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Quantum superresolution and noise spectroscopy with quantum computing

James W. Gardner, Federico Belliardo, Gideon Lee, Tuvia Gefen, Liang Jiang

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.

Quantum superresolution and noise spectroscopy with quantum computing

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.
Paper Structure (7 sections, 2 theorems, 33 equations, 1 figure, 1 table)

This paper contains 7 sections, 2 theorems, 33 equations, 1 figure, 1 table.

Table of Contents

  1. Appendix
  2. Proof of Proposition \ref{['prop:kl']}
  3. Support-preserving case
  4. Scaling in signal size
  5. Proof of Proposition \ref{['prop:wss']}
  6. Proof of Eq. \ref{['eq:QSP sample complexity']}
  7. Kraus operator detection

Key Result

Proposition 1

Let $\hat{\rho}_n$ be a state on a $d$-dimensional Hilbert space $\mathcal{H}=\mathcal{H}_\parallel\oplus\mathcal{H}_\perp$ with $\text{supp}(\hat{\rho}_n)=\mathcal{H}_\parallel$. Consider a support-extending perturbation $\vartheta_0\hat{\Delta}$ with $\text{supp}(\hat{\rho}_n+\vartheta_0\hat{\Delt

Figures (1)

  • Figure 1: (Left) Sources of weak incoherent signals encoded in bosonic modes. We study unitarily invariant properties of these signals to be robust to nuisance processes such as spatial misalignment. (Right) Circuit of a quantum computer to sense such signals. Many copies of the unknown quantum state are stored in a qubit-based memory, then combined coherently following some algorithm, and finally measured.

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2