Finite Impulse Response Digital Filter Implementation Using Quantum Computation and Orthogonal Triangular Decomposition

In digital signal processing, the finite impulse response (FIR) filter is a fundamental tool for processing discrete-time signals. This paper explores the implementation of FIR filters using quantum computation methods. In this study, a quantum circuit for the FIR filter is designed using a normalized filter coefficient vector, orthogonal triangular decomposition commonly known as QR decomposition, and the transpilation tools provided by IBM’s software Qiskit SDK V2.3. Then, each block of the input signal is normalized to a unit-norm vector, loaded into a quantum register, and processed by the FIR filter quantum circuit to produce an output state. Quantum measurement is then performed on the output state to obtain a histogram, from which the first-bin data are scaled to compute the output sample of the filter. Finally, signal filtering experiments using FIR mean filters are conducted to demonstrate the effectiveness of the proposed quantum computation approach.