We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over $99.2%$ on the spin state of the nitrogen-vacancy center are realized with average durations shortened by $21.5%$ compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds $96.5%$ on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over $99.2%$ on the spin state of the nitrogen-vacancy center are realized with average durations shortened by $21.5%$ compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds $96.5%$ on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.

arXiv:2105.05481Physical Review ResearchDec 13, 202122 citations

A geometric approach to quantum control in a classical-like framework

Davide Pastorello

Aug 28, 20150 citations

Self-Adaptive Quantum System Control via Geometric Mapping

Jincheng Zhang

This paper investigates the application of geometric mapping to self-adaptive quantum system control. Traditional quantum control methods often rely on fixed, classical parameters, presenting limitations in adaptability and precision. We propose a novel algorithm that leverages geometric transformations to dynamically adjust the quantum system's state, offering a significant improvement in control fidelity and optimization capabilities. The core mechanism centers on a self-adaptive control algorithm predicated on geometric transformations, enabling precise state manipulation and optimization. We demonstrate the effectiveness of this approach through simulations, showcasing enhanced control accuracy and improved performance compared to existing methods.This paper investigates the application of geometric mapping to self-adaptive quantum system control. Traditional quantum control methods often rely on fixed, classical parameters, presenting limitations in adaptability and precision. We propose a novel algorithm that leverages geometric transformations to dynamically adjust the quantum system's state, offering a significant improvement in control fidelity and optimization capabilities. The core mechanism centers on a self-adaptive control algorithm predicated on geometric transformations, enabling precise state manipulation and optimization. We demonstrate the effectiveness of this approach through simulations, showcasing enhanced control accuracy and improved performance compared to existing methods.

Aug 31, 20260 citations

Pulse Quality Optimisation in Quantum Optimal Control

Dylan Lewis, Roeland Wiersema

Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.

quant-pharXiv:2604.25768Apr 29, 20260 citations

Advances in Quantum Control Theory

Jeffrey L. Krause

APSMar 1, 20010 citations

99.2%

on the spin state of the nitrogen-vacancy center are realized with average durations shortened by

21.5%

compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds

96.5%

on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.