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Transfer of a power tool from mathematics to quantum calculations



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The Fourier transform is an important mathematical instrument that decomposes a function or set of data into its constituent frequencies, similar to how one can decompose a musical chord into a combination of its notes. It is used in all areas of engineering in one form or another and accordingly algorithms have been developed for its efficient calculation ̵

1; ie. at least for conventional computers. But what about quantum computers?


Although quantum computing remains a huge technical and intellectual challenge, it has the potential to accelerate extremely many programs and algorithms, provided that appropriate quantum schemes are designed. In particular, the Fourier transform already has a quantum version called quantum Fourier transform (QFT), but its applicability is quite limited, as its results cannot be used in subsequent quantum arithmetic operations.

To address this problem, in a recent study published in Quantum information processing, scientists from the University of Tokyo in Science have developed a new quantum chain that performs quantum fast Fourier transform (QFFT) and takes full advantage of the peculiarities of the quantum world. The idea for the study came to Mr. Rio Asaka, a first-year master’s student and one of the scientists in the study, when he first learned about QFT and its limitations. He believes that it would be useful to create a better alternative based on a variant of the standard Fourier transform called fast Fourier transform (FFT), an indispensable algorithm in conventional calculations that significantly speeds things up if the input data meet some basic conditions.

To design the quantum chain for QFFT, scientists first had to invent quantum arithmetic circuits to perform basic FFT operations, such as adding, subtracting, and moving numbers. A remarkable advantage of their algorithm is that no “garbage bits” are generated; the calculation process does not lose any qubits, the basic unit of quantum information. Given that increasing the number of qubits of quantum computers has been a difficult battle over the last few years, the fact that this new quantum scheme for QFFT can use qubits effectively is very promising.

Another merit of their quantum chain over traditional QFT is that their performance uses a unique property of the quantum world to significantly increase computational speed. Associate Professor Kazumitsu Sakai, who led the study, explains: “In quantum computing, we can process a large amount of information at once, taking advantage of a phenomenon known as ‘state superposition’. This allows us to convert a lot of data, such as multiple images and sounds, into the frequency domain at the same time. “The processing speed is regularly mentioned as a major advantage of quantum calculations, and this new QFFT scheme is a step in the right direction.

In addition, the QFFT chain is much more flexible than QFT, as noted by assistant Rioko Yahagi, who is also involved in the study: “One of the main advantages of QFFT is that it is applicable to any problem that can be solved by conventional FFTs, such as filtering digital images in the medical field or analyzing sounds for engineering applications. “With quantum computers (hopefully) just around the corner, the results of this study will make it easier to adopt quantum algorithms to solve the many engineering problems that rely on FFT.


The new quantum computational algorithm skips past time constraints imposed by decoherence


More information:
Ryo Asaka et al, Quantum chain for fast Fourier transform, Quantum information processing (2020). DOI: 10.1007 / s11128-020-02776-5

Provided by the University of Tokyo Science

Quote: Bringing a power tool from mathematics into quantum calculations (2020, October 14) extracted on October 14, 2020 from https://phys.org/news/2020-10-power-tool-math-quantum.html

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