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Background cancellation for frequency-selective quantum sensing

Ricard Puig, Nathan Constantinides, Bharath Hebbe Madhusudhana, Daniel Bowring, C. Huerta Alderete, Andrew T. Sornborger

Abstract

A key challenge in quantum sensing is the detection of weak time dependent signals, particularly those that arise as specific frequency perturbations over a background field. Conventional methods usually demand complex dynamical control of the quantum sensor and heavy classical post-processing. We propose a quantum sensor that leverages time independent interactions and entanglement to function as a passive, tunable, thresholded frequency filter. By encoding the frequency selectivity and thresholding behavior directly into the dynamics, the sensor is responsive only to a target frequency of choice whose amplitude is above a threshold. This approach circumvents the need for complex control schemes and reduces the post-processing overhead.

Background cancellation for frequency-selective quantum sensing

Abstract

A key challenge in quantum sensing is the detection of weak time dependent signals, particularly those that arise as specific frequency perturbations over a background field. Conventional methods usually demand complex dynamical control of the quantum sensor and heavy classical post-processing. We propose a quantum sensor that leverages time independent interactions and entanglement to function as a passive, tunable, thresholded frequency filter. By encoding the frequency selectivity and thresholding behavior directly into the dynamics, the sensor is responsive only to a target frequency of choice whose amplitude is above a threshold. This approach circumvents the need for complex control schemes and reduces the post-processing overhead.
Paper Structure (10 sections, 74 equations, 3 figures)

This paper contains 10 sections, 74 equations, 3 figures.

Table of Contents

  1. Filtering a single amplitude of a frequency
  2. Proof of the protocol
  3. The protocol for a zero signal
  4. The response function at first order for a nonzero signal
  5. Control along $\boldsymbol{n}_{\omega_{0}} = \pm \hat{x}$.
  6. Control along $\boldsymbol{n}_{\omega_{0}} = \pm \hat{y}$.
  7. Control along $\boldsymbol{n}_{\omega_{0}} = \pm \hat{z }$.
  8. Bound on the error
  9. The final response function
  10. Heisenberg scaling

Figures (3)

  • Figure 1: Two qubits are prepared in a Bell state. Qubit 1 couples to both the signal $\boldsymbol{s}(t)$ and the background $\boldsymbol{b}(t)$, while qubit 2 couples only to the background. The joint evolution coherently cancels the background contribution, isolating the response to the signal.
  • Figure 2: Frequency selection of the protocol. Box plot of the sensor response for different control frequencies $\omega_0$. Each data point corresponds to evolution over one signal period, with the background field randomized across 200 realizations. The background is a normalized random function with support on ten frequencies, while the signal is a single sinusoid at $\omega = 10\pi$.
  • Figure 3: Error of the response function. Error $|r|$ in the estimated probability as a function of the signal strength $\epsilon = \|\boldsymbol{s}\|_2 = \|\boldsymbol{b}\|_2$, with random Fourier coefficients. The blue curve shows the average deviation between the estimator and the exact probability, while the brown curve shows the maximum error observed. Polynomial regressions $f(\epsilon) = b\epsilon^3 + c \epsilon^4$ are fitted to both data sets, yielding $f_{\rm A}(\epsilon) = 9.78\times10^{-4}\,\epsilon^3 + 6.56\times10^{-3}\,\epsilon^4,\ R^2=0.9999$ for the average case and $f_{\rm W}(\epsilon)=4.57\times10^{-2}\,\epsilon^3 + 2.74\times10^{-2}\,\epsilon^4,\ R^2=0.94681$ for the worse case. Errors are computed from 2000 randomly generated functions with fixed frequency support ($10$ and $7$ for $\boldsymbol{b}(t),\boldsymbol{s}(t)$ respectively).