Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Implementing Finite Impulse Response Filters on Quantum Computers

Aishwarya Majumdar, Bojko N. Bakalov, Dror Baron, Yuan Liu

TL;DR

The paper builds a unified framework linking classical and quantum signal processing by encoding classical time-domain data into quantum states and implementing FIR filtering and filter cascading via carefully constructed block-encoded unitaries. It demonstrates how time-domain DSP concepts can translate to unitary quantum operations, and discusses strategies for both classical-to-quantum and quantum-to-classical processing, including practical simulation on IBM Qiskit and the challenges posed by noise and measurement. The work provides concrete design recipes for amplitude encoding, unitary realization of multi-tap filters, and cascading schemes, while identifying open problems such as circuit-depth, measurement for phase information, and efficient quantum-classical interfaces. Overall, this work lays a foundation for cross-fertilization of classical DSP and quantum algorithms, with potential speedups in domain-specific filtering tasks and a roadmap for extending quantum signal processing techniques to broader applications.

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.

Implementing Finite Impulse Response Filters on Quantum Computers

TL;DR

The paper builds a unified framework linking classical and quantum signal processing by encoding classical time-domain data into quantum states and implementing FIR filtering and filter cascading via carefully constructed block-encoded unitaries. It demonstrates how time-domain DSP concepts can translate to unitary quantum operations, and discusses strategies for both classical-to-quantum and quantum-to-classical processing, including practical simulation on IBM Qiskit and the challenges posed by noise and measurement. The work provides concrete design recipes for amplitude encoding, unitary realization of multi-tap filters, and cascading schemes, while identifying open problems such as circuit-depth, measurement for phase information, and efficient quantum-classical interfaces. Overall, this work lays a foundation for cross-fertilization of classical DSP and quantum algorithms, with potential speedups in domain-specific filtering tasks and a roadmap for extending quantum signal processing techniques to broader applications.

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.
Paper Structure (8 sections, 15 equations, 3 figures)

This paper contains 8 sections, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Classical to Quantum
  3. Classical Digital to Quantum Digital Converter
  4. Processing Quantum Signals in Time Domain
  5. Filter Design, but Quantumly
  6. Filter Cascading, but Quantumly
  7. Quantum to Classical
  8. Discussion and Conclusions

Figures (3)

  • Figure 1: Interconnections between various signal processing domains.
  • Figure 2: Various schemes for processing classical digital signals on quantum digital systems. a) classical to quantum signal conversion; b) time-domain processing to implement the filters on quantum computers; c) cascading two filters on quantum computers.
  • Figure 3: Simulation results for a symmetric 3-tap high pass filter with low and high-frequency signal at the input. b)-d) depict the output of the classical filter, ideal quantum filter and quantum machine-simulator quantum filter.