Abstract Fast and accurate quantum operations of a single spin in room-temperature solids are required in many modern scientific areas, for instance in quantum information, quantum metrology, and magnetometry. However, the accuracy is limited if the Rabi frequency of the control is comparable with the transition frequency of the qubit due to the breakdown of the rotating wave approximation (RWA). We report here an experimental implementation of a control method based on quantum optimal control theory which does not suffer from such restriction. We demonstrate the most commonly used single qubit rotations, i.e. - and π-pulses, beyond the RWA regime with high fidelity and , respectively. They are in excellent agreement with the theoretical predictions, and . Furthermore, we perform two basic magnetic resonance experiments both in the rotating and the laboratory frames, where we are able to deliberately ‘switch’ between the frames, to confirm the robustness of our control method. Our method is general, hence it may immediately find its wide applications in magnetic resonance, quantum computing, quantum optics, and broadband magnetometry.
We present a theoretical study of single-qubit operations by oscillatory fields on various semiconductor platforms. We explicitly show how to perform faster gate operations by going beyond the universally used rotating-wave approximation (RWA) regime, while using only two sinusoidal pulses. We first show for specific published experiments how much error is currently incurred by implementing pulses designed using standard RWA. We then show that an even modest increase in gate speed would cause problems in using RWA for gate design in the singlet-triplet (ST) and resonant-exchange (RX) qubits. We discuss the extent to which analytically keeping higher orders in the perturbation theory would address the problem. More strikingly, we give a new prescription for gating with strong coupling far beyond the RWA regime. We perform numerical calculations for the phases and the durations of two consecutive pulses to realize the key Hadamard and $\frac{\ensuremath{\pi}}{8}$ gates with coupling strengths up to several times the qubit splitting. Working in this manifestly non-RWA regime, the gate operation speeds up by two to three orders of magnitude and nears the quantum speed limit without requiring complicated pulse shaping or optimal control sequences.
The applicability and performance of qubits dressed by classical fields are limited because their control protocols give rise to an undesired counter-rotating term (CRT). This in turn forces operation in a regime where a (dressed) rotating-wave approximation (RWA) is valid, thereby restricting key aspects of their operation. Here, using only a single coupling axis in the laboratory frame, we introduce a dressed-qubit control protocol that optimally removes the CRT, eliminating the need for the RWA and delivering substantial improvements in multiple performance metrics, including single-qubit gate speed, two-qubit gate fidelity, spectroscopic range, clock stability, and coherence preservation. In addition, we provide a general parameterization together with a Floquet-based coherence-time expression, which elucidates the protocol's working principles and lowers the barrier to adoption. Collectively, these advances position our scheme as the state-of-the-art strategy for qubit control, paving the way for a wider class of quantum technologies to be realized using dressed-qubit architectures.
In many quantum platforms, single-qubit gates are applied using a linear drive resonant with the qubit transition frequency, which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to consider the contribution from counterrotating terms to the qubit dynamics. The inclusion of counterrotating terms into the theoretical description gives rise to two challenges. First, it becomes challenging to analytically calculate the time evolution as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we derive and verify a correction to the drive pulses that minimizes the effect of these counterrotating terms in a two-level system. We then derive a second correction term that arises from noncomputational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware and calibration complexities.
We present investigations of radio-frequency (RF) resonances observed in an optically pumped rubidium vapor. By measuring the systematic shifts (the Bloch–Siegert shifts) of RF resonances in low magnetic fields, we demonstrate limitations of the rotating-wave approximation in the case of angular momentum F ≥ 1. The resonance shifts and deformations are characterized in a wide range of parameters and it is shown that the observed behavior is far more complex than in a standard two-level system. It is also demonstrated that the shifts can be controllably turned on or off by switching between the oscillating and rotating magnetic field. Experimental results are supported with numerical calculations, reproducing all features of the observed signals. Besides fundamental aspect of the research, application of rotating magnetic field helps to suppress/evaluate spectroscopic-measurement and precise-metrology systematic errors. The reported study has also important implications for quantum metrology and information processing beyond RWA and standard two-state qubit dynamics.
Quantum information processing comprises physical processes, which obey the quantum speed limit (QSL): high speed requires strong driving. Single-qubit gates using Rabi oscillation, which is based on the rotating wave approximation (RWA), satisfy this bound in the form that the gate time
T is inversely proportional to the Rabi frequency
Ω, characterizing the driving strength. However, if the gate time is comparable or shorter than the qubit period
T0≡2π/ω0, the RWA actually breaks down since the Rabi frequency has to be large compared to the qubit frequency
ω0 due to the QSL, which is given as
T≳π/Ω. We show that it is possible to construct a universal set of single-qubit gates at this strong-coupling and ultrafast regime, by adjusting the central frequency
ω and the Rabi frequency
Ω of the driving pulse. We observe a transition in the scaling behavior of the central frequency from the long-gate time regime (
T≫T0) to the short-gate time (
T≪T0) regime. In the former, the central frequency is nearly resonant to the qubit, i.e.,
ω≃ω0, whereas in the latter, the central frequency is inversely proportional to the gate time, i.e.,
ω∼π/T. We identify the transition gate time at which the scaling exponent
n of the optimal central frequency
ω∼Tn changes from
n=0 to
n=−1.
Abstract Fully autonomous precise control of qubits is crucial for quantum information processing, quantum communication, and quantum sensing applications. It requires minimal human intervention on the ability to model, to predict, and to anticipate the quantum dynamics, as well as to precisely control and calibrate single qubit operations. Here, we demonstrate single qubit autonomous calibrations via closed-loop optimisations of electron spin quantum operations in diamond. The operations are examined by quantum state and process tomographic measurements at room temperature, and their performances against systematic errors are iteratively rectified by an optimal pulse engineering algorithm. We achieve an autonomous calibrated fidelity up to 1.00 on a time scale of minutes for a spin population inversion and up to 0.98 on a time scale of hours for a single qubit
2π π 2 -rotation within the experimental error of 2%. These results manifest a full potential for versatile quantum technologies.