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 what’s going on, it’s useful to take a step back and examine what exactly it is that computers do.

Let’s start with today’s 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. Today’s cars, dishwashers, and boilers all have some kind of computer embedded in them — and that’s 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) that 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, today’s 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 we’ll 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.

## The Value of Quantum

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, it’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 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 than 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 can’t: perform combinatorics calculations quickly. As we describe in our paper, *Commercial Applications of Quantum Computing**, *that’s 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.

**Chemical and biological engineering.**Chemical and biological engineering involve the discovery and manipulation of molecules. Doing so involves the motion and interaction of subatomic particles. In other words, it involves quantum mechanics. The simulation of quantum mechanics was a key motivation in Richard Feynman’s initial proposal to build a quantum computer. As molecules get more complex, the number of possible configurations grows exponentially. It becomes a combinatorics calculation, suitable for a quantum computer. For example, programmable quantum computers 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 helps predict the properties of new molecules, engineers will be able to consider molecule configurations that would otherwise be challenging to model. This ability means that quantum computers will play an important role in accelerating current efforts in materials discovery and drug development.**Cybersecurity.**Combinatorics have been central to encryption for over a thousand years. Al-Khalil’s 8^{th}century*Book of Cryptographic Messages*looked at permutations and combinations of words. Today’s encryption is still built on combinatorics, emphasizing the assumption that combinatoric calculations are essentially unmanageable. With quantum computing, however, cracking encryption becomes much easier, which poses a threat to data security. A new industry is growing that helps companies prepare for upcoming vulnerabilities in their cybersecurity.

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

**Artificial intelligence.**Quantum computing potentially opens up new opportunities in artificial intelligence, which often involves the combinatoric processing of very large quantities of data in order to make better predictions and decisions (think facial recognition or fraud detection). A growing research field in quantum machine learning identifies ways that quantum algorithms can enable faster AI. The current limitations on the technology and software make quantum artificial general intelligence a fairly remote possibility — but it certainly makes thinking machines more than a subject for science fiction.**Financial services.**Finance was one of the earliest domains to embrace Big Data. And much of the science behind the pricing of complex assets — such as stock options — involves combinatoric calculation. When Goldman Sachs, for example, prices derivatives it applies a highly computing-intensive calculation known as a Monte Carlo simulation, which makes projections based on simulated market movements. Computing speed has long been a source of advantage in financial markets (where hedge funds vie to get millisecond advantages in obtaining price information). Quantum algorithms can increase speed for an important set of financial calculations.**Complex manufacturing.**Quantum computers can be used in taking large manufacturing data sets on operational failures and translating them to combinatoric challenges that, when paired with a quantum-inspired algorithm, can identify which part of a complex manufacturing process contributed to incidents of product failure. For products like microchips where this production process can have thousands of steps, quantum can help reduce costly failures.

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 it’s not about how many qubits we have; maybe it’s about how many hackers we have.”