Digital signal processing (DSP) is an engineering field involved with increasing the precision and dependability of digital communications and mathematical processes, including equalization, modulation, demodulation, compression, and decompression, which can be used to produce a signal of the highest caliber. To execute vital tasks in DSP, an essential electronic circuit such as a multiplier plays an important role, continually performing tasks such as the multiplication of two binary numbers. Multiplier is a crucial component utilized to implement a wide range of DSP tasks, including convolution, Fourier transform, discrete wavelet transforms (DWT), filtering and dithering, multimedia information processing, and more. A multiplier device includes a clock and reset buttons for more flexible operational control. Each digital signal processor constitutes a multiplier unit. A multiplier unit functions entirely autonomously from the central processing unit (CPU); consequently, the CPU is burdened with a significantly reduced amount of work. Since DSP algorithms must constantly carry out multiplication tasks, the employment of a high-speed multiplier to execute fast-speed filtering processes is vital. The previous multipliers had lots of weaknesses, such as high energy, low speed, and high area, because they implemented this necessary circuit based on traditional technology such as complementary metal-oxide semiconductor (CMOS) and very large-scale integration (VLSI). To solve all previous drawbacks in this necessary circuit, we can use nanotechnology, which directly affects the performance of the multiplier and can overcome all previous issues. One of the alternative nanotechnologies that can be used for designing digital circuits is quantum dot cellular automata, which is high speed, low area, and low power. Therefore, this manuscript suggests a quantum technology-based multiplier for DSP applications. In addition, some vital circuits, such as half adder, full adder, and ripple carry adder (RCA), are suggested for designing a multiplier. Moreover, a systolic array, accumulator, and multiply and accumulate (MAC) unit are proposed based on the quantum technology-based multiplier. Nonetheless, each of the suggested frameworks has a coplanar configuration without rotated cells. The suggested structure is developed and verified utilizing the QCADesigner 2.0.3 tools. The findings showed that all circuits have no complicated configuration, including a higher number of quantum cells, latency, and an optimum area.