Implementing Finite Impulse Response Filters on Quantum Computers

TL;DR

This paper explores how to implement classical finite impulse response (FIR) filters on quantum computers by encoding signals into quantum states and designing specific unitaries, opening new avenues for quantum signal processing.

Contribution

It introduces methods to realize FIR filters on quantum systems and strategies to cascade filters for higher-order processing, bridging classical signal processing with quantum computing.

Findings

Quantum encoding of classical signals achieved

Unitary designs for FIR filters developed

Framework for cascading filters proposed

Abstract

While signal processing is a mature area, its connections with quantum computing have received less attention. In this work, we propose approaches that perform classical discrete-time signal processing using quantum systems. Our approaches encode the classical discrete-time input signal into quantum states, and design unitaries to realize classical concepts of finite impulse response (FIR) filters. We also develop strategies to cascade lower-order filters to realize higher-order filters through designing appropriate unitary operators. Finally, a few directions for processing quantum states on classical systems after converting them to classical signals are suggested for future work.