Engineered Nonadiabatic Geometric Quantum Gates Achieve Robustness with Infidelity Scaling As, Surpassing Conventional Gate Performance

Geometric quantum gates promise inherent resistance to control errors, but realising this potential in practice has proven challenging. Xuan Zhang, from Southern University of Science and Technology, alongside Xiao-le Li and Jingjing Niu from the International Quantum Academy, and colleagues, now present a streamlined approach to nonadiabatic geometric quantum gates that significantly enhances their robustness. The team’s framework incorporates carefully designed constraints to minimise unwanted dynamical effects, achieving remarkably stable performance, and allows for the creation of gates using more flexible, noncyclic paths. Implementing their scheme on transmon qubits, researchers demonstrate high-fidelity single-qubit gates that exhibit exceptional resilience to errors in Rabi amplitude, with infidelity scaling far better than conventional methods, and they identify key considerations for extending this approach to two-qubit operations, paving the way for more reliable quantum computation across various quantum technologies.

Non-Adiabatic Geometric Control of Qubits

This work presents a comprehensive overview of geometric quantum control, exploring its application to superconducting qubits and related theoretical and experimental techniques. The research focuses on utilizing geometric phases and holonomy to create quantum gates inherently less sensitive to control errors than traditional methods. A key focus is on non-adiabatic geometric control, which enables faster gate operations and helps mitigate the effects of decoherence, a major obstacle to building scalable quantum computers. Researchers employ dynamical invariants and Lewis-Riesenfeld invariants as mathematical tools to design control pulses that preserve crucial quantum properties, leading to more robust and efficient gates.

The team investigates techniques to optimize the path a quantum state takes during gate operations, minimizing sensitivity to errors and maximizing fidelity. A central theme is the development of geometric gates resilient to various error types, including control inaccuracies, qubit frequency drifts, and unwanted interactions between qubits. Experimental work primarily utilizes transmon qubits and employs parametric coupling to implement two-qubit gates. Researchers also explore the use of first-order sideband transitions for gate operations, aiming to achieve high-fidelity single- and two-qubit gates essential for building larger quantum computers. This work represents a significant step towards building robust and scalable quantum computers, offering advantages over traditional dynamical control methods in terms of error resilience and paving the way for advancements in quantum information processing.

Geometric Gate Design with Robustness Constraints

Scientists have developed a novel framework for designing nonadiabatic geometric quantum gates, incorporating constraints to suppress unwanted dynamical effects and enhance robustness. This work centers on designing gates using noncyclic evolution paths, offering greater flexibility in gate construction. The team successfully implemented this scheme using transmon qubits, realizing high-fidelity single-qubit gates demonstrably robust against Rabi amplitude error, a common source of inaccuracy in quantum systems. The infidelity of these gates scales favourably compared to conventional dynamical gates, indicating improved performance.

The method involves systematically designing quantum gate evolution using the Lewis-Riesenfeld dynamical invariant and reverse-engineering techniques, with a focus on the geometric properties of the evolution. Researchers defined a cyclic process characterized by a closed curve in the parameter space of the drive signal’s amplitude and phase, choosing a complete set of auxiliary states and designing the evolution of orthogonal states to satisfy specific initial conditions. This process involved relating the evolving states to the auxiliary states via a unitary transformation determined by integrating a matrix composed of geometric and dynamical terms. To achieve purely geometric control, the team carefully selected parameterized auxiliary states and imposed constraints linking the drive signal’s amplitude and phase to these states, ensuring the cancellation of off-diagonal elements in the geometric and dynamical matrices.

By further imposing a constraint that eliminates accumulated dynamical phases, the team achieved a time evolution operator consisting solely of a geometric term, effectively realizing a pure geometric phase. This approach allows for the construction of arbitrary single-qubit gates by choosing appropriate initial values and satisfying the established constraints, and can be extended to realize iSWAP-type two-qubit gates. The study further investigated the robustness of these geometric gates against fluctuations in the driving pulse amplitude, revealing that while theoretically robust, the gates become susceptible to dynamical contamination under such perturbations. This finding underscores the importance of precise waveform calibration and control to maintain the desired performance characteristics.

Robust Geometric Gates Resist Control Errors

Scientists have achieved a breakthrough in the design of geometric quantum gates, demonstrating a streamlined framework for nonadiabatic geometric quantum gates that significantly enhances robustness against control errors. This work addresses a key challenge in quantum computing, where maintaining the fidelity of quantum operations is paramount. The team implemented this scheme on superconducting transmon qubits, realizing high-fidelity single-qubit gates that exhibit exceptional resilience to Rabi amplitude error, a common source of inaccuracy in quantum systems. Measurements confirm that the infidelity of these gates scales as O(ε⁴), where ε represents the Rabi amplitude error.

This represents a substantial improvement over conventional dynamical gates, which typically exhibit an O(ε²) scaling, indicating a four-fold reduction in error for a given level of amplitude fluctuation. The researchers achieved this enhanced performance by incorporating additional auxiliary constraints into the gate design, effectively suppressing dynamical contamination and bolstering the gate’s overall stability. This approach leverages the geometric properties of quantum evolution, creating gates less susceptible to local perturbations. Further analysis extended this framework to two-qubit gates utilizing parametric driving techniques.

Experiments revealed subtle limitations in two-qubit scenarios, identifying that performance can be compromised without careful attention to phase compensation and waveform calibration. Specifically, the team discovered that precise control over these parameters is crucial for maintaining the super-robustness observed in single-qubit gates. These findings underscore the importance of meticulous calibration and control in multi-qubit systems, paving the way for more reliable and scalable quantum computations. The demonstrated simplicity and generality of this super-robust gate scheme make it applicable across diverse quantum platforms, offering a promising pathway towards fault-tolerant quantum computing.

Robust Geometric Gates With Imperfect Control

This research establishes a streamlined framework for constructing nonadiabatic geometric quantum gates, demonstrating high fidelity even when control imperfections are present. By incorporating an additional constraint to minimize dynamical contamination, the team achieved consistent suppression of sensitivity to Rabi amplitude errors, a significant improvement over conventional dynamical gates. Experimental validation on transmon qubits confirms that infidelity scales favourably, indicating robust performance. The work extends beyond single-qubit operations, exploring the application of this approach to two-qubit gates via parametric driving.

However, analysis reveals limitations in these scenarios, specifically highlighting the importance of precise phase compensation and waveform calibration to maintain performance. While geometric gates do not automatically offer protection from all noise, this research demonstrates their value as a powerful design framework, offering a mathematically tractable foundation that simplifies the search for optimal solutions. This framework, combined with modern numerical optimization and error suppression techniques, provides a promising path toward developing high-fidelity, noise-resilient quantum gates applicable across diverse quantum platforms.