State-Space-Based FIR Filtering on a Quantum Computer
Abstract
Many signal processing tasks require intensive computations. Quantum computing promises to accelerate certain tasks, but algorithms must be designed around the limitations of quantum mechanics. This paper provides a quantum implementation of finite impulse response (FIR) filters, which are a widely used tool in classical signal processing. The filter can be parallelized and composed as part of larger quantum algorithms, with potential for speedups using quantum amplitude estimation and future fault-tolerant quantum hardware. To accomplish these properties, we introduce a state-space framework wherein sample-based signal processing is performed with unitary quantum circuits. We present the quantum delay gate as the quantum analog of the delay line in discrete-time signal processing. Unitary circuits intrinsically describe lossless systems, but we also implement lowpass and other bounded filters by emulating a projection operator. The FIR filter implementation is tested and demonstrated with a quantum circuit simulator.
Related
- Finite-temperature transition-window weights on a fault-tolerant quantum computer: duplex filtering on a thermal purification
- Bell Test and Quantum State-Space Geometry
- Mamba Quantum Eigensolver (MQE): A Selective State Space Model for Scalable Ground State Simulations in Quantum Chemistry
- Quantum ensembles as waves on state space
- Classical and Quantum Dynamics in State Space: Projective Hilbert Space, Measurement, and Classical Emergence
BibTeX
@misc{salmi2026statespacebased,
title = {{State-Space-Based FIR Filtering on a Quantum Computer}},
author = {Roope Salmi and Davide Rocchesso and Vesa Välimäki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20331},
eprint = {2609.20331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20331},
}
RIS
TY - UNPB
TI - State-Space-Based FIR Filtering on a Quantum Computer
AU - Roope Salmi
AU - Davide Rocchesso
AU - Vesa Välimäki
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20331
UR - https://arxiv.org/abs/2609.20331
AB - Many signal processing tasks require intensive computations. Quantum computing promises to accelerate certain tasks, but algorithms must be designed around the limitations of quantum mechanics. This paper provides a quantum implementation of finite impulse response (FIR) filters, which are a widely used tool in classical signal processing. The filter can be parallelized and composed as part of larger quantum algorithms, with potential for speedups using quantum amplitude estimation and future fault-tolerant quantum hardware. To accomplish these properties, we introduce a state-space framework wherein sample-based signal processing is performed with unitary quantum circuits. We present the quantum delay gate as the quantum analog of the delay line in discrete-time signal processing. Unitary circuits intrinsically describe lossless systems, but we also implement lowpass and other bounded filters by emulating a projection operator. The FIR filter implementation is tested and demonstrated with a quantum circuit simulator.
ER -