Quantum superresolution and noise spectroscopy with quantum computing

TL;DR

This paper demonstrates how quantum computing techniques can significantly speed up the detection of weak incoherent signals in quantum metrology, with applications in astrophysics, dark matter, and quantum gravity.

Contribution

It introduces quantum algorithms for superresolution and noise spectroscopy that outperform traditional tomography methods in speed and efficiency.

Findings

Quantum algorithms accelerate detection of weak signals.

Speedup over full-state tomography scales with quantum system dimension.

Applicable to diverse fields like astrophysics and quantum gravity.

Abstract

Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are not precisely known. In particular, we consider weak Schur sampling, density matrix exponentiation, and quantum signal processing for testing the rank, purity, and spectral gap of the unknown quantum state to detect the incoherent signal. We show that these algorithms are faster than full-state tomography, which scales with the dimension of the Hilbert space. We apply our results to detecting exoplanets, stochastic gravitational waves, ultralight dark matter, geontropic quantum gravity, and Pauli noise.