Hadamard sensing channel: deterministic artifact suppression for quantum sensors

Abstract

Dynamical decoupling sequences are essential for nanoscale quantum sensing, but the finite duration of microwave pulses generates spurious responses. While phase randomization (PR) protocol can suppress these artifacts, they rely on probabilistic averaging. This introduces an inherent statistical variance that demands excessive sequence lengths and stringent hardware capabilities for true random phase generation. Here, we propose Hadamard sensing channel (HSC), a deterministic phase-design framework based on Hadamard matrices. HSC completely eliminates the statistical variance of PR by exactly and deterministically canceling spurious signals using a finite set of orthogonal phase patterns. Simulations confirm that HSC matches the ideal suppression of PR but exhibits superior robustness against control errors. HSC offers a mathematically exact and hardware-friendly solution for reliable high-resolution nanoscale nuclear magnetic resonance.