Bringing a power tool from math into quantum computing

Date:
October 14, 2020
Source:
Tokyo University of Science
Summary:
The Fourier transform is a mathematical operation essential to
virtually all fields of physics and engineering. Although there
already exists an algorithm that computes the Fourier transform in
quantum computers, it is not versatile enough for many practical
applications. In a recent study, scientists tackle this problem
by designing a novel quantum circuit that calculates the Fourier
transform in a much quicker, versatile, and more efficient way.



FULL STORY ==========================================================================
The Fourier transform is an important mathematical tool that decomposes
a function or dataset into a its constituting frequencies, much like
one could decompose a musical chord into a combination of its notes. It
is used across all fields of engineering in some form or another and, accordingly, algorithms to compute it efficiently have been developed --
that is, at least for conventional computers. But what about quantum
computers?

========================================================================== Though quantum computing remains an enormous technical and intellectual challenge, it has the potential to speed up many programs and algorithms immensely provided that appropriate quantum circuits are designed. In particular, the Fourier transform already has a quantum version called
the quantum Fourier transform (QFT), but its applicability is quite
limited because its results cannot be used in subsequent quantum
arithmetic operations.

To address this issue, in a recent study published in Quantum Information Processing, scientists from Tokyo University of Science developed a new
quantum circuit that executes the "quantum fast Fourier transform (QFFT)"
and fully benefits from the peculiarities of the quantum world. The
idea for the study came to Mr. Ryo Asaka, first-year Master's student
and one of the scientists on the study, when he first learned about
the QFT and its limitations. He thought it would be useful to create a
better alternative based on a variant of the standard Fourier transform
called the "fast Fourier transform (FFT)," an indispensable algorithm
in conventional computing that greatly speeds things up if the input
data meets some basic conditions.

To design the quantum circuit for the QFFT, the scientists had to first
devise quantum arithmetic circuits to perform the basic operations of
the FFT, such as addition, subtraction, and digit shifting. A notable
advantage of their algorithm is that no "garbage bits" are generated;
the calculation process does not waste any qubits, the basic unit of
quantum information. Considering that increasing the number of qubits
of quantum computers has been an uphill battle over the last few years,
the fact that this novel quantum circuit for the QFFT can use qubits efficiently is very promising.

Another merit of their quantum circuit over the traditional QFT is that
their implementation exploits a unique property of the quantum world to
greatly increase computational speed. Associate Professor Kazumitsu Sakai,
who led the study, explains: "In quantum computing, we can process a large amount of information at the same time by taking advantage of a phenomenon known as 'superposition of states.' This allows us to convert a lot of
data, such as multiple images and sounds, into the frequency domain in
one go." Processing speed is regularly cited as the main advantage of
quantum computing, and this novel QFFT circuit represents a step in the
right direction.

Moreover, the QFFT circuit is much more versatile than the QFT, as
Assistant Professor Ryoko Yahagi, who also participated in the study,
remarks: "One of the main advantages of the QFFT is that it is applicable
to any problem that can be solved by the conventional FFT, such as the filtering of digital images in the medical field or analyzing sounds
for engineering applications." With quantum computers (hopefully) right
around the corner, the outcomes of this study will make it easier to
adopt quantum algorithms to solve the many engineering problems that
rely on the FFT.


========================================================================== Story Source: Materials provided by Tokyo_University_of_Science. Note:
Content may be edited for style and length.


========================================================================== Journal Reference:
1. Ryo Asaka, Kazumitsu Sakai, Ryoko Yahagi. Quantum circuit for
the fast
Fourier transform. Quantum Information Processing, 2020; 19 (8)
DOI: 10.1007/s11128-020-02776-5 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/10/201014114615.htm

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