Bringing powerful mathematical tools into quantum computing

Fourier transform is an important mathematical tool, which can decompose a function or data set into its constituent frequencies, just as music chords are decomposed into combinations of their notes. It is used in all fields of Engineering in one form or another, so algorithms have been developed to efficiently compute them, that is, at least for conventional computers. But what about quantum computers? Although quantum computing is still a huge technical and intellectual challenge, it has the potential to speed up many programs and algorithms as long as the appropriate quantum circuits are designed. In particular, Fourier transform has a quantum version called quantum Fourier transform, but its applicability is limited because its results can not be used in subsequent quantum arithmetic operations. < / P > < p > to solve this problem, scientists from Tokyo University of Science published a study in a recently published journal. They have developed a new quantum circuit that can perform fast four-dimensional transformation of quantum and fully benefit from the particularity of the quantum world. The idea came from Mr. Chao Xiangliang, a first-year master student and one of the scientists involved in the study. When he first understood QFT and its limitations, it was useful to create better alternatives based on a variant of the standard Fourier transform called fast Fourier transform. Fast Fourier transform is an indispensable algorithm in conventional calculation. If the input data meets some basic conditions, it can greatly speed up the processing. < / P > < p > in order to design quantum circuits for qfft, scientists must first design quantum arithmetic circuits to perform the basic operations of FFT, such as addition, subtraction and digital shift. A significant advantage of their algorithm is that it does not generate “garbage bits”. The calculation process will not waste any basic unit qubits of qubits. Considering that increasing the number of quantum bits in quantum computers has been a tough battle in recent years, the fact that this new quantum circuit for qfft can effectively utilize qubits is very promising. Another advantage of their quantum circuits over the traditional QFT is that their implementation takes advantage of the unique properties of the quantum world and can greatly improve the computing speed. “In quantum computing, we can use a phenomenon called” superposition of States “to process large amounts of information at the same time,” explained associate professor Sakai Ichigo, who led the study. This allows us to convert large amounts of data into the frequency domain at one time. ” Processing speed is usually regarded as the main advantage of quantum computing. This novel qfft circuit represents a step in the right direction. < / P > < p > in addition, the qfft circuit is much more versatile than QFT. As Liu Mu Liangzi, an assistant professor who also participated in the research, pointed out: “one of the main advantages of qfft is that it can be applied to any problem that can be solved. Traditional FFT, such as digital image filtering in medical field or sound analysis in engineering application With quantum computers, the results of this study will make it easier to solve many engineering problems that rely on FFT using quantum algorithms. Continue ReadingXiaomi new machine real machine exposure center dig hole screen design or high color thousand yuan machine