Quantum computers perform FIR signal filtering using state-space methods
State-Space-Based FIR Filtering on a Quantum Computer
Sound
Summary
Many signal processing tasks need a lot of computing power, and quantum computers might speed these up. The authors created a way to run finite impulse response (FIR) filters—a common tool in signal processing—on quantum computers using unitary circuits. They introduce a special quantum delay gate that acts like delay lines in digital signals and show how to build lowpass and other filters in this framework. They tested their method using a simulator that mimics quantum circuits.
What this means in practice
- •For quantum algorithm developers: Build quantum signal processing modules integrating FIR filtering in larger quantum algorithms.
- •For digital signal processing engineers: Explore future designs of FIR filters adapted for fault-tolerant quantum hardware to accelerate classical signal tasks.
Tested on simulated data.
Authors
Roope Salmi, Davide Rocchesso, Vesa Välimäki
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.