#### 8 October 2019

### The development of quantum computers could spark the technological revolution of the 21st century. GAM Systematic’s Dr Lars Jaeger explains why this is such a symbolic milestone, and considers their amazing problem-solving potential.

The quantum computer – a term that to most people seems to be as weirdly bizarre as excitingly futuristic is pushing its way into the sphere of public attention. It combines the technological omnipotence of digital computing with the awe-inspiring complexity and abstraction of the most important physical theory of the 20th century. It promises a new technological revolution that could shape the 21st century just as strongly as the development of digital circuits did with the 20th century.

For a long time quantum computers were the stuff of science fiction and their construction lay far in the future. But it is well known that the future is approaching us faster and faster. It has now emerged that Google’s engineers have succeeded in designing a quantum computer which, for the first time ever, has solved a problem a conventional computer is not able to. In concrete terms, Google’s computer chip (known as Sycamore) needed just 200 seconds for a special computing task for which the world’s best supercomputer needs 10,000 years. A few years ago Google baptised the concept of a quantum computer being superior to any existing classical computer in the accomplishment of a certain tasks as ‘quantum supremacy’. The moment of such ‘quantum supremacy’ seems to have arrived now. We could thus be witnessing a Sputnik moment in information technology. Although this is more of a symbolic milestone, since the problem solved by Sycamore is of a very academic nature, Google’s achievement could enormously stimulate the development of quantum information technology, similar to what the historic Sputnik moment in the 1950s did for space travel.

So what is a quantum computer? First, although conventional computers (with their ever smaller components) are subject to quantum effects, their principle functionality is entirely based on classical physics. The so-called ‘von Neumann architecture’ all computers today are based on ensures that calculation steps are processed sequentially, ie bit by bit. The smallest possible information units each take a well-defined state of either 1 or 0. Quantum computers in contrast employ the very properties of quantum theory directly and are thus subject to a completely different information theory. The equivalent of the classical bit in quantum computers is the quantum bit, or qubit for short. Qubits have some amazing properties: For example, they can assume both states – 0 and 1 – simultaneously, as well as all intermediate values in between, ie ‘half 1’ and ‘half 0’. This is due to the possibilities of quantum states to exist in so-called ‘superpositions’, the overlapping of classically mutually exclusive states. This bizarre property of quantum particles was once the cause of heated discussions among the fathers of quantum physics, which eventually found their expression in the well-known thought experiment of Schrödinger’s cat. In addition, various quantum particles can be brought into so-called ‘entangled states’. This is another bizarre property of the quantum world which holds no equivalence of in our classical world. It is as if the qubits are coupled to each other with an invisible spring. Through a ‘spooky action at a-distance’ (a term originally invented by Albert Einstein to convey ironical intention, as he considered entanglement impossible), qubits are all in direct contact with each other. Each quantum bit ‘knows’, so to speak, what the others are currently doing.

Thus entangled qubits exist in a superposition of infinitely many different states at the same time. And they are all connected through an invisible and unmeasurable band. To put it bluntly: the multi particle system is in all possible states simultaneously. Specified individual states are realised (with a respective probability) only after a physical measurement. Before that, they are objectively undetermined – yet another strange property in the quantum world. Now with the help of a corresponding algorithm, entangled qubits can all be processed simultaneously. It is as if many chocolate factories had started their assembly lines at the same time and now produce chocolate in parallel. And the more qubits are entangled, the more states can be processed in parallel. Unlike conventional computers, whose computing power increases linearly with the number of computing components, the power of a quantum computer increases exponentially with the number of qubits employed. The performance of a quantum computer is therefore not doubled when another 100 qubits are added to the existing 100 qubits, rather it doubles when only a single qubit is added to the original 100 qubits. If 10 more qubits are added, its performance increases a thousand times (to be more precise 1024 times), with 20 new qubits the quantum computer is already a million times faster and with 50 new qubits a million billion times faster. Therefore, with 100 new information carriers, when the performance of a classical computer has just doubled, the increase in the performance of a quantum computer can hardly be quantified any longer. With this enormous power of parallel computing, problems could be solved that are still far too difficult to process even for the ‘supercomputers’ used today in physics, biology, weather research and elsewhere.

Upon closer inspection, however, the massive parallelisation reached with help of entangled states is not quite comparable to parallel working chocolate factories. Information stored and processed in entangled systems is very different from the information processed by ordinary digital computers. Quantum computers do not literally work in parallel, but they organise the information such that it is distributed over many entangled components of the overall system. Imagine a book with 100 pages. For an ordinary 100-page book, every time you read a page, you have captured another 1% of the book’s content. After reading all the pages one by one, you know everything that is in the book. In a quantum book, where the pages are entangled, things are different. Looking at the pages one at a time, one sees only random gibberish, and after reading all pages one after the other, one still knows very little about the contents of the book. This is because the information in the quantum book is not printed on the individual pages, but is encoded almost exclusively in the correlation of the pages with each other. Anyone who wants to read the book must do so by looking at the pages simultaneously.

Here we highlight five problems, which are beyond the limits of today’s computers, that show the amazing possibilities that could arise with quantum computers:

- Cryptography: Today’s common encryption methods are based on the re-factorisation of the products of two very large prime numbers. From a certain number size on, this task can no longer be solved by a classical computer. In 1994, the computer scientist Peter Shor developed an algorithm which, with the help of a quantum computer, could factorise the largest products of prime numbers used today into their divisors within minutes.
- Solving complex optimisation problems: The task of finding the optimal solution from many variants is considered particularly tricky by mathematicians. Such problems occur in industrial logistics, in the design of microchips or in the optimisation of traffic flow. Even with a small number of variations classical computers fail in the calculation of optimal solutions. Quantum computers, on the other hand, could solve such optimisation problems in a comparatively short time.
- Significant applications could also arise in the field of artificial intelligence: The ‘deep neural networks’ used therein come with hard combinatorial optimisation problems, which can be solved much faster and better by quantum computers than by classical computers. This could make machines smarter by multiples than they are today.
- Large databases searches: Searching through unsorted data sets, a classical computer has to examine each data point individually. The search time therefore increases linearly with the number of data points given and for large amounts of data can becomes too time consuming for a classical computer. In 1996, the computer scientist Lov Grover published a quantum computer algorithm for which the number of necessary calculation steps increases only with the square root of the number of data points. Instead of needing a thousand times longer for one billion data entries compared to one million, with the Grove algorithm it would take a quantum computer only a little over 30 times longer – which would be a breath taking improvement for large numbers.
- Finding new chemical compounds: In the simulation of quantum systems complex optimisation problems occur again and again, where the aim is to find the best possible, ie most energy-efficient, configuration of the electrons in an atom or molecule from many alternatives. Theoretical physicists and chemists have been dealing with such problems for decades with limited success. The corresponding quantum equations are simply too complex to solve for classical computers. Quantum computers could directly map and model the behaviour of the electrons involved, since they behave like a quantum system themselves. The better understanding of molecular behaviour, and of the detailed chemical reactions, could be used to find new drugs or develop much more efficient battery technologies.

Some physicists even believe quantum computers will enable us to calculate any problems occurring in nature, from the behaviour of black holes, the development of the very early universe, the collisions of high-energy elementary particles to the superconductivity and the modelling of the 100 billion of neurons (and the one thousand times plus connections in our brain). In any case, it will be worth reading the science section of the daily newspapers more carefully in the coming weeks and months to see what is uncovered.

*Source: www.larsjaeger.ch*

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**Important legal information**The information in this document is given for information purposes only and does not qualify as investment advice. Opinions and assessments contained in this document may change and reflect the point of view of GAM in the current economic environment. No liability shall be accepted for the accuracy and completeness of the information. Past performance is no indicator for the current or future development. Reference to a security is not a recommendation to buy or sell that security.