Quantum compressed sensing

TL;DR

Quantum compressed sensing (QCS) leverages quantum evolution to drastically reduce measurements needed for sparse signal reconstruction, achieving linear scaling with sparsity and independent of signal dimension.

Contribution

This work introduces QCS, a novel quantum paradigm that encodes signals into quantum states and performs support-set search without measurement trials, surpassing classical bounds.

Findings

Measurement number scales linearly with sparsity K

Reconstruction reduces to linear estimation

Experimental validation confirms linear scaling with sparsity

Abstract

How many measurements are fundamentally required to capture a signal. Shannon's information theory established the bedrock of this question in 1948, the Nyquist Shannon theorem set the first answer, and compressed sensing (CS) rewrote it in 2006 by reducing the required measurement number to M = O(Klog(N/K)) for a K sparse signal. Here, we propose quantum compressed sensing (QCS), a paradigm that reframes signal acquisition as a unitary quantum evolution. By encoding high dimensional signal information into a single quantum probe state, then introducing domain-alignment evolution,a physically realizable unitary transformation that maps the sparse basis directly onto the measurement basis. QCS executes the support-set search at the quantum level without consuming measurement trials. The logarithmic penalty vanishes, compressing the required measurement number from the classical bound to M =O(K) and reducing reconstruction from ill posed optimization to linear estimation. We experimentally validate QCS using frequency and time domain sparse signals, confirming that the measurement number scales linearly with sparsity and decouples entirely from the signal dimension. Our work provides a physical pathway toward ultimate information acquisition efficiency, with broad implications for sensing, imaging, and communication.