Xanadu’s photonic quantum computer has gained quantum dominance

It’s one of the buzz of the moment, the Canadian start-up Xanadufounded in 2016 in Toronto, has announced that it has achieved quantum supremacy – or what can be said to be very similar – with its programmable quantum computer on photons.

Remember that we tend to define quantum domination as being able to execute an algorithm on a machine using the laws of Quantum mechanicsmainly those of superposition of states andentanglementto perform a calculation very quickly, e.g. in seconds, whereas the best algorithm that could perform the same calculation on a conventional supercomputer would take so long that a human’s life might not be enough to wait for the result.

There is not yet a precise and unanimous wording on what is to be understood by quantum superiorityor the quantum advantage, which means almost the same, if not a general idea close to the explanation that has just been given.

Specifically, in the case of Xanadu, and as its members explain in an open access article published in the journal Naturetheir quantum machine baptized Borealis performed in about 36 microseconds a calculation that would take a conventional supercomputer about 9,000 years, a dizzying speed factor.

A presentation of Borealis from Xanadu. To get a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles were then to appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Automatically translate”. Select “French”. © Xanadu

From Planck to Feynman with quantum mechanics

However, it is customary to take a pair of tweezers with this kind of results because it has sometimes happened that the discovery of a new classical algorithm makes it possible to achieve the same result, or even faster. A calculator, or a universally programmable quantum computer, also does not systematically achieve quantum domination.

Let us finally remember that quantum calculations are physically affected by physical systems of very significant perturbations, which at least produce many errors or make it impossible to perform the execution of an algorithm, as much faster as it requires a large number qubitsthe quantum equivalents classic information. It’s the famous one the problem of decoherence which has actually made many specialists skeptical of the real performance that could have quantum computers universally programmable. Although many in recent years have become more optimistic about the performance of machines that can be called computers or quantum simulators – because they specialize in performing certain algorithms – we can still be on the threshold of a quantum revolution.

It would at least prove itself once again the visionary genius of Richard Feynmana pioneer in quantum computer theory who had proposed using the physical laws and systems of quantum mechanics to quickly simulate the behavior of other quantum systems that were unmanageable with classical computers or at least very difficult, such as. properties of molecules in quantum chemistry or the behavior of quarks and gluoner in hadrons.

Experience in animated video the history of quantum physics: from the ultraviolet catastrophe to the promises of the quantum computer that passes through the first and second quantum revolutions with the ideas of Feynman and Peter Shors. A video animation co-produced with The Spirit of the Wizard. © CEA Research

Qubits with photonic compressed states

But back to Xanadu and Borealis. The machine works with photons and it does not need to be nearly cooled down absolutely zero unlike many other quantum circuits that protect themselves from thermal noise that rapidly degrades quantum calculations.

Quantum calculations with photons are often performed with two photon polarization states, which makes it possible to have a quantum qubit with a superposition of these two states corresponding to a quantum superposition of 1 and 0. But in the case of Borealis, these quantum states of electromagnetic field of light various used, examples of what are called compressed states el squeezed states English.

Technically, an example of these states is realized in quantum mechanics with a harmonic oscillator, i.e. substantially corresponding to an oscillating weight at the end of a spring. We can consider an electromagnetic field as a set of such springs, since charged particles in an oscillating field would behave like these harmonic oscillators. A compressed state would be that, or in accordance with Heisenberg’s relations, the product of “uncertainties” about the position and the amount of movement of the particle at the end of an oscillating spring would have the least possible value and would therefore in a way characterize the least blurred and quantum noisy state of an oscillator – it is slightly different in the case of states compressed with photons, but the purpose and the idea are very much alike.

Borealis therefore utilizes a quantum superposition of compressed states of photons and in this case 216 qubits with these states.

A description of the machine can be found on the Xanadu website and in the accompanying videos.

Basically, it can be perceived as a black box of photons coming in through multiple channels and coming out through others with detectors to count the number of those leaving each channel in each performed experiment.

The interior of the box is a set of units (leaves that separate light rays and interferometers in particular) to affect incoming light rays, first by producing compressed states from pulses laserthen divide them into other rays, change what is called their phase and produce entanglements between the photons present as well as interferences

All of these devices behave like doors elementary logics of classical computers that can be combined to form many operations and therefore perform a wide variety of algorithms that one may wish to program. But these are quantum gates like the ones discussed in the video below.

A further presentation of the concept of computer and quantum algorithm. © CEA Research

Graph theory quantum calculations

Technically, Borealis behaves mathematically as a matrix, a matrix of numbers that allows to produce from a column of numbers in input, a column of numbers in output (the channels of photons with a number of them arriving for each channel). This matrix encodes a programmable algorithm, just as many matrices, just as many algorithms.

Ultimately, Borealis performs what is also called Gaussian bosonic sampling (photons are bosoner) is still called Gaussian boson sampling (GBS) in English. In each experiment, the photons entering through the channels follow different paths in the machine and leave according to a different distribution in the final channels.

But the average distribution of photons for each detector at the channel output must behave according to a probability distribution that is proportional to a quantity calculated with the matrix of the algorithm implemented in Borealis, a magnitude that mathematicians call Hafnian of a matrix (not to be confused with what is called the determinant). Hafnian is becoming more and more difficult to calculate classically with the number of inputs and outputs – which is the same, the matrix is ​​square as we say.

But as we said, Borealis performed a Hafnian calculation of 36 microseconds instead of 9,000 years, which would be necessary on the Fugaku 415-PFLOPS (a Japanese supercomputer developed by Fujitsu on behalf of the Japanese scientific institute RIKEN and presented in 2020 as the most powerful supercomputer in the world) and this 50 million times faster than with previous quantum computers with photons. Cherry on top of that, Xanadu has provided free online cloud access to its machine, so basically anyone can try programming an algorithm on Borealis.

Xanadu uploaded tutorials to program into python with some ” software ” as Penny lane and Strawberry fields.

A presentation of the Xanadu photonic chip. To get a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles were then to appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Automatically translate”. Select “French”. © Xanadu

Among the perspectives opened by Xanadu is there machine learning quantum and the fact that the technology behind Borealis makes it possible in theory to easily increase the size of the photonic quantum computer. The members of Xanadu even think they can reach the millions of qubits!

Achieving supremacy or what is called the quantum advantage is one thing, but speeding up the execution of an algorithm incredibly only has an effect if that algorithm has the potential to concretely solve important practical problems. . So what’s the point to be able to quickly calculate Hafnian for large matrices?

It turns out that Hafnian, for GBS regulations, is involved in calculations of graph theory to make optimization, machine learning and in quantum chemistry when trying to determine spectra of molecules which vibrates. In the latter case, it makes it possible to predict and study how materials absorb light at different frequencies. That absorption spectra investigated can be useful to optimize the yield of solar cells or in the development of pharmaceutical products, as explained on one of the pages of Xanadu, whose comments we include in this section and the following.

Let us finally remember that graph theory can be used to model financial markets, biological networks and social network. The graphs are composed of a set of knob interconnected, and one of the problems we often try to solve with them is to find clusters, that is, regions with a high level of connectivity. They can correspond to communities in social networks, correlated assets in a market or protein mutually influential in a biological network.

A quantum computer with a photonic chip like Borealis’ should be able to work with 1 million Qubits. To get a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles were then to appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Automatically translate”. Select “French”. © Xanadu

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