Fast, Robust Qutrit Systems Achieve Non-Adiabatic Holonomic Gates with Error Suppression

Quantum computing seeks increasingly robust and efficient methods for manipulating quantum information, and researchers are now exploring techniques that move beyond traditional, slow adiabatic processes. Jie Lu, Jie-Dong Huang from Shanghai University, and Yang Qian, along with Ying Yan, demonstrate a new framework for creating fast and reliable quantum gates in qutrit systems, utilising a technique called non-adiabatic holonomic quantum computing. This work addresses a critical challenge in quantum computation, namely the susceptibility of quantum gates to errors caused by imperfections in control pulses and system parameters. By combining inverse engineering with time-dependent perturbation theory, the team develops a method that suppresses these errors, paving the way for more stable and scalable quantum computers applicable to a range of platforms, including superconducting circuits and trapped ions.

Motivated by shortcuts to adiabaticity, researchers develop a framework that combines inverse engineering with time-dependent perturbation theory to implement non-adiabatic holonomic quantum computing in qutrit systems under realistic error conditions. They derive analytical conditions that suppress second-order Rabi errors through tailored pulse parameters and eliminate detuning errors via a compensation pulse, demonstrating cancellation through careful pulse design. This analysis reveals the effectiveness of the compensation pulse in ensuring robust gate operations, offering a pathway towards more reliable quantum computation by actively mitigating common sources of error in qutrit-based systems.

Fidelity Mapping of Quantum Gate Performance

These contour maps illustrate the fidelity of NOT and S gates implemented on a quantum system as a function of Rabi error and detuning error. The detuning error is measured in megahertz, while the Rabi error represents the amplitude of a control pulse. The color scale indicates fidelity, ranging from low to high. Results are presented for scenarios both without and with a compensation pulse designed to mitigate the effects of control imperfections. The maps demonstrate that without compensation, gate fidelity significantly decreases as both Rabi and detuning errors increase, but applying the compensation pulse substantially improves fidelity across a wider range of error values, indicating its effectiveness.

Qutrit Gates Achieve High Fidelity Control

Scientists have developed a new method for implementing quantum computing using qutrit systems, achieving robust gate operations under realistic error conditions. This work focuses on non-adiabatic holonomic quantum computing and introduces a framework combining inverse engineering with time-dependent perturbation theory. The team derived analytical conditions to suppress second-order Rabi errors through tailored pulse parameters and eliminate detuning errors using a compensation pulse, demonstrating cancellation through careful pulse design. Experiments reveal that by setting specific parameters for pulse design, the second-order Rabi error terms are entirely eliminated, leading to a fidelity approaching one, limited only by detuning errors and excited-state population.

The team then introduced a compensation pulse to address these remaining detuning errors, effectively cancelling them and further enhancing gate performance. Measurements confirm that the compensation pulse fully eliminates second-order detuning errors, demonstrating its efficacy in experimental settings. The fidelity, accounting for both gate and compensation stages, is significantly improved, reaching values close to one under typical experimental conditions. Numerical simulations, using parameters and fidelities for four quantum gates, NOT, Hadamard, S, and T, demonstrate the effectiveness of the method. This approach delivers a pathway to fast and error-resilient holonomic gates, potentially enabling scalable quantum computing.

Holonomic Qutrit Gates Eliminate Key Errors

Scientists have developed a new strategy for implementing fast and robust quantum gates using non-adiabatic holonomic quantum computing in systems employing qutrits, quantum units extending beyond the standard qubit. The research team successfully designed tailored pulse parameters that eliminate second-order Rabi errors, a significant source of inaccuracy in quantum operations, and a compensation pulse that cancels second-order detuning errors. Analytical and numerical results closely align for four fundamental quantum gates, NOT, Hadamard, S, and T, demonstrating the reliability and feasibility of this approach. This framework demonstrates enhanced fidelity compared to existing methods, particularly in mitigating Rabi and detuning errors, and is adaptable to various quantum platforms including superconducting qubits, trapped ions, and atom-based systems. The team acknowledges that the compensation pulse doubles gate duration, potentially increasing susceptibility to decoherence, a process where quantum information is lost. Future work may focus on integrating time-optimal control methods to reduce evolution time and further enhance the robustness of these quantum gates, paving the way for more stable and scalable quantum computation.