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arXiv:2608.06119

Hadamard sensing channel: deterministic artifact suppression for quantum sensors

Weibin Ni, Lei Sun

quant-phSubmitted Aug 6, 2026• Announced Aug 7, 2026• 0 citations
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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.

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7 pages, 3 figures

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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.
We develop theoretically and demonstrate experimentally a universal dynamical decoupling method for robust quantum sensing with unambiguous signal identification. Our method uses randomization of control pulses to simultaneously suppress two types of errors in the measured spectra that would otherwise lead to false signal identification. These are spurious responses due to finite-width π pulses, as well as signal distortion caused by π pulse imperfections. For the cases of nanoscale nuclear-spin sensing and ac magnetometry, we benchmark the performance of the protocol with a single nitrogen vacancy center in diamond against widely used nonrandomized pulse sequences. Our method is general and can be combined with existing multipulse quantum sensing sequences to enhance their performance.
We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to π pulse imperfections and spurious responses due to finite-width π pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond.
Quantum coherence remains a fundamental challenge for advancing quantum technologies. Although dynamical decoupling can suppress decoherence noise, it frequently misestimates decoherence times due to control errors -- a previously underappreciated issue. Here, we present Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method using group-structured phase configurations to filter spurious dynamics. Validated across molecular electron spins, nitrogen-vacancy centers in diamond, nuclear spins, trapped ions, and superconducting qubits, this technique enables accurate decoherence time characterization and enhanced state fidelity with linear complexity. Our results indicate that many reported ultralong decoherence times stem from artifacts like coherence-population mixing rather than genuine noise suppression. By ensuring dynamical authenticity, Hadamard phase cycling establishes a robust framework for reliable quantum control, paving the way for reassessment and advancement of coherence benchmarks in the NISQ era.
Nanoscale sensing experiments based on defects in diamond are at the forefront of quantum-technology research. Nanoscale NMR and MRI employ microwave pulses to decouple the quantum sensor from sources of decoherence, and to enhance weak signals from a single nuclear spin. Here finite pulse duration has been largely considered a source of experimental error, but the authors see it differently: A quantum model shows that seemingly spurious signals due to nonzero pulse width are predictable, allowing experimental protocols for either their full suppression, or their exploitation to increase resolution.
Sensing, localizing, and identifying individual nuclear spins or frequency components of a signal in the presence of a noisy environment requires the development of robust and selective methods of dynamical decoupling. An important challenge that remains to be addressed in this context are spurious higher-order resonances in current dynamical decoupling sequences as they can lead to the misidentification of nuclei or of different frequency components of external signals. Here we overcome this challenge with engineered quantum sensing sequences that achieve both enhanced robustness and the simultaneous suppression of higher-order-harmonic resonances. We experimentally demonstrate the principle using a single nitrogen-vacancy center spin sensor which we apply to the unambiguous detection of external protons.
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