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In this work, we describe examples for calculating the 1-D circularconvolution of signals represented by 3-qubit superpositions. The case isconsidered, when the discrete Fourier transform of one of the signals is knownand calculated in advance and only the QFT of another signal is calculated. Thefrequency characteristics of many linear time-invariant systems and filters arewell known. Therefore, the considered method of convolution can be used forthese systems in quantum computation. The ideal low pass and high pass filtersare considered and quantum schemes for convolution are presented. The method ofthe Fourier transform is used with one addition qubit to prepare the quantumsuperposition for the inverse quantum Fourier transform.

3-Qubit Circular Quantum Convolution Computation using Fourier Transform with Illustrative Examples