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arXiv:2601.19719

Optimally Driven Dressed Qubits

Alon Salhov, Sagi Nechushtan, Alex Retzker

quant-phphysics.app-phphysics.atom-phphysics.chem-phphysics.opticsSubmitted Jan 27, 2026• Announced Jan 28, 2026• 0 citations
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Abstract

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.

Comments
Main: 11 pages, 5 figures; SM: 6 pages, 1 figures

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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.
Single-qubit quantum gates are implemented as the time-controlled unitary evolution of a two-level system under harmonic driving. The rotating-wave approximation (RWA) provides closed-form gate parameters for weak coupling. Larger amplitudes, desirable to speed up the dynamics, make the RWA-designed gates inaccurate because of the neglected counter-rotating term, which also shifts the resonance (Bloch-Siegert shift). Here we study theoretically the infidelity of gates beyond the RWA, using the effective Magnus-Taylor Hamiltonian through second order in the inverse of the driving frequency. By detuning the driving frequency by an amplitude-dependent shift of Bloch-Siegert type and rescaling the operation time, the RWA gate conditions are recovered with corrected parameters. Numerical solutions of the Schrodinger equation show that these corrections lower the gate infidelity by several orders of magnitude, extending the range of usable amplitudes
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.
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 propose a general approach to implement ultrafast nonadiabatic geometric single- and two-qubit gates by employing counter-rotating effects. This protocol is compatible with most optimal control methods used in previous rotating-wave approximation (RWA) protocols; thus, it is as robust as (or even more robust than) the RWA protocols. Using counter-rotating effects allows us to apply strong drives. Therefore, we can improve the gate speed by 5--10 times compared to the RWA counterpart for implementing high-fidelity ($\ensuremath{\ge}\phantom{\rule{0.2em}{0ex}}99.99\mathrm{%}$) gates. Such an ultrafast evolution (nanoseconds, even picoseconds) significantly reduces the influence of decoherence (e.g., the qubit dissipation and dephasing). Moreover, because the counter-rotating effects no longer induce a gate infidelity (in both the weak and strong driving regimes), we can achieve a higher fidelity compared to the RWA protocols. Therefore, in the presence of decoherence, one can implement ultrafast geometric quantum gates with $\ensuremath{\ge}\phantom{\rule{0.2em}{0ex}}99\mathrm{%}$ fidelities.
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.
Qubit decoherence unavoidably degrades the fidelity of quantum logic gates. Accordingly, realizing gates that are as fast as possible is a guiding principle for qubit control, necessitating protocols for mitigating error channels that become significant as gate time is decreased. One such error channel arises from the counter-rotating component of strong, linearly polarized drives. This error channel is particularly important when gate times approach the qubit Larmor period and represents the dominant source of infidelity for sufficiently fast single-qubit gates with low-frequency qubits such as fluxonium. In this work, we develop and demonstrate two complementary protocols for mitigating this error channel. The first protocol realizes circularly polarized driving in circuit QED through simultaneous charge and flux control. The second protocol—commensurate pulses—leverages the coherent and periodic nature of counter-rotating fields to regularize their contributions to gates, enabling single-qubit gate fidelities reliably exceeding 99.997%. This protocol is platform independent and requires no additional calibration overhead. This work establishes straightforward strategies for mitigating counter-rotating effects from strong drives in circuit QED and other platforms, which we expect to be helpful in the effort to realize high-fidelity control for fault-tolerant quantum computing. Published by the American Physical Society 2024