We can say that the concept of quantum computer was born during the 1980s, thanks in particular to the reflections of the brilliant Nobel Prize in physics Richard Feynman. Long considered a utopia, it has for several years been the subject of a growing global race between laboratories and competing companies which are planning a next technological revolution with it. Google has just communicated on its latest results, announcing a breakthrough with so-called error-correcting codes.

« *Quantum computers have the potential to bring tangible benefits to the lives of millions of people. We believe that quantum computers will be used to create new medicines, reduce the energy needed to produce fertilizers, design more efficient sustainable technologies, from batteries to nuclear fusion reactors, and contribute to physics research that will lead to advances that we cannot yet imagine* “. This is the declaration of Sundar Pichai, the CEO of Google and Alphabet, which can be read on the French version of the Google blog and which accompanies a publication by the company’s researchers in the newspaper *Nature*.

It is a good illustration of the hopes of several laboratories and companies in the global noosphere launched into the race for quantum computers. We can be convinced of this by also reading the prospects envisaged by the launch last year of SiQuance, a French start-up resulting from joint work by researchers from the CEA and the CNRS.

The members of Google report that they have succeeded in producing and using what they call logical qubits, made up of several physical qubits, and that this opens the way for the first time in practice to the use of logical qubits for apply what they also call quantum correcting codes in order to solve the problem of quantum decoherence. For those who are not yet versed in the rudiments of quantum theory and quantum calculations, the CEA has made two videos which allow you to land gently in these territories of science and technology of which a comparable revolution is expected from the second. to that of the first to the XX^{e} century.

Commentary on Google’s latest progress with quantum computers. To obtain a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles should then appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Translate automatically”. Choose “French”. © *Google Quantum AI*

## Calculations using quantum physics

In concrete terms, to do better than conventional supercomputers in solving certain problems that would require, for example, thousands of years using these machines, there must already be an algorithm using quantum physics and able to beat a conventional algorithm. We know of certain algorithms capable of doing this in theory, such as that of Peter Shor which would allow the secrecy of bank codes to be broken in a few minutes, but nothing proves that there is always one for each problem that we can hope to solve with a computer.

Crucially, quantum computers, which would truly be able to perform miracles, would require thousands or even millions of qubits, the quantum analogues of the classical bits of information in the form of 0s and 1s but which quantum computers can process with logic gates, cousins of classic logic gates but in parallel.

An introduction to quantum physics, its first and its second revolution. © CEA Research

Unfortunately, the quantum effects involved are very fragile and the slightest disturbance of the quantum circuits used makes the calculations all the more quickly impossible when a large number of quantum qubits is used. This so-called decoherence effect is so serious that just a decade ago, many researchers thought that truly revolutionary quantum computers were destined to remain utopias.

One can fight against decoherence by isolating the circuits as much as possible, for example from thermal noise by having them work under vacuum and cooling them with liquid helium. However, it is also possible to use error-correcting codes to correct the quantum calculation errors that accumulate. But it was necessary to prove on the one hand that this was indeed possible and above all, on the other hand, that the technology used could be transposed to increasingly large quantities of qubits.

This is the essence of what Google announces that it has accomplished, even if there is still a long way to go towards the creation of mythical quantum computers, as can be seen with explanations in English still given on the Google blog.

More detailed explanations on the notion of Qubits, algorithms and quantum computers. © CEA Research

## Quantum cousins of classical error-correcting codes

Let’s finish by specifying a bit what error-correcting codes are in the field of quantum information, close cousins to those well known in the context of classical information theory.

In the well-studied case of classical information processing, for example, with the mythical works of the father of information theory Claude Shannon, error-correcting codes are most often applied to the transmission of data in binary to eliminate the effects of noise. These are coding techniques based on redundancy making it possible to detect and correct errors in a transmitted message, sound or images for example. They also find applications with the hard disks and the RAM of the computers with there also transfers of information.

A famous code example is that of Hamming, which Richard Feynman cites in his Computer Science Lessons. The idea of a correcting code can be quickly grasped with the example of binary signals that are transmitted with “0”s and “1s” separated by a time interval. By tripling the data, for example, by systematically sending “000” and “111” for each “0” and each “1”, it is possible to verify that a transmission error has not been made by counting the number of repetitions of a given bit. Thus, “001” or “011” will be indicators of such an error. A correction will be made taking into account the majority of “0” or “1”.

The problem with qubits is that you can’t make copies of a quantum state. We can prove a non-cloning theorem. It is therefore not possible to verify the quantum information carried by a state by comparing it to that contained in several copies of this state. Fortunately, it is possible to entangle each qubit with several others, so that it is possible to detect errors during information processing and to remedy them. The entangled state with several physical qubits, which is therefore at this time the logical qubit, indeed carries the memory of the qubit used for quantum calculations with logic gates as for all computers.

The whole problem is to be able to implement a quantum correction code in this way which becomes more and more efficient with a large number of qubits growing, and for a long calculation time.

Which is not self-evident, but that is precisely what Google announces that it has succeeded in doing, even if, for the moment, we are only at one logical qubit.