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arXiv:2310.15630 · Physical Review A

Compressive quantum waveform estimation

Alex Tritt, Joshua Morris, Christopher C. Bounds, Hamish A. M. Taylor, James Saunderson, Lincoln D. Turner

Published Feb 24, 2025• 0 citations
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Abstract

Quantum waveform estimation, in which quantum sensors sample entire time series, promises to revolutionize the sensing of weak and stochastic signals, such as the biomagnetic impulses emitted by firing neurons. For long duration waveforms with rapid transients, regular quantum sampling becomes prohibitively resource intensive as it demands many measurements with distinct control and readout. In this paper, we demonstrate how careful choice of quantum measurements, along with the modern mathematics of compressive sensing, achieves quantum waveform estimation of sparse signals in a number of measurements far below the Nyquist requirement. We sense synthesized neural-like magnetic waveforms with radio-frequency-dressed ultracold atoms, retrieving successful waveform estimates with as few measurements as compressive theoretical bounds guarantee.

DOI
10.1103/physreva.111.022625

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Quantum waveform estimation, in which quantum sensors sample entire time series, promises to revolutionize the sensing of weak and stochastic signals, such as the biomagnetic impulses emitted by firing neurons. For long duration waveforms with rapid transients, regular quantum sampling becomes prohibitively resource intensive as it demands many measurements with distinct control and readout. In this paper, we demonstrate how careful choice of quantum measurements, along with the modern mathematics of compressive sensing, achieves quantum waveform estimation of sparse signals in a number of measurements far below the Nyquist requirement. We sense synthesized neural-like magnetic waveforms with radio-frequency-dressed ultracold atoms, retrieving successful waveform estimates with as few measurements as compressive theoretical bounds guarantee.
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.
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We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to significantly reduce the number of signal coefficients that are required for reconstruction of time-varying parameters with high fidelity. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Random measurement matrices satisfying the restricted isometry property can be used efficiently to reconstruct signals that are sparse in any basis. Because many physical processes are approximately sparse in some basis, these methods can benefit a variety of applications such as quantum sensing and magnetometry with nitrogen-vacancy centers.
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