Agnostic Dynamical Decoupling for Single-Qubit Gates

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.

Figures (5)

• Figure 1: The three smooth pulses needed to control all the generators, $\sigma_x$, $\sigma_y$, and $\sigma_y$ of SU(2). The gate implemented is an $R_z(\theta)$ gate with $\theta = 0.025 \pi$.
• Figure 2: Simultaneous control of 2 qubits while in presence of noise terms that couple them to an intermediate qubit. This, to demonstrate the second-order decoupling of said target qubits from one another for any intermediary quantum degrees of freedom. The gate implemented is an $R_z(\theta)$ gate with $\theta = 0.025 \pi$.
• Figure 3: Trotterized Representation of the simultaneous control of two-qubits. The target qubits for the $R_z$ gates are $q_0$ and $q_2$ and $q_1$ represents the bath qubit. The choice of error terms are $IZZ$ and $ZZI$
• Figure 4: Smooth pulses generated when the gate implemented is chosen at random.
• Figure 5: The decoupling also succeeds when the implemented gate (See \ref{['fig:pulses_random_gate']}), and we obtain a second-order error.