Fast Geometric Gates Achieve High Fidelity through Superadiabatic Transitionless Driving

Quantum computation increasingly explores geometric principles to build more resilient quantum gates, but achieving these gates typically demands lengthy operation times which leave systems vulnerable to errors. Researchers, including M. Estefanía Rus, Alejandro Ferrón, and Omar Osenda, alongside Sergio S. Gomez, now demonstrate a method for creating fast and accurate geometric gates by combining a technique called Superadiabatic Transitionless Driving with the concept of dressed states. Their work focuses on applying this approach to a two-level system, specifically the nitrogen-vacancy centre in diamond, and reveals how to eliminate unwanted dynamical phases to achieve purely geometric control. The results demonstrate robust gate performance even with significant environmental noise, and importantly, extend the protocol to create more complex two-qubit gates, paving the way for scalable quantum technologies.

Nitrogen-Vacancy Centers as Solid-State Qubits

Quantum computers rely on qubits, the quantum equivalent of classical bits, and scientists are exploring various physical systems to build these qubits. This research focuses on nitrogen-vacancy (NV) centers in diamond, defects in the diamond structure where a nitrogen atom replaces a carbon atom next to an empty space. These NV centers possess unique quantum properties, making them promising candidates for qubits due to their ability to store and process quantum information, with the electron spin within the NV center serving as the qubit itself. A key challenge in quantum computing is implementing quantum gates, the fundamental building blocks of quantum computations.

This work explores geometric quantum gates, a method that manipulates the qubit’s state along a specific path, offering increased resilience to certain types of noise, with researchers particularly interested in exceptionally robust holonomic gates and practical non-adiabatic gates. This research is conducted alongside studies of superconducting qubits to provide a broader context for qubit development. Maintaining the quantum state of a qubit for a sufficient duration, known as coherence time, is crucial for performing complex calculations. Long coherence times are essential because qubits are highly susceptible to environmental noise that can cause errors.

This research aims to improve coherence times and enhance the robustness of qubits and gates against this noise, exploring ways to harness the hyperfine interaction between the electron spin of the NV center and the nuclear spins of nearby carbon atoms. Scientists are actively developing techniques to implement high-fidelity geometric quantum gates using NV centers, utilizing the geometric phase acquired by the qubit as it evolves along a specific path and finding ways to speed up these gates without sacrificing accuracy. Efforts to extend coherence times involve using diamond enriched with the isotope 12C, improving the quality of the diamond material, and applying pulses to the qubit to suppress noise, with the ultimate goal of creating scalable quantum registers to build more powerful quantum computers. This research contributes to the advancement of quantum computing by focusing on solid-state qubits, which are potentially scalable and compatible with existing microfabrication techniques. This approach, applied to a nitrogen-vacancy (NV) center in diamond, allows for rapid gate operations while maintaining robustness against decoherence, a major limitation in quantum computing. The team designed microwave pulses to drive the qubit state along a specific path, ensuring the accumulation of a purely geometric phase. Initial attempts to accelerate these gates using SATD introduced an unwanted dynamical phase, which researchers overcame by exploiting the flexibility in choosing the basis for describing the qubit’s state, effectively eliminating this dynamical phase and enabling the implementation of the desired geometric gates.

Experiments employed a static magnetic field to simplify the NV center’s spin system, reducing it to an effective two-level subspace for easier control. The method involves carefully controlling the frequency and amplitude of the microwave field, designing pulses that drive the system along a specific trajectory on the Bloch sphere, accumulating a geometric phase that defines the quantum gate operation. Researchers investigated the influence of decoherence and systematic errors in the control pulses, demonstrating that the approach remains robust and suitable for reliable quantum gate implementation, and extended the protocol to design a two-qubit gate, demonstrating the viability of this method for practical quantum computing and scalable information processing.

Fast, High-Fidelity Gates via Geometric Phase Control

Scientists have developed a method for creating high-fidelity quantum gates using the geometric phase, a technique that promises robust quantum operations. Experiments revealed that by carefully manipulating the microwave field driving the NV center, the unwanted dynamical phase can be canceled, resulting in purely geometric operations. Analysis of the gate performance demonstrates the ability to achieve high fidelities even when subjected to systematic errors and environmental decoherence.

The team assessed gate fidelity by defining a metric that quantifies the overlap between the ideal and realized quantum gates, revealing that the SATD protocol induces pulse modifications that are experimentally feasible. Further investigations into gate robustness show that different types of gates respond differently to systematic errors. For example, the NOT gate maintains significantly higher fidelities than the S gate when there are errors in the frequency of the driving field, while the S gate proves more robust when there are deviations in the strength of the driving field, aligning with the underlying physical mechanisms of each operation. Measurements confirm that even with substantial shifts in the qubit’s frequency, fidelities remain high, and simulations incorporating environmental decoherence demonstrate a linear decay of gate fidelity with increasing dephasing rates, with the S gate being more sensitive to dephasing processes. These results demonstrate the potential of this method for building scalable quantum information processing systems.

Fast, Robust Quantum Gates via Geometric Control

This research demonstrates a method for creating fast and highly accurate quantum gates using geometric principles combined with a technique called shortcuts-to-adiabaticity. The team successfully designed single and two-qubit gates that leverage the robustness of geometric quantum computation while significantly reducing the time needed for operations, thereby mitigating the effects of decoherence. Numerical simulations indicate these gates can maintain fidelities exceeding 99. 9% under typical systematic errors and over 99. 4% even with substantial environmental noise, suggesting practical feasibility in systems like nitrogen-vacancy centers in diamond.

The approach involves carefully shaping microwave pulses to drive the quantum system, effectively canceling unwanted dynamical phases and enabling purely geometric operations. While the current work focuses on a specific trajectory for gate implementation, the authors emphasize the protocol’s generality and are actively extending it to accommodate a wider range of paths. Acknowledging experimental limitations, the team notes that the fidelity of two-qubit gates is constrained by fixed hyperfine coupling values.