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.
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.
Robust and high-fidelity control of electron spins in solids is the cornerstone for facilitating applications of solid-state spins in quantum information processing and quantum sensing. However, precise control of spin systems is always challenging due to the presence of various noises originating from the thermal environment and control fields. Here, noise-resilient quantum gates, designed with robust optimal control (ROC) algorithms, are demonstrated experimentally with nitrogen-vacancy centers in diamond to realize tailored robustness against detunings and Rabi errors simultaneously. In the presence of both 10% off-resonance detuning and 10% deviation of a Rabi frequency, we achieve an average single-qubit gate fidelity of up to 99.89%. Our experiments also show that, ROC-based multipulse quantum sensing sequences can suppress spurious responses resulting from finite widths and imperfections of microwave pulses, which provides an efficient strategy for enhancing the performance of existing multipulse quantum sensing sequences.
The ability to sense and control nuclear spins near solid-state defects might enable a range of quantum technologies. Dynamically decoupled radio-frequency (DDrf) control offers a high degree of design flexibility and long electron-spin coherence times. However, previous studies have considered simplified models and little is known about optimal gate design and fundamental limits. Here, we develop a generalized DDrf framework that has important implications for spin sensing and control. Our analytical model, which we corroborate by experiments on a single NV center in diamond, reveals the mechanisms that govern the selectivity of gates and their effective Rabi frequencies, and enables flexible detuned gate designs. We apply these insights to numerically show a 60 × sensitivity enhancement for detecting weakly coupled spins and study the optimization of quantum gates in multiqubit registers. These results advance the understanding for a broad class of gates and provide a toolbox for application-specific design, enabling improved quantum control and sensing.
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.
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 (Xπ/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.
Atom-like emitters in solids have emerged as promising platforms for quantum sensing and information processing. Among the major challenges are inhomogeneities in emitter fine structure, which complicates quantum control. Here, we introduce a framework that leverages this emitter diversity to simplify the experimental resources needed to create optically heralded spin cluster states across N q emitters from the conventional order O ( N q ) to O ( 1 ) within ensembles of N q ∼ 10 – 100 . Specifically, the optimized pulse sequence simultaneously corrects parameter variations (pulse-length error and frequency detuning error), achieving single-qubit gate fidelities exceeding 99.99% for errors (normalized relative to Rabi-drive strength) up to 0.3, while maintaining fidelities above 99% even for errors as large as 0.4. Applying this optimized pulse sequence in the form of a Carr-Purcell-Meiboom-Gill (CPMG) based dynamical decoupling protocol to the dominant noise spectral density of silicon-vacancy centers in diamond, our approach enhances ensemble-average coherence times by more than a factor of 7 relative to interleaved bang-bang-based CPMG. For state-of-the-art dilution refrigeration systems, we further estimate sharply reduced heating when driving a global resonant optimal dynamical decoupling across N q silicon-vacancy spins, potentially resolving the current trade-off between spin coherence and scaling to N q ≫ 1 . We further introduce a modified single-photon entanglement protocol with an efficient algorithm for deterministic entanglement compilation. Depending on the decoupling window, our method yields order O ( 10 2 – 10 4 ) more entanglement links than bang-bang sequences, with theoretical guarantees of order Ω ( N q ) unique links—improvable via control-parameter tuning. Our approach thus offers enhanced fidelity, scalability, and robustness. Together, these techniques provide foundational tools—including global unitary control, phase denoising, remote entanglement, and compilation—for scalable quantum computing architectures based on heterogeneous spin ensembles.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.