Quantum Compressive Sensing Meets Quantum Noise: A Practical Exploration

TL;DR

This paper explores the practical implementation of Quantum Compressive Sensing on real quantum hardware, analyzing its robustness under quantum noise and proposing modifications for improved performance in quantum signal processing.

Contribution

It presents the first practical deployment of Quantum Compressive Sensing on Amazon Braket, incorporating Quantum Imaginary Time Evolution and evaluating noise effects.

Findings

QCS can be implemented on current quantum hardware.

Quantum noise significantly affects QCS performance.

Proposed modifications improve robustness under noise.

Abstract

Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the Quantum Compressive Sensing (QCS) architecture, a quantum data-driven approach to compressive sensing where the state of the tensor network is represented by a quantum state over a set of entangled qubits, have shown promise in advancing quantum data-driven methods for compressive sensing. However, the QCS framework has remained largely untested on quantum computing resources or in the presence of quantum noise. In this work, we present a practical implementation of QCS on Amazon Braket, utilizing the Quantum Imaginary Time Evolution (QITE) projection technique to assess the framework's capabilities under quantum noise. We outline the necessary modifications to the QCS framework for deployment on Amazon Braket, followed by results under four types of quantum noise. Finally, we discuss potential long-term directions aimed at unlocking the full potential of quantum compressive sensing for applications such as signal recovery and image processing.