Quantum Sensing of Fast Time-Varying Magnetic Field With Daubechies Wavelets

The waveform of the time-varying magnetic field can be reconstructed by combining the use of quantum sensing technology and orthogonal functions, such as Walsh and Haar wavelet functions, as the control sequences of qubits. However, the piecewise-constant nature of Walsh and Haar wavelet functions induces pulse-shaped artifacts in the reconstructed waveform. In this article, we propose a robust quantum sensing protocol by driving the qubits with control sequences based on high-smoothness Daubechies wavelets. The time-varying magnetic field waveform is reconstructed with negligible artifacts and higher accuracy. The essential mathematical relations between the qubit readout, the accumulated phase of the quantum state, and the wavelet coefficient are derived based on an intuitive model represented on the Bloch sphere. By controlling each qubit with a continuous microwave control sequence modulated by a Daubechies wavelet function, the yielded qubit readout can be related to a designated wavelet coefficient. These coefficients are then used to reconstruct the time-varying magnetic field waveform with higher smoothness and accuracy via an inverse wavelet transform. The reconstructions of single-tone, triple-tone, and noisy waveforms are simulated under various parameter designs of Daubechies wavelets to manifest the efficacy and accuracy of the proposed method. The waveform reconstruction method based on Daubechies wavelets can also be applied in magnetic resonance spectroscopy and measurements of gravity, electric fields, and temperature.