Quantum representation and basic operations of digital signals

doi:10.3969/j.issn.1007-5461.2026.03.012

Abstract

Abstract: To address the limitations of digital signal representation, a quantum representation for one-dimensional finite-length digital signals is proposed in this paper. Similar to the existing flexible representation of quantum audio, this representation approach employs two sets of qubits to encode the amplitude and timing information of the signal separately. Specifically, the amplitude is represented by an (n+1)-bit signed number in the binary original code, consisting of one sign bit, m integer bits, and n - m fractional bits. Subsequently, the fundamental operations on this representation, including addition, subtraction, multiplication, division, and circular convolution of two digital signals, are introduced, and corresponding quantum circuits are designed to implement these operations. And then, based on the number of elementary quantum gates employed, the complexity of the circuits is analyzed. The results demonstrate that the proposed quantum digital signal processing scheme achieves acceleration compared to classical processing methods. Meanwhile, simulations conducted on a classical computer confirm the correctness of the designed quantum circuits.

Key words: quantum image processing, quantum signal representation, quantum signal processing; quantum true code multiplication, quantum true code division, quantum circular convolution

CLC Number:

TP391

LIU Xiande , LI Xiao. Quantum representation and basic operations of digital signals[J]. Chinese Journal of Quantum Electronics, 2026, 43(3): 456-471.

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