lucrative prize, the Breakthrough Prize in Fundamental Physics, demonstrated that a quantum computer could factor a large integer in cases where classical computers could not.14 A sufficiently large quantum computer could factor these larger integers in days or less, whereas a classical computer might need more time than it would take for the sun to run out of hydrogen.15

While this might sound abstract, the difficulty that classical computers have in factoring very large numbers is actually what enables modern encryption. The relative ease with which quantum computers could theoretically perform the calculations involved in decryption provides an example of where we expect clear-cut quantum advantage to exist. If a quantum computer could implement Shor’s algorithm, then much of the information encrypted in the past could be decoded — and that includes a great deal of encrypted data that has been stolen from organizations in cyberattacks.

This threat is remote right now, because the quantum community is years away from building fault-tolerant quantum computers large enough to use Shor’s algorithm to break codes. But it warrants the attention of managers in almost all industries, who will eventually make up a large market for new, quantum-robust encryption standards. Here, quantum computers’ ability to generate random numbers can play a role in supporting more advanced cybersecurity defenses.

Quantum computers are probabilistic, which means they can generate truly random numbers.16 Their classical counterparts, in contrast, are deterministic and thus can generate only pseudo-random numbers. However, even when a quantum computer can do something with a clear practical application that a classical computer cannot do, business leaders must still weigh the trade-offs. In some cases, the classical approach may be deemed good enough, limiting the organization’s incentives to switch to quantum. This may be the case with some other potential applications for quantum random number generators (RNGs), such as in the lottery and casino gambling sectors.17

Lotteries select winning numbers either electronically or physically, such as by drawing numbered balls from bins. The resulting numbers are not truly random. Because the process is deterministic, it would be possible for someone to predict the numbers if they knew something about the underlying process that generated them, or to manipulate the process to generate certain numbers.

Even when a quantum computer can do something with a clear practical application that a classical computer cannot do, business leaders must still weigh the trade-offs.

While such manipulations have indeed occurred, lotteries will probably not abandon their current processes anytime soon, despite what appears to be a clear argument for using quantum computing. First, lottery fraud through manipulation of the number-generating process is rare, perhaps due to the significant costs of getting caught, strict rules against insiders participating in lotteries, and the existence of powerful analytical tools to detect fraud. Second, in the absence of fraud, pseudo-RNGs yield results that are often indistinguishable from their quantum counterparts. While it may be theoretically possible to predict the outcome of a lottery before drawing balls from multiple bins, it is practically infeasible to do so. Lotteries thus have little incentive to switch to quantum machines. Managers confronting similar cases where quantum computing provides a capability that is entirely lacking in classical computing will likewise need to weigh the relative costs and benefits of the optimal versus the good-enough solution.

### Preparing for Quantum Computing in Business

To fulfill its promise and create new value and new commercial opportunities, a quantum machine does not have to accomplish a currently impossible task. It only needs to accomplish something useful. That time is coming, as billions of dollars in investments from venture capitalists, major tech companies, and national governments fuel rapid improvements in quantum computers that will make them more efficient than classical ones.

The consensus among most government and industry players seems to be that large-scale fault-tolerant quantum computers almost certainly won’t appear before the end of this decade. Although it may take years for commercially relevant quantum computers to exist at scale, business leaders can already take several steps to prepare their businesses for this era.

**Make a list of your “If we could only …” or “What if …?” challenges.** Most businesses have such daunting challenges but rarely address them because they are too resource-intensive and those resources have better short-term uses. The speedups and alternative solutions from quantum computing can make the transformative solutions to these problems feasible. What elements of your business are constrained by combinatorial optimization? And how much would a solution be worth to you?

**Help your organization become quantum ready.** We anticipate that the impact and scale of commercial applications will accelerate rapidly once fully fault-tolerant quantum computers emerge. Organizations have several ways to prepare themselves. Companies with a higher likelihood of lucrative applications — financial services companies, pharmaceutical manufacturers, and makers of specialty materials — can invest in hardware and software and develop a network of experts. Other organizations can familiarize themselves with the basics of quantum computing, connect with academics, and start to train team members.

**Start experimenting now.** Companies can already allocate a portion of R&D resources to experiment with near-term quantum hardware. They can set up problems in ways the computers can understand, even if existing hardware might not allow them to capitalize on those opportunities yet. These investments are important to the ongoing development of the technology: Quantum computing will not scale solely through academic research.

The startups we have worked with in the Creative Destruction Lab at the University of Toronto’s Rotman School of Management have already achieved short-term benefits from experimenting with quantum — for example, by creating innovations that have led to new materials. The long-term benefit from experimenting with quantum computing today is that a company will be prepared when sufficiently coherent, fault-tolerant quantum computers exist at scale. Those organizations will have a considerable first-mover advantage and be well positioned to capture new opportunities as this emerging technology comes to market.

#### References

**1.** C. Metinko, “Quantum Technology Gains Momentum as Computing Gets Closer to Reality,” Crunchbase, May 13, 2022, http://news.crunchbase.com; “What America’s Largest Technology Firms Are Investing In,” The Economist, Jan. 22, 2022, www.economist.com; and M. Aboy, T. Minssen, and M. Kop, “Mapping the Patent Landscape of Quantum Technologies: Patenting Trends, Innovation, and Policy Implications,” International Review of Intellectual Property and Competition Law 53, no. 10 (November 2022): 853-882.

**2.** F. Arute, K. Arya, R. Babbush, et al., “Quantum Supremacy Using a Programmable Superconducting Processor,” Nature 574, no. 7779 (Oct. 24, 2019): 505-510.

**3.** L.S. Madsen, F. Laudenbach, M.F. Askarani, et al., “Quantum Computational Advantage With a Programmable Photonic Processor,” Nature 606, no. 7912 (June 2, 2022): 75-81.

**4.** A.K. Fedorov, N. Gisin, S.M. Beloussov, et al., “Quantum Computing at the Quantum Advantage Threshold: A Down-to-Business Review” (preprint, submitted in March 2022), https://arxiv.org; L. Mueck, C. Palacios-Berraquero, and D.M. Persaud, “Towards a Quantum Advantage,” Physics World, Feb. 5, 2020, https://physicsworld.com; and S. Chen, “Quantum Advantage Showdowns Have No Clear Winners,” Wired, July 11, 2022, www.wired.com.

**5.** F. Bova, A. Goldfarb, and R.G. Melko, “Quantum Economic Advantage,” Management Science, Articles in Advance, published online Dec. 2, 2022.

**6.** “Near term” in this context refers to the quantum computers of the next few years, which will be better than today’s but still not fully fault tolerant.

**7.** “Value of Assets Under Management Worldwide in Selected Years From 2003 to 2021,” Statista, July 8, 2022, www.statista.com.

**8.** “Wall Street’s Latest Shiny New Thing: Quantum Computing,” The Economist, Dec. 19, 2020, www.economist.com.

**9.** S. Mugel, C. Kuchkovsky, E. Sanchez, et al., “Dynamic Portfolio Optimization With Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks,” Physical Review Research 4, no. 1 (January 2022): 1-12.

**10.** L.K. Grover, “A Fast Quantum Mechanical Algorithm for Database Search,” in “STOC ’96: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing” (Philadelphia: Association for Computing Machinery, 1996).

**11.** F. Bova, A. Goldfarb, and R.G. Melko, “Commercial Applications of Quantum Computing,” EPJ Quantum Technology 8 (2021): 1-13.

**12.** S.N. Genin, I.G. Ryabinkin, N.R. Paisley, et al., “Estimating Phosphorescent Emission Energies in Ir(III) Complexes Using Large-Scale Quantum Computing Simulations” (preprint, submitted in November 2021), https://arxiv.org. Since atoms and electrons themselves are quantum objects, they are natural candidates for study by quantum computers. In fact, such “simulation” (or emulation) was the first value proposition made for a quantum computer by California Institute of Technology physicist Richard Feynman in 1982.

**13.** S. Lee, J. Lee, H. Zhai, et al., “Is There Evidence for Exponential Quantum Advantage in Quantum Chemistry?” (preprint, submitted in August 2022), https://arxiv.org.

**14.** P.W. Shor, “Algorithms for Quantum Computation: Discrete Logarithms and Factoring,” in “Proceedings 35th Annual Symposium on Foundations of Computer Science” (Santa Fe, New Mexico: IEEE, 1994).

**15.** R. Van Meter and D. Horsman, “A Blueprint for Building a Quantum Computer,” Communications of the ACM 56, no. 10 (October 2013): 84-93.

**16.** It should be noted that quantum computers are not the only quantum technology that can produce true random numbers.

**17.** J. Melia, “The Odds Are in Quantum Security’s Favor,” QuintessenceLabs, March 2, 2017, www.quintessencelabs.com; and “Rigged Random Number Generators,” QuintessenceLabs, May 27, 2016, www.quintessencelabs.com.

**i.** Bova, Goldfarb, and Melko, “Commercial Applications of Quantum Computing.”

**ii.** D. Layden, G. Mazzola, R.V. Mishmash, et al., “Quantum-Enhanced Markov Chain Monte Carlo” (preprint, submitted in March 2022), https://arxiv.org; and S. Chakrabarti, J. Krishnakumar, G. Mazzola, et al., “A Threshold for Quantum Advantage in Derivative Pricing” (preprint, submitted in December 2020), https://arxiv.org.