Quantum Signal Processing Delay Effects: Optimization and Next Steps

A delay line is a fundamental building block for time-based effects in classical signal processing. Preliminary quantum signal-processing circuits found in the literature implement signal delays through quantum time-shifting operations. In this work, we present an optimization that reduces the qubit and gate counts required by these existing quantum delay circuits. The paper begins by reviewing the classical concept of a delay line, comparing it with its quantum counterpart, and discussing previous work on quantum delay operations. The methodology section then introduces the quantum circuits used to implement both the original and optimized versions of the delay operation. The final sections provide a complexity analysis of the different circuits, present simulation examples in which the operation is applied to signals, and discuss possible extensions of the proposed approach. These include scaling the circuits to larger numbers of audio samples, incorporating signal mixing after the time-shifting modules to obtain a complete delay effect in the classical sense, and exploring their creative potential for audio and music applications.