Digital computing has limitations in an important category of computation called combinatorics, where the order of data is important for the optimal solution. These complex, iterative calculations can take a long time for even the fastest computers to process. Computers and software based on the assumptions of quantum mechanics have the potential to perform combinatorial and other computations much faster, and as a result, many companies are already exploring the technology, whose known and likely applications are already cybersecurity. , bioengineering, 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 within five years. honeywell expects quantum to form a $1 trillion industry in the coming decades. But why are companies like Goldman taking this leap — especially now that commercial quantum computers may still be years away?

To understand what’s going on, it’s helpful to take a step back and examine exactly what computers do.

Let’s start with today’s digital technology. In essence, the digital computer is a calculator. It made performing mathematical calculations cheap and the impact on society was enormous. Advances in both hardware and software have enabled the application of all kinds of computers to products and services. Today’s cars, dishwashers, and water heaters all have some sort of computer built in — and that’s before we even get to smartphones and the Internet. Without computers, we would never have reached the moon or orbited the Earth.

These computers use binary signals (the famous ones and zeros of code) that are measured in “bits” or bytes. The more complicated the code, the more computing power is required and the longer the processing time. What this means is that for all their advancements — from self-driving cars to beating grandmasters at Chess and Go — there are still tasks that traditional computing devices struggle with, even when the task is spread across millions of machines.

One particular problem they struggle with is a category of computations called combinatorics. These calculations involve finding an arrangement of items that optimizes a particular goal. As the number of items grows, the number of possible arrangements grows exponentially. To find the best setup, today’s digital computers basically have to go through each permutation to find an outcome and then identify which one is best to achieve the goal. In many cases, this can require a lot of calculation work (think of cracking passwords, for example). The challenge of combinatorial computation, as we’ll see in a moment, applies to many key areas, 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 offers a similar cost reduction as calculating daunting combinatorial problems.

## The value of quantum

Quantum computers (and quantum software) are based on a very 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 appear in a well-defined state after we have observed them. Prior to our observation, the states of two objects and how they are related are a matter of probability. From a computing perspective, this means that data is captured and stored in a different way – through non-binary qubits of information rather than binary bits, which reflect the multitude of states in the quantum world. This multiple can allow faster and cheaper computation for combinatorial arithmetic.

If that sounds mind-blowing, that’s 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 isn’t the place to try a full-blown explanation. But what we can say is that quantum mechanics can explain many aspects of the natural world better than classical physics, and it houses almost all the theories that classical physics has produced.

In the world of commercial computer science, quantum translates to machines and software that can basically do many of the things that classical digital computers can do and one big thing that classical computers can’t: perform combinatorial calculations quickly. As we describe in our article, *Commercial Applications of Quantum Computing**, *that is becoming a major problem in a number of key domains. In some cases it is already known that the importance of combinatorics is central to the domain.

**Chemical and biological engineering.**Chemical and biological engineering involves the discovery and manipulation of molecules. This involves the movement and interaction of subatomic particles. In other words, it’s about quantum mechanics. The simulation of quantum mechanics was an important motivation in Richard Feynman’s first proposal to build a quantum computer. As molecules become more complex, the number of possible configurations grows exponentially. It will be a combinatorial calculation, suitable for a quantum computer. Programmable quantum computers, for example, have already demonstrated successful simulations of simple chemical reactions, paving the way for increasingly complex chemistry simulations in the near future. With the emerging feasibility of quantum simulations, which help predict the properties of new molecules, engineers will be able to consider molecular configurations that would otherwise be challenging to model. This capability means that quantum computers will play an important role in accelerating current materials discovery and drug development efforts.**Cybersecurity.**Combinatorics is central to encryption for more than a thousand years. Al-Khalil’s 8^{this}century*Book with cryptographic messages*looked at permutations and combinations of words. Today’s coding is still based on combinatorics, emphasizing the assumption that combinatorial calculations are essentially unwieldy. However, quantum computing makes cracking encryption much easier, posing a threat to data security. A new industry is growing that helps companies prepare for emerging vulnerabilities in their cybersecurity.

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

**Artificial intelligence.**Quantum computing may offer new opportunities in artificial intelligence, often requiring very large amounts of data to be combined to make better predictions and decisions (such as facial recognition or fraud detection). A growing field of research in Quantum machine learning identifies ways in which quantum algorithms can enable faster AI. The current limitations of the technology and software make quantum artificial general intelligence a pretty distant possibility — but it certainly makes thinking machines more than a subject for science fiction.**Financial services.**Finance was one of the first domains to embrace Big Data. And much of the science behind the pricing of complex assets — such as stock options — involves combinatorial calculation. For example, when Goldman Sachs uses price derivatives, it applies a very computationally intensive calculation known as a Monte Carlo simulation, where forecasts are made based on simulated market movements. Computing speed has long been a source of advantage in financial markets (where hedge funds compete for millisecond advantages in obtaining price information). Quantum algorithms can speed up an important set of financial calculations.**Complex manufacturing.**Quantum computers can be used to take large production data sets about operational failures and translate them into combinatorial challenges that, when combined with a quantum-inspired algorithm, can identify which part of a complex manufacturing process contributed to product failure incidents. For products such as microchips, where this manufacturing process can involve thousands of steps, quantum can help reduce costly failures.

The ability for quantum computing to solve large-scale combinatorial problems faster and cheaper has generated billions of dollars in investment in recent years. Perhaps the greatest opportunity lies in finding more new applications that take advantage of the solutions offered by quantum. As a professor and entrepreneur Alan Aspuru-Guzik said:, there is “a role for imagination, intuition and adventure. Maybe it’s not about how many qubits we have; maybe it’s about how many hackers we have.”