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UDC-3: A Tunable Composite Pulse for Mixed-Axis Drift Suppression in Single-Qubit Gates

Sharma, Rishabh

Published Nov 16, 2025• 0 citations
Publisher

Abstract

We introduce UDC-3, a compact three-pulse composite control sequence designed to suppress mixed-axis coherent drift in single-qubit rotations. Standard composite pulses such as SK1 and BB1 primarily target symmetric amplitude errors, assuming that the control Hamiltonian remains aligned with the intended rotation axis. However, real quantum hardware often exhibits distorted effective rotation axes due to asymmetric calibration drift in multiple control channels. UDC-3 uses a short XYX prefix whose rotation angles are numerically optimized to maximize worst-case fidelity over two-axis drift (εx, εy ∈ [−0.12, 0.12]). Our optimized sequence improves worst-case fidelity from 66% (unoptimized UDC-3) to 98.79%, while preserving near-perfect performance at zero drift (99.91%). The optimized pulse also displays complete immunity to pure Y-axis drift, achieving 0% fidelity drop, outperforming SK1 and matching BB1 in symmetric regions while using fewer pulses. These results suggest that UDC-3 is an adaptable, hardware-aware correction primitive for coherent error suppression in near-term quantum devices. The sequence is compact, tunable, and suitable for calibration-limited platforms such as superconducting qubits, trapped ions, and spin qubits.

DOI
10.5281/zenodo.17624356

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We introduce UDC-3, a compact three-pulse composite control sequence designed to suppress mixed-axis coherent drift in single-qubit rotations. Standard composite pulses such as SK1 and BB1 primarily target symmetric amplitude errors, assuming that the control Hamiltonian remains aligned with the intended rotation axis. However, real quantum hardware often exhibits distorted effective rotation axes due to asymmetric calibration drift in multiple control channels. UDC-3 uses a short XYX prefix whose rotation angles are numerically optimized to maximize worst-case fidelity over two-axis drift (εx, εy ∈ [−0.12, 0.12]). Our optimized sequence improves worst-case fidelity from 66% (unoptimized UDC-3) to 98.79%, while preserving near-perfect performance at zero drift (99.91%). The optimized pulse also displays complete immunity to pure Y-axis drift, achieving 0% fidelity drop, outperforming SK1 and matching BB1 in symmetric regions while using fewer pulses. These results suggest that UDC-3 is an adaptable, hardware-aware correction primitive for coherent error suppression in near-term quantum devices. The sequence is compact, tunable, and suitable for calibration-limited platforms such as superconducting qubits, trapped ions, and spin qubits.
This work introduces UDC-3, a three-pulse composite control sequence designed to suppress coherent drift in quantum gates. We experimentally evaluate UDC-3 inside a quantum teleportation protocol on the IBM Quantum Platform under a deliberately injected 5% over-rotation drift. Statevector simulations and hardware runs show that UDC-3 improves the teleportation fidelity from approximately 0.80 to 0.83, corresponding to a ~12% reduction in coherent error. This paper presents the methodology, circuit design, and experimental data.
Composite pulse sequences, which produce arbitrary predefined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to 8 orders of experimental errors in the pulse amplitude and the pulse duration. Composite sequences for three basic quantum gates, X (not), Hadamard and arbitrary rotation, are derived. Three classes of composite sequences are presented: one symmetric and two asymmetric. They contain as their lowest members two well-known composite sequences: the three-pulse symmetric SCROFULOUS pulse and the four-pulse asymmetric BB1 pulse, which compensate first- and second-order errors, respectively. The shorter sequences are derived analytically, and the longer ones numerically (instead by nesting and concatenation, as usually done hitherto). Consequently, the composite sequences derived here match or outperform the existing ones in terms of either speed or accuracy, or both. For example, we derive a second-order composite sequence, which is faster (by about 13%) than the famous BB1 sequence. For higher-order sequences, the speedup becomes much more pronounced. This is important for quantum information processing as the sequences derived here provide more options for finding the sweet spot between ultrahigh fidelity and high speed.
Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for Rx(π/2)R_x(π/2)Rx​(π/2), which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.
The rapid growth in size of quantum devices demands efficient ways to control them, which is challenging for systems with thousands of qubits or more. Here, we present a simple yet powerful solution: robust, site-dependent control of an arbitrary number of qubits in parallel with only minimal local tunability of the driving field. Inspired by recent experimental advances, we consider access to only one of three constrained local control capabilities: local control of either the phase or amplitude of the beam at each qubit, or individual Z rotations. In each case, we devise parallelizable composite pulse sequences to realize arbitrary single-qubit unitaries robust against quasistatic amplitude and frequency fluctuations. Numerical demonstration shows that our approach outperforms existing sequences such as BB1 and CORPSE in almost all regimes considered, achieving average fidelity > 0.999 under a decoherence rate of ∼ 10 − 5 , even with a few percent amplitude and frequency error. Our results indicate that even for very large qubit ensembles, accurate, individual manipulation can be achieved despite substantial control inhomogeneity.
Ensemble nitrogen-vacancy (NV) centers are widely used for quantum sensing and magnetometry, where performance depends on the accurate implementation of microwave pulse sequences. In these systems, inhomogeneous broadening and short coherence times limit reliable multi-pulse control, while hardware imperfections and off-resonant excitation distort implemented rotations, making direct calibration of arbitrary gates tedious. To address this, we implement a control framework with a ZXZXZ gate decomposition which uses fixed-angle, phase-parameterized pulses, enabling universal single-qubit control from a single calibrated $ π/2$ primitive (Xπ/2X_{π/2}Xπ/2​) along with virtual Z operations. We compare a standard pulse with a composite pulse designed for high-power operation in a regime where the Rabi frequency is comparable to the hyperfine splitting, leading to non-uniform evolution across hyperfine levels. Using pre-determined combinations of π/2π/2π/2 pulse sequences, we observe that standard pulses rapidly deviate from ideal behavior under repeated application, while the composite pulse suppresses this error accumulation by more than 70%\%% for longer sequences despite its longer duration. In contrast, randomized benchmarking yields similar decay factors for both implementations, highlighting its limited sensitivity to coherent control errors. These results establish a practical route to robust control in short-coherence ensemble systems and emphasize the importance of pulse-level characterization.
Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below 10−310^{-3}10−3 within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.