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Digital computing has limitations in regards to an important category of calculation called combinatorics, in which the order of data is important to the optimal solution. These complex, iterative calculations can take even the fastest computers a long time to process. Computers and software that are predicated on the assumptions of quantum mechanics have the potential to perform combinatorics and other calculations much faster, and as a result many firms are already exploring the technology, whose known and probable applications already include cybersecurity, bio-engineering, AI, finance, and complex manufacturing.

Quantum technology is approaching the mainstream. Goldman Sachs recently announced that they could introduce quantum algorithms to price financial instruments in as soon as five years. Honeywell anticipates that quantum will form a $1 trillion industry in the decades ahead. But why are firms like Goldman taking this leap especially with commercial quantum computers being possibly years away?

To understand whats going on, its useful to take a step back and examine what exactly it is that computers do.

Lets start with todays digital technology. At its core, the digital computer is an arithmetic machine. It made performing mathematical calculations cheap and its impact on society has been immense. Advances in both hardware and software have made possible the application of all sorts of computing to products and services. Todays cars, dishwashers, and boilers all have some kind of computer embedded in them and thats before we even get to smartphones and the internet. Without computers we would never have reached the moon or put satellites in orbit.

These computers use binary signals (the famous 1s and 0s of code) which are measured in bits or bytes. The more complicated the code, the more processing power required and the longer the processing takes. What this means is that for all their advances from self-driving cars to beating grandmasters at Chess and Go there remain tasks that traditional computing devices struggle with, even when the task is dispersed across millions of machines.

A particular problem they struggle with is a category of calculation called combinatorics. These calculations involve finding an arrangement of items that optimizes some goal. As the number of items grows, the number of possible arrangements grows exponentially. To find the best arrangement, todays digital computers basically have to iterate through each permutation to find an outcome and then identify which does best at achieving the goal. In many cases this can require an enormous number of calculations (think about breaking passwords, for example). The challenge of combinatorics calculations, as well see in a minute, applies in many important fields, from finance to pharmaceuticals. It is also a critical bottleneck in the evolution of AI.

And this is where quantum computers come in. Just as classical computers reduced the cost of arithmetic, quantum presents a similar cost reduction to calculating daunting combinatoric problems.

Quantum computers (and quantum software) are based on a completely different model of how the world works. In classical physics, an object exists in a well-defined state. In the world of quantum mechanics, objects only occur in a well-defined state after we observe them. Prior to our observation, two objects states and how they are related are matters of probability.From a computing perspective, this means that data is recorded and stored in a different way through non-binary qubits of information rather than binary bits, reflecting the multiplicity of states in the quantum world. This multiplicity can enable faster and lower cost calculation for combinatoric arithmetic.

If that sounds mind-bending, its because it is. Even particle physicists struggle to get their minds around quantum mechanics and the many extraordinary properties of the subatomic world it describes, and this is not the place to attempt a full explanation. But what we can say is quantum mechanics does a better job of explaining many aspects of the natural world that classical physics does, and it accommodates nearly all of the theories that classical physics has produced.

Quantum translates, in the world of commercial computing, to machines and software that can, in principle, do many of the things that classical digital computers can and in addition do one big thing classical computers cant: perform combinatorics calculations quickly. As we describe in our paper, Commercial Applications of Quantum Computing, thats going to be a big deal in some important domains. In some cases, the importance of combinatorics is already known to be central to the domain.

As more people turn their attention to the potential of quantum computing, applications beyond quantum simulation and encryption are emerging:

The opportunity for quantum computing to solve large scale combinatorics problems faster and cheaper has encouraged billions of dollars of investment in recent years. The biggest opportunity may be in finding more new applications that benefit from the solutions offered through quantum. As professor and entrepreneur Alan Aspuru-Guzik said, there is a role for imagination, intuition, and adventure. Maybe its not about how many qubits we have; maybe its about how many hackers we have.

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Quantum Computing Is Coming. What Can It Do? - Harvard Business Review