Sunday, October 1

Qudits are the great hope of quantum computing to get where it is not possible with qubits

In the field of quantum computing, a qubit has the same role as a bit in classical computing: it is the minimum unit of information. The word cubit comes from the contraction of the English terms quantum Y bitand stands for quantum bit.

The bits we are all familiar with, the ones our computers handle, can adopt at any given time one of two values possible: 0 or 1.

However, qubits, unlike bits, do not have a single value at any given time; what they have is A combination of states zero and one simultaneously.

They can have a lot of state zero and little of state one. Or a lot of state one and a little of state zero. Or the same for both. or any other combination of these two states that occur to us.

Precisely this property is largely responsible for the great capabilities that have the prototypes of quantum computers that we currently have.

The complexity of nature fits better in a multidimensional structure

The definitions of bit and qubit we have just delved into clearly describe essentially binary nature of the minimum unit of information with which both classical and quantum computers work. its two-dimensional character.

But, interestingly, the information that can be processed by a quantum computer is not necessarily binary in nature.

Many problems contain information with a very rich multidimensional structure that is often artificially restricted to only two dimensions.

In fact, many of the problems that a fully functional quantum computer is likely to face in the future in quantum chemistry, quantum simulation, and many other disciplines contain information with a multidimensional structure very rich that is often artificially restricted to just two dimensions.

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What is a cudit and why is it important?

In recent years, several research groups have realized that a very important part of the calculation capacity that fully functional quantum computers will put in our hands will be diminished if we deal with problems using a classical approach.

If information describing the complexity of those problems looks necessarily simplified in order for it to adopt a two-dimensional structure there is a chance that the efficiency of quantum algorithms will sink.

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Everything we have reviewed so far allows us to intuit what is a cudit And what strategy are you pursuing? The mathematical formulation of it is very complex, so we will ignore it in order not to overcomplicate this article.

A cudit is a multidimensional computational unit of information that we can use as an alternative to qubits.

However, for readers who are comfortable with Hilbert matrices and spaces, I suggest you take a look at the article in which a group of researchers from Purdue University, in the United States, and the University of Calgary, in Canada, mathematically describes the concept of cudit.

In any case, what we are interested in knowing is that a cudit is a unit of multidimensional computational information that we can use as alternative to qubitswhich operate on two levels or dimensions, in the field of quantum computers.

quantum computer

The cudits allow researchers to more accurately describe the complexity inherent in some problems that we can tackle using quantum algorithms. And, in addition, they have the ability to reduce the complexity of the logic and increase efficiency of these algorithms.

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Sounds good. Of that there is not the slightest doubt. However, in practice, betting on this problem-solving strategy, betting on qudits as an alternative to qubits, requires rethinking the way in which the hardware of quantum computers is physically implemented.

From the language of cudits to ion traps

Quantum computing researchers frequently argue that many of the problems in chemistry, physics, cryptography or materials engineering, among other disciplines, can be expressed in a completely natural way in the language of the cúdits.

Describing them using the two-dimensional structure proposed by qubits entails giving up part of the potential that quantum computers bring to the table, at least from a strictly theoretical point of view. Of course, the physical implementation of the cudits not identical to that of the qubits, as we can guess.

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But we have something very important in our favor: nature is full of physical systems that operate in more than two states. The ion traps with which many research groups are familiar do so, but the implementation of hardware using superconductors, nuclear magnetic resonance or photonic systems also fits into this premise.

Good news: nature is full of physical systems that operate in more than two states

We have good reason to be optimistic. And it is that, despite how complex it is to approach quantum computing from the perspective proposed by the language of cudits, several research groups have already managed to formally describe its logical structure.

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They have even elaborated the version in the language of the cúdits of some of the most representative algorithms in the field of quantum computing, such as the quantum Fourier transform, the quantum phase estimation algorithm or the Deutsch-Jozsa algorithm, among others.

There is no doubt that there is still much to do and much research to tackle, but the enormous potential of quantum computing amply justifies the effort that so many people are doing backed by research groups that are scattered all over the planet.

Images: IBM

More information: Frontiers | arXiv

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