**Will another promise of science soon become reality? – What is the status of the quantum computer?**

A concept that strikes most people as eerily bizarre as excitingly futuristic is increasingly forcing its way into the sphere of public attention. It combines the apparent technological omnipotence of digital computing with the awe-inspiring abstractness of the most important physical theory of the 20th century. We are talking about the „quantum computer“. Behind this there are no esoteric dreams of miracle cures and soul cleansing („quantum healing“), spiritual home furnishings („quantum feng shui“), universally perfect love relationships („quantum resonance“) or any other nonsense, that esotericists like to associate with „quantum“, nor fraudulently operating financial trading platforms such as *QuantumAITrade*, recently wrongly associated with Elon Musk, but a real emerging technological revolution that could shape the 21st century in a similarly significant way as the development of digital circuits, lasers and atomic energy did in the 20th century.

With the elements of conventional chips now operating at near-atomic scales and thus the appearing expiration of Moore’s Law in terms of computational speed, problem-solving capacity and efficiency in information processing the end of the rope is beginning to show for classical computers. However, a completely new possibility of building computers that are much faster, even millions and billions of times more powerful than today’s fastest computers is slowly taking shape: quantum computers. With their help, problems could be solved that are still far too complex for the „supercomputers“ used today in physics, biology, weather research and elsewhere.

But are the building blocks of conventional computers not already based to a large extent on quantum mechanical laws, such as the transistor effect? In fact, the digital revolution of the 20th century would not have been possible without quantum physics. Nevertheless, the structure and functionality of conventional computers, the so-called „Von Neumann architecture“, are in principle possible without quantum physical effects. And indeed, the first computers in the 1940s still consisted of macroscopic tubes, diodes and capacitors. Only their extreme miniaturization required quantum physics, which ultimately enabled their enormous performance. However, while quantum effects often disturb conventional („classical“) chips, quantum computers are already based at their core on the bizarre properties of quantum theory and thus have a fundamentally different architecture and mode of operation as classical computers. In them, no longer do the *currents of many electrons* serve for information processing and storage as in classical computers; rather, for data storage and processing, *individual quantum particles* control and steer the calculation by directly exploiting their quantum properties. This potentially enables quantum computers to achieve unimaginably faster computational speeds compared to current computers and could let them master complexities that still cause us today to shudder in awe because of the unpredictability and uncontrollability of those.

Six fields, the problems in which overwhelm today’s computers, no matter how large they may be, show concretely what fantastic possibilities quantum computers may open up:

- Cryptography: Today’s common ciphers are based on the re-factorization of the products of two very large prime numbers. Above a certain number size, this task can no longer be solved by a classical computer. In 1994, computer scientist Peter Shor developed an algorithm that would allow a quantum computer to factorize the largest products of primes in use today into their divisors within minutes. Thus, a quantum computer could easily crack conventional encryption methods for digital data thus threatening the entire global data security, which makes them both interesting and threatening not only for the military.
- Solving complex optimization tasks: The task of finding the optimal solution from many variants is considered particularly tricky among mathematicians. Such problems occur in as different areas as industrial logistics, in the design of microchips or the optimization of traffic flows. Even with a small number of variants, classical computers quickly drop out when calculating optimal solutions. Quantum computers, on the other hand, could solve larger optimization problems in a comparatively short time.
- Significant applications could lie in the field of artificial intelligence: The „deep neural networks“ used there involve hard combinatorial optimization problems that quantum computers could solve far faster and better than classical computers. This could make machines many times smarter again.
- Searching in large databases: When searching unsorted data sets, a classical computer must consider each data point individually. The search time therefore increases linearly with the number of data points and thus in the case of outsized data sets quickly becomes too large for a classical computer. In 1996, the computer scientist Lov Grover published a quantum computer algorithm for which the number of necessary calculation steps only increases with the root of the number of data points. Instead of taking a thousand times as long for a billion data entries as for a million, this would only take a little more than 30 times as long with a quantum computer and the „Grove algorithm“ – a breathtaking improvement in the case of very large numbers.
- Finding new chemical compounds: Even in the simulation of quantum systems, complex optimization problems arise again and again, where the goal is to find the best possible, i.e. energetically most favorable configuration of electrons in complex molecules or atomic assemblies from among many alternatives. Theoretical physicists and chemists have been struggling with such problems for decades, with rather limited success. The corresponding quantum equations are simply too difficult for conventional computers to solve. Quantum computers, on the other hand, could directly map the behavior of the electrons involved, since they themselves behave like a quantum system. The resulting better understanding of molecules and the details of their chemical reaction dynamics could be used, for example, to simulate complex protein structures, find new drugs or even optimize the Haber-Bosch process for producing fertilizers.
- Elucidation of the electron structure in crystals, which would significantly advance solid-state physics and materials research. New findings in these fields would in particular give nanotechnology a tremendous boost – for example, the behavior of possible new energy storage devices or components of molecular electronics could be precisely calculated virtually overnight, which would enable far more efficient battery technologies. Another application of utmost relevance would be the search for new high-temperature superconductors.

Some physicists even believe that a quantum computer could be used to calculate *any problem* in nature, from the behavior of black holes, the development of the very early universe, the collisions of high-energy elementary particles, to the phenomenon of superconductivity and the modeling of the 100 billion neurons and their thousand times greater number of connections (synapses) in our brain. However, so far all this is purely theoretical, because no functioning universal quantum computer exists yet.

How exactly does a quantum computer work? Classical computers use „bits“ as the smallest possible information units, which have either the state 1 or 0 (i.e. can assume two values, hence the term „digital“). In them, the calculation steps are processed sequentially, i.e. bit by bit, on the basis of digital information theory. Quantum computers, on the other hand, are subject to a completely different information theory and processing algorithms. The simplest system in quantum mechanics is the so-called „quantum bit“, or for short „qubit“. And these already come with a quite something: Qubits can assume different states, i.e. 0 and 1, *simultaneously*, as well as all values in between (and even more, since their values lie in the plane of complex numbers). They can so to say be „half 1“ and „half 0“. This is due to the possibilities of quantum states to exist in so-called „superpositions“. These are overlappings of classically mutually exclusive states. This bizarre property of quantum particles once triggered heated discussions among the fathers of quantum physics, which finally found their expression in the well-known thought experiment of *Schrödinger’s cat*. In addition, different quantum particles can be brought into so-called *entangled states*. This is also a property which is unknown in our classical world (and around which there were no less heated discussions among the first generation of quantum physicists). It is as if the qubits are coupled to each other by an invisible spring. They are then all in contact with each other directly and without any interacting force acting between them. Each quantum bit instantly „knows“ so to say what the others are doing. Albert Einstein considered entanglement physically impossible and mockingly called it „spooky action at a distance“.

Entangled qubits thus exist in a superposition of infinitely many different states at the same time, which are also connected to each other by an invisible and unmeasurable band. To put it casually: the many-particle system simultaneously takes *all of its possible states*. Only through a measurement are individual physical values realized (with a respective probability). Before that they are *objectively indeterminate* – this is another strange property in the quantum world. With the help of an appropriate algorithm, entangled qubits can now be processed all at the same time. And in this parallel processing lies the potency of the quantum computer. Because the more qubits are entangled with each other, the more states can be processed in parallel. Unlike conventional computers, whose computing power increases linearly with the number of computing blocks, the power of a quantum computer thus increases *exponentially* with the number of qubits used. The performance of a quantum computer therefore does not double when another 100 qubits are added to 100 qubits, but already when only one single qubit is added to the 100 qubits. If 10 qubits are added, its performance is multiplied by a factor of a thousand (1024 times to be precise); with 20 new qubits, the quantum computer is already a million times faster; with 50 new qubits, it is a million billion times faster. And 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 expressed in numbers anymore.

It seems strange that quantum computers have not already been built. After all, quantum theory had long been established by the time modern computers were created. Nevertheless, decades passed before physicists addressed the possibilities of quantum information processing. One of the reasons for this is obvious: For a long time, neither physicists nor computer scientists knew too much about how to deal with the concrete phenomena of superposition and entanglement. But there is a second reason: In the 1940s, the U.S. mathematician Claude Shannon founded the classical theory of information, which is based on the use of bits. His essay *A Mathematical Theory of Communication* is still today considered the bible of the information age and is one of the most influential scientific works of the 20th century. Shannon claimed that the principle of bits applies to *any* form of information processing, and for a long time computer scientists followed this view. Moreover, according to the (extended) „Church-Turing thesis“ of the American mathematician Alonzo Church and the British logician Alan Turing any physical system can be effectively simulated on a classical computer. It was not until the 1980s that computer scientists realized that there are information concepts and physical simulations beyond digital bits that cannot be easily dealt with in classical computers but can be computed efficiently on the basis of qubits. However, this requires a completely new theoretical foundation, one that explicitly deals with superposition and entanglement of quantum states. Such a new information theory and algorithm were only created from the late 1990s onwards by the joint efforts of physicists and information theorists.

There are still enormous problems to be solved in the construction of quantum computers. The biggest of these is: Entangled quantum states decay very quickly under the omnipresent influence of heat and radiation – often too quickly to perform the desired operations without errors. In this context, physicists speak of „decoherence“ of quantum states. Working with qubits seems almost like trying to write not on a sheet of paper, but on the surface of water. While paper can last for centuries, what is written on water disappears after a fraction of a second. So it comes down to mastering an insane speed. To overcome this hurdle, quantum engineers are pursuing a twofold strategy: on the one hand, they are trying to extend the lifetime of qubits, i.e. to reduce their susceptibility to errors; on the other hand, they are developing algorithms that eliminate the errors that do occur. Physicists are able to decrease decoherence with the help of ultra-cold refrigerators. In turn, they are developing ever better methods for handling errors in individual qubits caused by decoherence (so-called quantum error correction), which can be used to increase the reliability of quantum computers.

For many years, the concepts of qubits and quantum computers were largely theoretical. However, in their efforts to apply those in practical tools quantum engineers have in recent years made considerable progress. Today, for example, there are numerous different promising approaches to concretely fabricate qubits and entangling them with each other. In principle, this always involves „capturing“ individual quantum systems, such as atoms or electrons, using some tricks for entangling them with each other, and then manipulating them accordingly. Here are some examples of how this can be done:

- Ions (electrically charged atoms) are held in place and are made to oscillate back and forth in a controlled manner with the use of electric and magnetic fields. They are thus coupled together as qubits.
- The spins of atoms, which are aligned by external magnetic fields as in nuclear magnetic resonance technology, are entangled with each other.
- Qubits can also be realized with the help of so-called quantum dots. These are special points in a solid body where the mobility of electrons in all directions is severely restricted and which, according to the laws of quantum physics, can therefore no longer release or absorb energy continuously, but only in discrete values. They therefore behave like giant artificial atoms.
- Electrons sent on an infinite loop in circular superconductors, with this loop being interrupted by very thin insulator layers (so-called SQUIDs –
*superconducting quantum interference devices*), are promising candidates for qubits. This is a particular focus of companies like Google, Microsoft, IBM and Intel. Researchers are thereby exploiting what is known as the Josephson effect: The superconductor’s Cooper electron pairs can tunnel through the insulating barrier, and in this process they can thus be in different quantum states – they then flow simultaneously both clockwise and counterclockwise. Such superpositions can be used as qubits and be entangled with each other. - Special chemical compounds could also be suitable as qubits. One example is a complex of a vanadium ion encased in organic sulfur compounds. The shell shields the spin of the ion inside so well that its state (as well as thus possible entanglements) are preserved for a long time.
- A still purely theoretical concept is the so-called topological quantum computer. The concept behind it originally comes from mathematics, and it is not yet entirely clear whether and how it can be implemented physically. It is based on so-called anyons (not to be confused with the anions from aqueous solutions). These are states with particle properties in two-dimensional space and are therefore also called „quasi-particles“. Anyons occur, for example, at the interfaces of insulators. Such topological qubits should form relatively stable braids and would be much better protected against perturbations than other concepts.
- A rather new method is to encode qubits with single photons that travel along silicon photonic waveguides and are then entangled using networks of optical components (mirrors, beam splitters, and phase shifters).
- There is yet another concept of a quantum computer, based on so-called „adiabatic quantum computation“ (also called „quantum annealing“). It relies on the adiabatic behavior of quantum systems to perform calculations („adiabatic“ in physics means that an entire system changes without exchanging energy with its environment). In this process, a simple quantum system is placed in its ground state (state of lowest energy) and then slowly and continuously transformed into a more complicated quantum system the ground state of which is the solution to the problem in question. The
*adiabatic theorem*in theoretical physics states that if this transformation is performed slowly enough, the evolving system will remain in its ground state throughout the process. A computer based on this principle was already developed by the company*D-Wave Systems*back in 2007. However, its results remain controversial to this day.

Meanwhile, there are a dozen other physical realization attempts to generate entangled qubits that can then operate as computers. Most of these are still in their infancy, despite rapid progress in the field. So far, the efforts of quantum physicists have not yet yielded reliably functioning (and universal) quantum computers. But companies such as IBM, Google, Microsoft and Intel have recently announced they have built, or will soon build quantum processors consisting of 50 or more qubits. At this size, these could arguably exceed the computational capacity of any current (classical) supercomputer – at least for some very specialized computational problems. Google calls this „quantum supremacy“ and announced in October 2019 that its engineers had succeeded in building a quantum computer that could, for the first time, solve a problem (though a quite exotic one) that any conventional computer would cut its teeth on. Specifically, its *Sycamore* computer chip had taken just 200 seconds to complete the special computing task that would have taken the world’s best supercomputer 10,000 years. Google’s competitor IBM, however, doubted these results and claimed Google’s calculation contained an error.

Since then, not much has been heard from the big U.S. tech companies about possible progress in building quantum processors. Is this perhaps the calm before the storm? In late 2018, the U.S. Congress signed the *National Quantum Initiative Act* to invest more than $1.2 billion in quantum computing technology over the next 10 years. China is investing even more heavily into the field, with Xi Jinping’s government providing $10 billion for the *National Laboratory for Quantum Information Sciences *in Hefei. Meanwhile, Chinese researchers have also announced progress in building quantum computers. The team led by Jian-Wei Pan, a German- and Austrian trained, award-winning researcher at the National Laboratory for Quantum Information Sciences at the University of Science and Technology of China in Hefei, reported in December 2020 that their quantum computer, named *Jiŭzhāng*, is 10 billion times faster than Google’s, at least in computing a very specific problem called „Gaussian boson sampling“ (for which purpose the quantum computer was exclusively built). In Jiŭzhāng, the qubits are realized as photons.

Quantum computers are not yet universal computing machines that can send e-mails, store or process files, and process any calculation very rapidly, but so-called „special purpose computers“ that so far can solve only a single, very exotic problem, for the purpose of demonstrating the general potential of quantum computing. However, Jian-Wei Pan already compares the speed between quantum computers and traditional computers to the difference between „nuclear weapons and machine guns or artillery shells.“