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arXiv:2609.31913

Gate Synthesis in Dephasing-Limited Nitrogen-Vacancy Ensembles

Ankita Chakravarty, Arnaud Carignan-Dugas, Eva Dupont-Ferrier, Yves Bérubé-Lauzière

quant-phSubmitted Sep 25, 2026• Announced Sep 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Ensemble nitrogen-vacancy (NV) centers are widely used for quantum sensing and magnetometry, where performance depends on the accurate implementation of microwave pulse sequences. In these systems, inhomogeneous broadening and short coherence times limit reliable multi-pulse control, while hardware imperfections and off-resonant excitation distort implemented rotations, making direct calibration of arbitrary gates tedious. To address this, we implement a control framework with a ZXZXZ gate decomposition which uses fixed-angle, phase-parameterized pulses, enabling universal single-qubit control from a single calibrated $ π/2$ primitive ($X_{π/2}$) along with virtual Z operations. We compare a standard pulse with a composite pulse designed for high-power operation in a regime where the Rabi frequency is comparable to the hyperfine splitting, leading to non-uniform evolution across hyperfine levels. Using pre-determined combinations of $π/2$ pulse sequences, we observe that standard pulses rapidly deviate from ideal behavior under repeated application, while the composite pulse suppresses this error accumulation by more than 70$\%$ for longer sequences despite its longer duration. In contrast, randomized benchmarking yields similar decay factors for both implementations, highlighting its limited sensitivity to coherent control errors. These results establish a practical route to robust control in short-coherence ensemble systems and emphasize the importance of pulse-level characterization.

Comments
12 pages, 8 figures

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The sensitivity of practical solid quantum sensing can be boosted up by increasing the number of probes. However, the effects of spin dephasing caused by inhomogeneous broadening and imperfect quantum control can reduce the fidelity of quantum control and the sensitivity of quantum sensing with the dense ensemble of probes, such as nitrogen-vacancy (NV) centers in diamond. Here, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening and control errors via optimized modulation of the control field. Such a composite-pulse was verified on NV center to keep high fidelity quantum control up to a spectrum detuning as large as 110% of Rabi frequency. The sensitivity of the magnetometer with NV center ensemble was experimentally improved by a factor of 4, comparing to dynamical decoupling with a normal rectangular pulse. Our work marks an important step towards high trustworthy ultra-sensitive quantum sensing with imperfect quantum control in practical applications. The used principle is universal and not restricted to NV center ensemble magnetometer.
Microwave control of the negatively charged nitrogen-vacancy (NV) defect in diamond is usually based on a two-level approximation of its ground state that is only valid in the regime of high bias magnetic fields or low microwave power. We present the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level, thanks to an effective Raman coupling. The protocol may be used in the low-field regime and for high-frequency sensing. Furthermore, we propose a scheme to perform fast single-qubit gates in the double quantum transition, consisting of pulse trains of constant frequency and intensity. We analyze its robustness with respect to pulse-timing errors resulting from inaccurate identification of system parameters or phase-control limitations. We also demonstrate that the technique can be implemented in the presence of unknown electric or strain fields.
Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for Rx(π/2)R_x(π/2)Rx​(π/2), which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.
Continuous gate sets are a key ingredient for near-term quantum algorithms. Here, we demonstrate a hardware-efficient, continuous set of controlled arbitrary-phase ( CZ θ ) gates acting on flux-tunable transmon qubits. This implementation is robust to control pulse distortions on time scales longer than the duration of the gate, making it suitable for deep quantum circuits. Our calibration procedure makes it possible to parameterize the continuous gate set with a single control parameter, the idle time between the two rectangular halves of the net-zero control pulse. For calibration and characterization, we develop a leakage measurement based on coherent amplification, and a new cycle design for cross-entropy benchmarking. We demonstrate gate errors of 0.7 % and leakage of 4 × 10 − 4 across the entire gate set. This native gate set has the potential to reduce the depth and improve the performance of near-term quantum algorithms compared to decompositions into CZ π gates and single-qubit gates. Moreover, we expect the calibration and benchmarking methods to find further possible applications.
Implementing high-fidelity quantum gates on solid-state spin ensembles is challenging in the strong-disorder regime, where the detuning spread is comparable to the maximum Rabi frequency of the control field. We address the challenges in this regime through two complementary approaches. When the hyperfine coupling produces a set of well-separated detuning peaks across subensembles of electron spins, as in ¹⁰B¹⁵N hBN V⁻_B centers, we map the problem onto quantum signal processing (QSP) with detuning as the signal variable and aim to generate different target unitaries at each peak. Averaging uniformly over all sets of four target x rotation gates, we achieved 97% gate fidelity. We furthermore uncovered an emergent low-dimensional geometric structure within a sub-family of the QSP pulses in the space of optimal control angles. When detuning is instead broadened into a regime where detuning fluctuation equals or exceeds the Rabi frequency, the QSP ansatz fails. We leverage the transformer architecture trained on “composite pulse tokenization” to address the challenge. The model effectively extract a non-perturbative disorder canceling mechanism from analytical composite pulses, and we achieved the high 99.1% average fidelity over all SU(2) gates with pulse duration of 13.1π, outperforming the state-of-the-art composite pulse optimized for the strongly disordered regime. Our work paves the way towards high-fidelity control of strongly disordered spin ensembles with limited control field strength, enabling sensitivity-limited quantum sensing on solid-state platforms and a route to electron-nuclear entangling gates in hBN that exploit, rather than suppress, the hyperfine structure.
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