Analytical two-pulse control of universal single-qubit gates in rotational ultracold NaCs molecules

TL;DR

This paper introduces an analytical two-pulse control method for high-fidelity single-qubit gates in ultracold NaCs molecules, enhancing quantum control precision and scalability.

Contribution

It develops a closed-form analytical framework for universal single-qubit gates using rotational states, achieving high fidelity and minimal leakage.

Findings

Gate fidelities above 0.9999 in simulations

Minimal population leakage in multi-gate sequences

Practical gate tomography via polarization detection

Abstract

Complex control protocols and sensitivity to experimental imperfections have limited the practical implementation of quantum gate operations. Here, we present an analytical framework for universal single-qubit gates using rotational states of ultracold NaCs molecules. By encoding qubits in the lowest rotational energy levels, we employ a first-order Magnus expansion to derive closed-form unitary evolution from an optimized two-pulse sequence. This approach establishes precise amplitude and phase conditions for arbitrary single-qubit rotations, achieving gate fidelities above 0.9999 in numerical simulations. We further demonstrate that complex multi-gate sequences, including phase-locked operations, can be executed with minimal population leakage into auxiliary states. The time-dependent molecular orientation is shown to faithfully encode both the gate truth table and coherence dynamics, enabling practical gate tomography via weak-field polarization detection. Our analytical method is also applicable to other molecules and physical platforms, offering a potential path to high-fidelity, scalable molecular quantum processors.