The Fourier transform is an essential mathematical instrument that breaks down a function or dataset into its component frequencies, similar to the process of decomposing a musical chord into a mix of its notes.
The tool is used across all engineering segments in some form or another and, therefore, algorithms to compute it effectively have been created. That is, at least for regular computers. However, when it comes to quantum computers, researchers have, so far, encountered only challenges.
The Fourier Transform Adapted to Quantum Computing
Even though quantum computing is still a massively technical and intellectual dare, it has the potential to accelerate many programs and algorithms in a colossal manner, considering that proper quantum circles are created.
In particular, the Fourier transform already has a quantum variant known as the quantum Fourier transform (QFT); however, its suitability is rather limited because its results cannot be employed in subsequent quantum arithmetic activities.
To solve this issue, in a recent study issued by the Quantum Information Processing journal, researchers from Tokyo University of Science created a new quantum circuit that uses the quantum fast Fourier transform (QFFT) and benefits from the oddities of the quantum universe.
Innovative Concept to Create a Quantum Circuit
The concept for the research came to Mr. Ryo Asaka, a first-year Master’s student and one of the experts on the study, when he first came across the QFT and its limitations. He thought it would be beneficial to create a better variant based on a version of the regular Fourier transform known as the fast Fourier transform (FFT). This is an imperative algorithm in conventional computing that massively accelerates things if the input data matches some basic rules.
To create the quantum circuit for the QFFT, the researcher had to initially devise quantum arithmetic circuits to carry out FFT’s basic operations, including addition, subtraction, and digit shifting. Their algorithm’s remarkable benefit is that no ‘garbage bits’ are created – the calculation process doesn’t lose any qubits, which is the basic unit of quantum information.
Considering that adding to the number of qubits of quantum computers has been a challenge in the last few years, the fact that this innovative quantum circuit for the QFFT can efficiently use qubits is very promising.
A Promising Step Forward
Another excellence of their quantum circuit over the regular QFT is that their implementation takes advantage of the quantum realm’s unique property to massively 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 usually noted as the key advantage of quantum computing, and this innovative QFFT circuit is a promising step in the right direction. With quantum computers expected to be within reach soon, this research’s outcomes will make it easier to use quantum algorithms to solve the numerous engineering issues that depend on the FFT.