Scientists from the Physics department, University of Warsaw, Poland, in association with the University of Oxford and NIST, have demonstrated that quantum interference facilitates the processing of huge sets of data faster and more accurately than with standard methods. The results of their work have been published in Science Advances. This research may enhance applications of quantum technologies in artificial intelligence, robotics, and medical diagnostics, for example.

In today’s fast-paced world, different branches of science and technology like contemporary science, medicine, engineering, and information technology demand efficient and quick processing of data—sound, still images, and radio signals, as well as information coming from different cameras and sensors. The Fast Fourier Transform algorithm(FFT) has made possible since the 1970s to efficiently compress and transmit data, broadcast digital TV, store pictures, and talk over a mobile phone. Minus this algorithm, medical imaging systems based on magnetic resonance or ultrasound would not have been designed. But then, it is still too slow for many demanding applications.

To achieve this goal, scientists have been trying for years to utilize quantum mechanics. It resulted in the unraveling of a quantum counterpart of the FFT, the Quantum Fourier Transform (QFT), which can be realized with a quantum computer. As the quantum computer instantaneously processes all possible values, called superpositions, of input data, the number of operations decreases considerably.

Regardless of the rapid development of quantum computing, there is a relative lack of progress in the field of quantum algorithms. Now scientists have revealed that this result can be improved and in a rather fantastic way.

Kravchuk transform

Many transformations are described by Mathematics. One of these changes is a Kravchuk transform. It is much the same to the FFT in function, as it allows processing of discrete data (e.g. digital), but uses Kravchuk functions to decompose the input sequence into the spectrum.

The Kravchuk transform was “rediscovered” in computer science at the end of the 1990s. This revival turned out to be outstanding for image and sound processing. It enabled scientists to develop new and much more accurate algorithms for the recognition of printed and handwritten text that also includes the Chinese language, gestures, sign language, people, and faces. Only a dozen years ago, it was shown that this transformation is ideal for processing low-quality, loud and distorted data, and hence it could be used for computer vision in robotics and autonomous vehicles. However, there is no fast algorithm to compute this transform, but it turns out that quantum mechanics allows one to bypass this limitation.

In the published article from Science Advances, researchers from the University of Warsaw – Dr.Adam Buraczewski and Dr. Magdalena Stobinska, and scientists from the University of Oxford and NIST, have shown that the simplest quantum gate that interferes between two quantum states, basically computes the Kravchuk transform. Such a gate could be a well-known optical device—such as a beam splitter, which divides photons between 2 outputs. When 2 states of quantum light enter its input ports from 2 sides, they interfere. For example, two identical photons, which simultaneously enter this device, bunch into pairs and exit out together by the same exit port — commonly known as the Hong-Ou-Mandel effect, which can also be extended to states made of many particles. By interfering “packets” consisting of many indistinguishable photons, which encrypt the information, one obtains a specialized quantum computer that computes the Kravchuk transform. It is very important that the photons are indistinguishable as its absence destroys the quantum effect.

A special setup was built in a quantum optical laboratory at the Department of Physics at the University of Oxford. An experiment was performed to produce multiphoton quantum states, so-called Fock states. This laboratory is equipped with TES (Transmission Edge Sensors), developed by NIST, which operates at near-absolute zero temperatures. A unique feature of these detectors enables them to actually count photons. This allows one to precisely read the quantum state leaving the beam splitter and thus, the result of the computation. Most significantly, such a computation of the quantum Kravchuk transforms always takes the same time, regardless of the size of the input data set. It is the “Holy Grail” or “Pot of Gold” of computer science: an algorithm consisting of just one operation, implemented with a single gate. Obviously, in order to obtain the result in practice, perform the experiment needs to be performed several hundred times to get the statistics. This is how every quantum computer works. However, it does not take long, because the laser produces dozens of millions of multiphoton “packets” per second.

The result obtained by scientists from Poland, the United Kingdom, and the United States will find utilizations in the development of new quantum technologies and quantum algorithms. Its range of uses goes beyond quantum photonics since a similar quantum interference can be witnessed in many different quantum systems. The University of Warsaw applied for an international patent for this latest innovation. The scientists hope that the Kravchuk transform will soon find use in quantum computation, where it will become a component of new algorithms, especially in hybrid quantum-classical computers that merge quantum circuits with “normal” digital layouts.

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