Marrying quantum computing and knot theory could create an unforgeable currency

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A “quantum” currency… This nebulous concept at first glance is the subject of very tangible research. And for good reason: the creation of such a currency could provide access to an unfalsifiable currency. Researchers from NTT Research recently published their advances on the subject. These are based on the famous “knot theory”.

For several years now, researchers have been looking very seriously at the creation of a “quantum currency”. In the 1970s, physicist Stephen Wiesner even mentioned this idea. But what is it, exactly? To better understand the notion of quantum money, we must remember what quantum computing is.

The principle of a quantum computer is to perform calculations based on the principles of quantum physics. Quantum physics can be roughly summarized as the science concerned with the behavior of matter and light at a microscopic, or atomic, level. Indeed, the first scientists who focused on the study of this scale noticed that matter behaves there according to physical principles very different from what we knew until then.


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Among these principles, there is “quantum superposition”, the key to the operation of quantum computers. Concretely, quantum superposition could be summed up as the fact that something can be “in two states at the same time”. In the case of a classical computer, the basic unit of information is the “bit”. This can be either in the “0” state or in the “1” state. In a quantum computer, there is therefore a sort of equivalent, called a “qubit”. With the difference that thanks to the famous law of superposition, in addition to these two simple states, qubits can somehow be both 0 and 1, and even be in states in between, such as 01, 10, 11… This allows them to deploy phenomenal computing power: this is what arouses so much interest in quantum computers.

How do we come to quantum money? In 2018, the CNRS had already done research to develop a quantum currency. On their sitewe therefore find a simplified explanation: Basically, we excite atoms with photons. These change state, which corresponds to a code. Then we re-excite them when we want to retrieve this code. On arrival: impossible to use two bank cards with the same numbers “says the institution. Because the famous “qubits” are indeed atoms, which are “trapped” by various methods and pushed to interact with each other.

New encryption keys to find

We are therefore obviously not talking here about cold hard currency, but about “codes” that are extremely difficult to decipher: so much so that it would be possible to make a very secure currency out of it. As the CNRS mentioned at the time, this research could prove to be a necessity, precisely because of quantum computers. Thanks to their very high computing power, they could one day be able to decipher our current encryption systems, including the one used for banking data, for example. Recently, we were just talking about in an article the research of a team of scientists. She claims to have already succeeded in finding an algorithm capable of achieving this feat on existing quantum computers. Even if their colleagues remain skeptical, the general opinion remains that they will certainly be able to do so one day: hence the need for new encryption keys.

It is in this idea of ​​quantum currency that the research of scientists working for NTT Research is part. In their model, they decided to rely on knot theory. And, yes, we are talking here about the equivalent of knots that can be made with a rope or a string. For those most interested, this excerpt from Mickaël Launay’s popularization video talks very well about this exciting mathematical field.

Indeed, knots pose many questions to scientists that are much more complex than it seems. One of these challenges, which particularly interests us here, is that of their “topological equivalence”. Indeed, the knots are considered “up to continuous deformations”, that is to say that a knot is considered equivalent to another according to certain criteria which exclude relaxation, positioning, etc.

Nodes as a verification method for quantum currency

Put simply, a loose, crooked figure-of-eight knot is still a figure-of-eight knot, even though it looks very different from a nice figure-of-eight knot that’s been pulled tight on itself. But determining whether a knot can be “rearranged” (tightening the figure-of-eight knot, in this example) to look like another is not so easy to calculate, even for a quantum computer.

To determine mathematically, with certainty, if a node is equivalent to another, the scientists looked for what are called “invariants”: criteria always valid for a type of node, which make it possible to distinguish them from each other. . In other words, the calculation of the invariants necessarily gives the same result for two equivalent nodes, which makes it possible to know that they are equivalent even if they are represented differently.

Mark Zhandry and his colleagues have therefore proposed a quantum monetary system where computing these invariants, for knots and similar classification problems, is the basis for verifying that money is genuine. In their system, each monetary unit comprises a series of qubits, each with a corresponding node, along with a list of the invariants present. A key part of verification is to analyze whether the qubits and their invariants match. The principle is quite simple, but it is impossible to come up with another list of nodes that would also match – and therefore to falsify this “currency”.

Moreover, making a direct copy of quantum currency would prove impossible under the “no cloning” law. In summary if someone learned enough information about quantum currency to duplicate it, the qubits would change so much in the process that they would become unusable.

However, the implementation of such a currency requires many quantum calculations, on very powerful computers. It is therefore not certain that we can quickly move from theory to practice to allow you to walk around with quantum money to pay for your shopping. But at least you’ll have learned about knots.

Source : arXiv

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Marrying quantum computing and knot theory could create an unforgeable currency

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