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Artyom M. Grigoryan^1,*, Sos S. Agaian²
Journal of Quantum Computing, Vol.6, pp. 1-14, 2024, DOI:10.32604/jqc.2023.026981
Abstract In this work, we describe a method of calculation of the 1-D circular quantum convolution of signals represented by 3-qubit superpositions in the computational basis states. The examples of the ideal low pass and high pass filters are described and quantum schemes for the 3-qubit circular convolution are presented. In the proposed method, the 3-qubit Fourier transform is used and one addition qubit, to prepare the quantum superposition for the inverse quantum Fourier transform. It is considered that the discrete Fourier transform of one of the signals is known and calculated in advance and only the quantum Fourier transform of… More >

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Mark Ariel Levin^*
Journal of Quantum Computing, Vol.6, pp. 15-24, 2024, DOI:10.32604/jqc.2024.047423
Abstract Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical answers that do not belong in the search space and reduce the efficiency of the algorithm due to the need to neglect, un-compute, or destructively interfere with them. Previous approaches to removing this auxiliary search space yielded large circuit depth and required the use of ancillary qubits. We have developed an optimized general solver for a circuit that prepares a uniform superposition of any N states while minimizing depth and… More >

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