Understanding and mitigating noise in two level quantum systems is essential for achieving high fidelity qubit control. Conventional frequency tracking techniques, such as Ramsey interferometry, are fundamentally limited by trade offs between sensitivity, bandwidth, and dynamic range. Here we introduce the adiabatic tangentially-modulated (ATM) pulse, a pulse derived from quantum adiabatic theory that maps qubit detuning onto a sigmoidal, near-binary response. Using numerical simulations supported by analytical modelling, we show that pulse sensitivity and detuning range can be independently engineered through simple design parameters. We derive scaling relations governing these quantities and demonstrate their agreement with simulation. A single shot ATM measurement achieves sensitivity comparable to that obtained from multi-shot Ramsey averaging, enabling tracking of substantially higher frequency noise components with a lower closed-loop white-noise floor. In addition, this pulse exhibits strong robustness to amplitude fluctuations compared with binary response pulses derived from the Shinnar-Le Roux formalism. Together, these properties establish the ATM pulse as a promising approach for robust qubit frequency tracking.
Understanding and mitigating noise in two level quantum systems is essential for achieving high fidelity qubit control. Conventional frequency tracking techniques, such as Ramsey interferometry, are fundamentally limited by trade offs between sensitivity, bandwidth, and dynamic range. Here we introduce the adiabatic tangentially-modulated (ATM) pulse, a pulse derived from quantum adiabatic theory that maps qubit detuning onto a sigmoidal, near-binary response. Using numerical simulations supported by analytical modelling, we show that pulse sensitivity and detuning range can be independently engineered through simple design parameters. We derive scaling relations governing these quantities and demonstrate their agreement with simulation. A single shot ATM measurement achieves sensitivity comparable to that obtained from multi-shot Ramsey averaging, enabling tracking of substantially higher frequency noise components with a lower closed-loop white-noise floor. In addition, this pulse exhibits strong robustness to amplitude fluctuations compared with binary response pulses derived from the Shinnar-Le Roux formalism. Together, these properties establish the ATM pulse as a promising approach for robust qubit frequency tracking.
Abstract Quantum sensors promise revolutionary advances in medical imaging, energy production, mass detection, geodesy, foundational physics research, and a host of other fields. In many sensors, the signal takes the form of a changing qubit frequency, which is detected with a Ramsey interference measurement. Unfortunately, environmental noise decoheres the qubit state, reducing signal. Here we introduce a protocol for enhancing the sensitivity of a measurement of a qubit's frequency in the presence of decoherence. We use a continuous drive to stabilize one component of the qubit's Bloch vector, enhancing the effect of a small static frequency shift. We demonstrate our protocol on a superconducting qubit, enhancing sensitivity per measurement shot by 1.65x and sensitivity per qubit evolution time by 1.09x compared to standard Ramsey interferometry. We explore the protocol theoretically and numerically, finding maximum enhancements of 1.96x and 1.18x, respectively. We also show that the protocol is robust to parameter miscalibrations. Our protocol provides an unconditional enhancement in signal-to-noise ratio compared to standard Ramsey interferometry. It requires no feedback and no extra control or measurement resources, and can be immediately applied in a wide variety of quantum computing and quantum sensor technologies to enhance their sensitivities.
Achieving high-fidelity single- and two-qubit gates is essential for executing arbitrary digital quantum algorithms and for building error-corrected quantum computers. We propose a theoretical framework for implementing quantum gates using frequency- and amplitude-modulated microwave control, which extends conventional amplitude modulation by introducing frequency modulation as an additional degree of control. Our approach operates on fixed-frequency qubits, converting the need for qubit frequency tunability into drive frequency modulation. Using Floquet theory, we analyze and design these drives for optimal fidelity within specified criteria. Our framework spans adiabatic to nonadiabatic gates within the Floquet framework, ensuring broad applicability across gate types and control schemes. Using typical transmon qubit parameters in numerical simulations, we demonstrate a universal gate set-including the X, Hadamard, phase, and CZ gates-with control error well below 0.1% and gate times of 25-40 ns for single-qubit operations and 125-135 ns for two-qubit operations. Furthermore, we show an always-on CZ gate tailored for driven qubits, which has gate times of 80-90 ns.
State-of-the-art single-qubit gates on superconducting transmon qubits can achieve the fidelities required for error-corrected computations. However, parameter fluctuations due to qubit instabilities, environmental changes, and control inaccuracies make it difficult to maintain this performance. To mitigate the effects of these parameter variations, we numerically derive gates robust to amplitude and frequency errors using gradient ascent pulse engineering (GRAPE). We analyze how fluctuations in qubit frequency, drive amplitude, and coherence affect gate performance over time. The robust pulses suppress coherent errors from drive amplitude drifts over 15 times more than a Gaussian pulse with derivative removal by adiabatic gate (DRAG) corrections. Furthermore, the robust gates, originally designed to compensate for quasi-static errors, also demonstrate resilience to stochastic, time-dependent noise, which is reflected in the dephasing time. They suppress added errors during increases in dephasing by up to 1.7 times more than DRAG.
Holonomic quantum computation (HQC) offers an inherently robust approach to quantum gate implementation by exploiting quantum holonomies. While adiabatic HQC benefits from robustness against certain control errors, its long runtime limits practical utility due to increased exposure to environmental noise. Nonadiabatic HQC addresses this issue by enabling faster gate operations but compromises robustness. In this work, we propose a scheme for fast holonomic quantum gates based on the π -pulse method, which accelerates adiabatic evolution while preserving its robustness. By guiding the system Hamiltonian along geodesic paths in the parameter space and applying phase-modulating π pulses at discrete points, we realize a universal set of holonomic gates beyond the conventional adiabatic limit. Our scheme allows for arbitrary single-qubit and two-qubit controlled gates within a single-loop evolution and provides additional tunable parameters for flexible gate design. These results demonstrate a promising path toward high-fidelity, fast, and robust quantum computation .
We propose an adiabatic protocol for implementing a controlled-phase gate ${\mathrm{CZ}}_{\ensuremath{\theta}}$ with continuous $\ensuremath{\theta}$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, 6P in 87Rb, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $\ensuremath{\theta}$ of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate can be accumulated on the logic qubit state ∣11⟩ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $\ensuremath{\theta}$, we can obtain the fidelity of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate over 99.7% in less than $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$, in the presence of spontaneous emission from intermediate and Rydberg states. And in particular for $\ensuremath{\theta}=\ensuremath{\pi}$, we benchmark the performance of the CZ gate by taking into account various experimental imperfections, such as Doppler shifts, fluctuation of Rydberg-Rydberg interaction strength, inhomogeneous Rabi frequency, and noise of driving fields, etc., and show that the predicted fidelity is able to maintain at about 98.4% after correcting the measurement error. This gate protocol provides a robustness against the fluctuation of pulse amplitude and a flexible way for adjusting the entangling phase, which may contribute to the experimental implementation of near-term noisy intermediate-scale quantum computation and algorithm with neutral-atom systems.
We developed a highly sensitive and long-term stable diamond quantum magnetometer by integrating a dual-feedback system that compensates for common- and differential-mode frequency shifts in double-quantum (DQ) 4-Ramsey interferometry. Detecting extremely weak magnetic-field signals requires extensive signal accumulation to enhance the signal-to-noise ratio. However, deviations from the optimal operating frequencies caused by thermal drift or environmental magnetic noise severely hinder the long-term stability of such a sensing system. To overcome the limitation, we first derived analytical solutions for the signal response to common- and differential-mode detunings based on a detuning-inclusive Hamiltonian to theoretically clarify the robustness limit in DQ 4-Ramsey sensing. Guided by this theoretical model, we introduced synchronized frequency modulation and a dual-feedback scheme to independently track and compensate for these frequency shifts while maintaining an optimal magnetic-field response. The proposed method enabled stable continuous operation against temperature variations of 2.8 K. By maintaining a magnetic field sensitivity of 7.0 pT/Hz^1/2 in the frequency range of 5-100 Hz for a prolonged duration of 4 hours, we achieved an extremely low noise floor of 64 fT/Hz^1/2. During prolonged continuous sensing, the system exhibited the expected 1/T^1/2 scaling with integration time T, and prevented both the underestimation of amplitude and waveform distortion. These results establish a robust approach for long-term DQ 4-Ramsey diamond magnetometry and demonstrate its potential for detecting weak biomagnetic signals.