Fast algorithms for quantum physics

Jamie Smith, Michele Mosca

Daniel S. Abrams, Seth Lloyd

We describe a new polynomial time quantum algorithm that uses the quantum fast Fourier transform to find eigenvalues and eigenvectors of a local Hamiltonian, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.

Zhaoyang Xu

The algorithm concept of fast Fourier transform, Heisenberg uncertainty, and the combination of the two are expounded. Fast Fourier Transform (FFT) is not a new discrete Fourier Transform, but a fast algorithm for Discrete Fourier Transform (DFT). For a long time, the DFT was not really used because of the large amount of computation, even if it was used by computers, it was difficult to deal with problems in real time. It was not until when Cooley and Key first proposed a fast algorithm for DFT operations, and later, when fast algorithms by G. Sullivan and. Key appeared in succession, that fundamental changes took place. People began to realize some inherent laws of DFT operation, and thus quickly developed and improved a set of high-speed and effective operation methods, which is now commonly known as the fast Fourier transform FF11 algorithm. Specifically, the position of a particle and its momentum cannot be determined simultaneously in a quantum mechanical system. It focuses on the proof and application of the Heisenberg inequality by TTF. Due to the different ways and methods of practical application, the practical significance and practical value of the application are for readers' reference. Besides, the space is limited and my knowledge is limited. Finally, the development direction of FFT in quantum physics is summarized.

Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino +1 more

Peter W. Shor

S.V. Ulyanoy, Giovanni Degli Antoni, K. Yamafuji +3 more

Principles of quantum soft computing, models of fast quantum searching algorithms and the possibility of its applications for intelligent control of micro-systems are introduced. The description problem of searching and decision-making support processes from more fundamental mutual positions of the new information technologies and a modern physics, information physics, are discussed: (1) in the quantum information theory-the information complexity theory of random symbolic sequences, computation complexity, quantum searching algorithms; and (2) in the modern physics-nonequilibrium thermodynamics and quantum mechanics.