Quantum computing is set to transform the way we understand many aspects of our world and tackle specific types of complex problems. Based on harnessing quantum mechanics to generate computing power, it can be as bewildering as it is fascinating.

This short introduction to quantum computing is based on a detailed beginner’s guide in OpenSpace 29, the latest issue of our thought leadership magazine.

Getting comfortable with uncertainty is an essential part of understanding quantum computing – even Einstein described one of the quantum characteristics being exploited for computing as “spooky”. Many of the underlying concepts are not intuitive and require complex mathematics to fully illustrate.

## Why quantum computing?

In many areas, we need to undertake spectacularly complex computations, whether it is to further our understanding or ensure our security. Some of these computational challenges go beyond the capabilities of classical computers, including supercomputers, because they cannot solve them, or cannot do so quickly enough to be useful.

Examples of this are optimization of complex systems, artificial intelligence, materials and chemical simulation, which require the manipulation of exceedingly large numbers. In chemical modelling, for example, we must consider every electron–electron interaction, as every electron exerts an electrical force on every other. Just one additional variable (an extra electron) creates an exponentially larger computing challenge.

## Understanding the exponential challenge

Consider the optimal seating arrangement for a table with six diners. In classical computing, each of the 720 seating options is examined in turn until the right answer is found. If we double the number of diners, the number of different seating options becomes 479,001,600.

This example shows how a seemingly small increase in a ‘problem’ creates an exponential increase in the number of potential answers – and therefore in the computing power required to find the optimal solution.

Sorting out where you will place dinner guests is unlikely to be a useful exploitation of quantum computing, but is a useful illustration of the challenge that is presented by, for example, traffic routing options across a city.

Currently, our ability to model complex situations, even with powerful supercomputers, requires computations that take weeks, months or years. Quantum computing has the potential to change this, enabling us to solve and understand in minutes far more complex problems in the areas of science, manufacturing, logistics, finance and security. This would reshape the innovation landscape and competition in many fields, and enable us to harness nature to improve the world in a transformational way.

## What is quantum computing?

Quantum computing exploits the properties of quantum mechanics to solve computational problems.

Classical computing utilizes ‘bits’ that can have a value of 1 or 0, with answers derived through complex sequences based on manipulating these 1s and 0s. In quantum computing, the equivalent to a ‘bit’ is a quantum bit (qubit). A qubit can have a value of 1 or 0, but, thanks to quantum behaviour, it can also have both values at the same time. This means that a qubit technically contains the ‘right’ value all the time.

(A useful analogy when thinking about qubits is the idea of tossing a coin. When it is in on the table it has a value of heads or tails, but when it is spinning it can be considered as having both.)

Because a quantum computer’s qubits can be in a state of 0 or 1 at the same time, it can try all the combinations in one go. This property of qubits to contain all the correct and incorrect numbers does, however, mean the output is both right and wrong, so algorithms must be applied to remove the wrong answers and leave only the right one. Nevertheless, the computational process to evaluate the options essentially happens just once in quantum computing, not multiple times sequentially.

Determining the ‘power’ of a quantum computer can be done by using 2^{N}, where N is the number of qubits. For example, a 50-qubit quantum computer could handle over one thousand trillion numbers. A 300-qubit computer could process more numbers than there are atoms in the universe! It is because these huge volumes of data can be addressed concurrently that quantum computers are attractive for exponentially complex computational problems.

## Applications

To see quantum computing as an evolutionary step from classical computing is not correct. Quantum computers are ideally suited to specific computational challenges: essentially those that have comparatively small inputs and outputs but infinite possibilities, as this directly maps on to the quantum mechanical behaviour of a qubit.

Undoubtedly, we will find new and extraordinary uses for quantum computers that we cannot conceive today. But for now, some potential uses include:

- logistics, including traffic flow management in smart cities and global shipment of goods
- quantum chemistry
- encryption
- weather forecasting
- energy sources and production
- financial market predictions
- optimization of remote space exploration missions during mission design
- modelling the brain and the world around us.