A quantum approach for digital signal processing

Abstract

We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the sequency-ordered Walsh-Hadamard transform, as well as quantum circuits for low-pass, high-pass, and band-pass filtering. Additionally, we provide a proof of correctness for the quantum circuit designed to perform the sequency-ordered Walsh-Hadamard transform. The performance and accuracy of the proposed approach for signal filtering were illustrated using computational examples, along with corresponding quantum circuits, for DC, low-pass, high-pass, and band-pass filtering. Our proposed algorithm for signal filtering has a reduced gate complexity and circuit depth of $O({\log }_{2}N)$, compared to at least $O(({\log }_{2}N{)}^2)$ associated with Quantum Fourier Transform (QFT) based filtering (excluding state preparation and measurement costs). In contrast, classical Fast Fourier Transform (FFT) based filtering approaches have a complexity of $O(N{\log }_{2}N)$. This shows that our proposed approach offers a significant improvement over QFT-based filtering methods and classical FFT-based filtering methods. Such enhanced efficiency of our proposed approach holds substantial promise across several signal processing applications by ensuring faster computations and efficient use of resources via reduced circuit depth and lower gate complexity.

arXiv comment29 pages

References in corpus (4)

• Elementary gates for quantum computation
• A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations
• A hybrid classical-quantum algorithm for digital image processing
• A generalization of Bernstein-Vazirani algorithm with multiple secret keys and a probabilistic oracle

Cited by in corpus (4)

• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Hybrid classical-quantum image processing via polar Walsh basis functions
• Implementing Finite Impulse Response Filters on Quantum Computers
• Efficient quantum algorithm for weighted partial sums and numerical integration