A recent announcement by Goldman Sachs suggested that quantum algorithms could be used to price financial instruments within five years. The Honeywell Group anticipates that quantum computing will create a $1 trillion industry in the coming decades. When commercial quantum computers may not even be available for several years, why are firms like Goldman Sachs taking this risk?

Understanding what is going on can be best accomplished by taking a step back and examining what computers actually do.

As we look at today’s digital technology, it is an arithmetic machine at its core. It reduced the cost of performing mathematical calculations, and its impact on society is huge. The application of all kinds of computing to products and services has been enabled by advances in hardware and software. Without computers we would not have reached the moon or put satellites into orbit – and that’s even before we get to smartphones and the internet.

The more complicated the code, the more power is needed, and the longer the processing time. Computers use binary signals (the famous 1s and 0s of code). Even when millions of machines are being used to perform the same task, traditional computing devices still have trouble handling tasks, even if they are self-driving cars or beating grandmasters at Chess and Go.

These students have difficulties with a type of calculation called combinatorics. This type of calculation involves finding an arrangement of items that maximizes some goal. As the number of items increases, the number of possible arrangements grows. Digital computers today iterate through every possible arrangement in order to determine which permutation leads to the best results before identifying which one achieves the desired result.

There are many fields where such calculations can prove useful (from finance to pharmaceuticals, for example). Let’s take a look at the field of combinatorics calculations in a moment. It is also a critical bottleneck in the evolution of **Artificial Intelligence**.

Quantum computing offers a similar approach to solving challenging combinatorial problems to classical computers.

**The Value of Quantum**

Computers based on quantum mechanics operate on a totally different basis from classical computers. In classical physics, the objects exist in a well-defined state. In quantum mechanics, objects become well-defined after we observe them. Prior to our observation, two objects’ states and how they are related are matters of probability. Computing reflects the multiplicity of states in the quantum world by recording and storing data in non-binary qubits instead of binary bits. Calculations using combinatoric arithmetic can be made faster and cheaper by taking advantage of this multiplicity.

In fact, quantum mechanics and the many extraordinary properties of the subatomic world it describes are mind-boggling. Even particle physicists may not be able to grasp it all, and this is not the place for a full explanation. However, we can conclude quantum mechanics is a much better exp.

A quantum computer, in the world of commercial computing, is something that can, in principle, perform many of the functions of a classical digital computer, plus one large function that classical computers cannot: perform combinatorics calculations quickly. The importance of combinatorics is already well known in some important domains. That is what we describe in the paper, Commercial Applications of Quantum Computing.

**Chemical and biological engineering.**Chemistry and biology are both concerned with discovering and manipulating molecules. This involves the motion and interaction of subatomic particles. This is the essence of quantum physics. Richard Feynman’s original proposal for a quantum computer was motivated by a simulation of quantum mechanics.

Molecular complexity increases exponentially, resulting in a combinatorics problem suitable for a quantum computer. In the near future, quantum computers will be able to simulate increasingly complex chemical reactions. Simple reactions, for example, have already been successfully simulated by programmable quantum computers. Engineers will be able to model configurations of molecules that would otherwise be difficult to model with the advent of quantum computations, which help predict the properties of new molecules. A quantum computer’s capability will make materials discovery and drug development more efficient.

**Cybersecurity.**Permutations and combinations of words have been at the core of encryption for over a thousand years. Al-Khalil’s 8th century Book of Cryptographic Messages examined such combinations. Combinatorics continues to be the foundation of encryption, emphasizing that combinatorial calculations are essentially unmanageable. Data security is weakening as quantum computing makes it easier to crack encryption, posing a threat to data security. As a result, a new industry is emerging that helps companies prepare for upcoming vulnerabilities in their cybersecurity.

In addition to quantum simulations and encryption, quantum computing is emerging into a host of new applications:

**Artificial intelligence.**Quantum computing offers novel opportunities in artificial intelligence, a field which often relies on combinatorics to process extremely large amounts of data in order to make better predictions and decisions (think facial recognition or fraud detection). Quantum algorithms can enable faster artificial intelligence, as a growing field of research in quantum machine learning identifies ways. Although quantum artificial general intelligence is still a very remote possibility owing to current limitations in technology and software, it certainly brings thinking machines beyond science fiction.

**Financial services.**Many of the scientific methods used to price complex assets – such as stock options – rely upon combinatorial calculations. Finance was one of the first to embrace Big Data. Goldman Sachs, for instance, uses a Monte Carlo simulation to price derivatives, which simulates market movements in order to make projections on prices. The ability to compute quickly has long been a significant advantage in the financial markets (where hedge funds compete to obtain price information milliseconds in advance). Quantum algorithms can increase the speed of an important set of financial calculations.

**Complex manufacturing.**When coupled with a quantum-inspired algorithm, quantum computers make it possible to combine large sets of manufacturing data on operational failures and translate them into combinatorial challenges, Quantum assists manufacturers in identifying which part of a complex manufacturing process contributed to failures in a product. Microchips are a good example of products where the production process can include thousands of steps.

Since quantum computing has the potential to solve complex combinatorics problems faster and cheaper, billions of dollars have been invested. According to Alan Aspuru-Guzik, there is “an important role for imagination, intuition, and adventure” in finding more applications that utilize quantum solutions. Maybe the most important thing isn’t how many qubits we have, but how many hackers we have.”

Source: **HBR**