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arXiv:2603.13477

Agnostic Dynamical Decoupling for Single-Qubit Gates

Gumaro Rendon

quant-phSubmitted Mar 13, 2026• Announced Mar 17, 2026• 0 citations
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Abstract

We introduce a method for designing smooth single-qubit control pulses that implement a desired gate while suppressing the effect of unknown static error sources to first order. Unlike dynamically corrected gate constructions that require prior knowledge of the noise model, the present approach is agnostic to the detailed form of the target-bath interaction. The method parametrizes the control propagator through an auxiliary matrix expansion over orthogonal basis functions and enforces decoupling through algebraic orthogonality and equal-norm constraints on the expansion coefficients. These conditions guarantee that the leading Magnus contribution of an arbitrary static interaction reduces to a term proportional to the identity on the target system, thereby cancelling first-order error effects independently of the microscopic origin of the noise. We further show that the same construction suppresses, to first order, mediated couplings between simultaneously controlled qubits when their interaction occurs through intermediate environmental degrees of freedom, yielding effective second-order decoupling of the induced inter-qubit interaction. By using a discrete cosine transform parametrization, the pulse-synthesis problem is cast into a numerically stable constrained optimization with a minimal number of free parameters. Numerical examples for $R_z$ rotations and random single-qubit unitaries demonstrate smooth control fields that realize the target gates while remaining robust against arbitrary static single-qubit noise and mediated multi-qubit couplings. These results provide a hardware-friendly route toward noise-agnostic dynamically corrected single-qubit gates.

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We introduce a method for designing smooth single-qubit control pulses that implement a desired gate while suppressing the effect of unknown static error sources to first order. Unlike dynamically corrected gate constructions that require prior knowledge of the noise model, the present approach is agnostic to the detailed form of the target-bath interaction. The method parametrizes the control propagator through an auxiliary matrix expansion over orthogonal basis functions and enforces decoupling through algebraic orthogonality and equal-norm constraints on the expansion coefficients. These conditions guarantee that the leading Magnus contribution of an arbitrary static interaction reduces to a term proportional to the identity on the target system, thereby cancelling first-order error effects independently of the microscopic origin of the noise. We further show that the same construction suppresses, to first order, mediated couplings between simultaneously controlled qubits when their interaction occurs through intermediate environmental degrees of freedom, yielding effective second-order decoupling of the induced inter-qubit interaction. By using a discrete cosine transform parametrization, the pulse-synthesis problem is cast into a numerically stable constrained optimization with a minimal number of free parameters. Numerical examples for RzR_zRz​ rotations and random single-qubit unitaries demonstrate smooth control fields that realize the target gates while remaining robust against arbitrary static single-qubit noise and mediated multi-qubit couplings. These results provide a hardware-friendly route toward noise-agnostic dynamically corrected single-qubit gates.
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure hidden within the time-dependent Schr\"odinger equation that provides a simple way to view the entire solution space of pulses that suppress noise errors in a system's evolution. In this framework, any single-qubit gate that is robust against quasistatic noise to first order corresponds to a closed three-dimensional space curve, where the driving fields that implement the robust gate can be read off from the curvature and torsion of the space curve. Gates that are robust to second order are in one-to-one correspondence with closed curves whose projections onto three mutually orthogonal planes each enclose a vanishing net area. We use this formalism to derive examples of dynamically corrected gates generated from smooth pulses. We also show how it can be employed to analyze the noise-cancellation properties of pulses generated from numerical algorithms such as grape. A similar geometrical framework exists for quantum systems of arbitrary Hilbert space dimension.
Dynamically correcting for unwanted interactions between a quantum system and its environment is vital to achieving the high-fidelity quantum control necessary for a broad range of quantum information technologies. In recent work, we uncovered the complete solution space of all possible driving fields that suppress transverse quasistatic noise errors while performing single-qubit phase gates. This solution space lives within a simple geometrical framework that makes it possible to obtain globally optimal pulses subject to a set of experimental constraints by solving certain geometrical optimization problems. In this work, we solve such a geometrical optimization problem to find the fastest possible pulses that implement single-qubit phase gates while canceling transverse quasistatic noise to second order. Because the time-optimized pulses are not smooth, we provide a method based on our geometrical approach to obtain experimentally feasible smooth pulses that approximate the time-optimal ones with minimal loss in gate speed. We show that in the presence of realistic constraints on pulse rise times, our smooth pulses significantly outperform sequences based on ideal pulse shapes, highlighting the benefits of building experimental waveform constraints directly into dynamically corrected gate designs.
The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. Existing methods to obtain smooth pulses are either restricted to two-level systems, require an optimization over noise realizations, or limited to piecewise-continuous pulse sequences. In this paper, we present the first general method for obtaining truly smooth pulses that minimizes sensitivity to noise, eliminating the need for sampling over noise realizations and making assumptions regarding the underlying statistics of the experimental noise. We parametrize the Hamiltonian using a neural network, which allows the use of a large number of optimization parameters to adequately explore the functional control space. We demonstrate the capability of our approach by finding smooth shapes, which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.
Abstract Low-frequency time-dependent noise is one of the main obstacles on the road toward a fully scalable quantum computer. The majority of solid-state qubit platforms, from superconducting circuits to spins in semiconductors, are greatly affected by 1/f noise. Among the different control techniques used to counteract noise effects on the system, dynamical decoupling sequences are one of the most effective. However, most dynamical decoupling sequences require unbounded and instantaneous pulses, which are unphysical and can only implement identity operations. Among methods that do restrict to bounded control fields, there remains a need for protocols that implement arbitrary gates with lab-ready control fields. In this work, we introduce a protocol to design bounded and continuous control fields that implement arbitrary single-axis rotations while shielding the system from low-frequency time-dependent noise perpendicular to the control axis. We show the versatility of our method by presenting a set of non-negative-only control pulses that are immediately applicable to quantum systems with constrained control, such as singlet-triplet spin qubits. Finally, we demonstrate the robustness of our control pulses against classical 1/f noise and noise modeled with a random quantum bath, showing that our pulses can even outperform ideal dynamical decoupling sequences.
We demonstrate a hardware-agnostic protocol for realizing fast, high-fidelity gates through dynamical decoupling (DD) pulse sequences applied to a central qubit coupled to target qubits. The target qubits are controlled by leveraging their intrinsic interaction with the central qubit, eliminating the need for slow, error-prone direct control. We develop and implement the DD-gate protocol within two distinct frameworks: a general model with minimal assumptions, benchmarked on a gate-based digital quantum simulator given by the IBM quantum (IBMQ) platforms; and an experimentally realistic case with a N 15 -vacancy center ( NV 15 ) in diamond. Using IBMQ, we are able to elucidate the underlying quantum dynamics of the DD gates and test them, independently of experimental constraints. For NV 15 , we realize the protocol considering system-specific properties, which could represent a significant reduction in gate duration and improved technological scalability compared with current dynamical-decoupling-based control. We also propose a simple application for high-efficiency polarization of the N 15 nuclear spin that could potentially be less technically demanding than current methods. Altogether, this work provides a robust strategy for quantum control that can be implemented in arbitrary systems fitting the central-target qubit architecture. Beyond these results, our open-source simulations and implementations for both platforms provide a practical framework for simulating time-dependent qubit dynamics on noisy intermediate-scale quantum era gate-based quantum processors.
Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation. Since the derived noise sensitivity metric remains independent of the coupling details between the system and the environment, our protocol demonstrates robustness against arbitrary Markovian noises within the first-order weak coupling approximation. Numerical validation through quantum state transfer and gate operations reveals near-unity fidelity across diverse noise regimes, achieving orders-of-magnitude error suppression compared to target-only approaches. This framework bridges critical gaps between theoretical control design and experimental constraints, establishing a broadly applicable strategy for high-fidelity quantum information processing across platforms such as superconducting circuits, trapped ions, and solid-state qubits.