Implementing Finite Impulse Response Filters on Quantum Computers

2025-01-17

AI Summary

Bridging the gap between classical digital signal processing (DSP) and quantum computing remains challenging, particularly for implementing linear time-invariant (LTI) systems such as finite impulse response (FIR) filters on quantum hardware. Method: This work proposes a systematic methodology to map classical discrete-time FIR filters onto quantum systems. It encodes classical signals into multi-qubit states, designs parameterized unitary operators capable of realizing arbitrary-order FIR responses, and constructs a modular, cascade-compatible quantum circuit architecture. Contribution/Results: The approach rigorously preserves LTI system properties and enables high-order filter synthesis via cascading low-order modules—enhancing design flexibility and hardware adaptability. Experimental validation confirms theoretical feasibility and circuit implementability. This work establishes the first scalable, programmable, and cascadeable quantum FIR filtering framework, thereby advancing quantum signal processing and narrowing the theoretical and practical divide between classical DSP and quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Quantum Computing
• Finite Impulse Response Filter
• Quantum-to-Classical Signal Processing

Innovation

• Quantum Computing
• FIR Filters
• Signal Processing