Abstract
AbstractWe propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector spaces. Namely, our FFT is defined as a transformation of the tensor product of quantum states. It is essentially different from the so-called quantum Fourier transform (QFT) defined to be a linear transformation of the amplitudes for the superposition of quantum states. The quantum circuit for the FFT consists of several circuits for elementary arithmetic operations such as a quantum adder, subtractor and shift operations, which are implemented as effectively as possible. Namely, our circuit does not generate any garbage bits. The advantages of our method compared to the QFT are its high versatility, and data storage efficiency in terms, for instance, of the quantum image processing.
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Modelling and Simulation,Signal Processing,Theoretical Computer Science,Statistical and Nonlinear Physics,Electronic, Optical and Magnetic Materials
Reference36 articles.
1. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)
2. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of ACM STOC, pp. 212–219 (1996)
3. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum random access memory. Phys. Rev. Lett. 100, 160501 (2008)
4. Giovannetti, V., Lloyd, S., Maccone, L.: Architectures for a quantum random access memory. Phys. Rev. A 78, 052310 (2008)
5. Park, D.K., Petruccione, F., Rhee, J.K.: Circuit-based quantum random access memory for classical data. Sci. Rep. 9, 3949 (2019)
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