Quantum Gates Become More Reliable with AI-Guided Calibration Techniques

A new method for calibrating quantum gates on two qutrits has been demonstrated by Amine Jaouadi and Sahel Ashhab at ECE-Paris School of Engineering, in collaboration with Advanced ICT Research Institute, Japan, Research Institute, Tokyo University of Science, and National Institute of Information and Communications Technology. The approach combines optimal control and deep reinforcement learning to address the difficulties in controlling higher-dimensional quantum systems, known as qudits, which offer advantages over traditional qubits. It initially generates high-fidelity control pulses, then uses reinforcement learning to adapt these pulses and account for imperfections in real-world hardware, sharply improving the key performance of gates across varying device parameters. This establishes reinforcement learning as a scalable technique for calibrating quantum gates in these complex, high-dimensional systems, enabling more stable and practical quantum computation.

Hybrid optimisation delivers sub-0.01 error rates for qutrit controlled-phase gates

Error rates for controlled-phase gates on two qutrits dropped to below 0.01, a threshold previously unattainable due to sensitivity to device imperfections. This improvement establishes a new benchmark for high-fidelity quantum control in these more complex, three-level systems. Conventional methods struggled with the increased spectral crowding and limited controllability inherent in qutrit-based computation. Spectral crowding arises because each additional energy level within a qudit introduces more possible transitions, leading to overlapping signal frequencies that complicate precise control. Furthermore, the control space expands significantly with each added level, making it harder to identify optimal pulse sequences. A calibration technique systematically reduces sensitivity to parameter fluctuations in two qutrit controlled-phase gates by integrating optimal control theory with contextual deep reinforcement learning. Optimal control, a well-established technique in quantum information science, is used to initially design control pulses that maximise gate fidelity, given a specific set of device parameters. However, real-world quantum devices inevitably exhibit variations in their physical properties due to manufacturing tolerances and environmental noise. These variations can significantly degrade gate performance, necessitating a robust calibration procedure.

Maintaining high fidelity was achieved even when device parameters varied by up to 10 per cent from their nominal values, as demonstrated across a set of virtual devices. This robustness is crucial for practical quantum computation, as it reduces the need for extremely precise and expensive hardware fabrication and control systems. A cosine-basis parametrization of residual corrections lowered the dimensionality of the reinforcement learning problem and ensured smooth control pulses, resulting in strong performance. The use of a cosine basis restricts the possible corrections to a set of smooth, oscillating functions, which simplifies the learning process and prevents the reinforcement learning agent from generating unrealistic or physically impossible control signals. This dimensionality reduction is essential for efficient training of the deep reinforcement learning agent, particularly as the complexity of the quantum system increases. The reinforcement learning step adapts optimal control solutions across ensembles of devices, systematically reducing the impact of parameter fluctuations. The contextual aspect of the deep reinforcement learning algorithm allows it to learn a mapping between device parameters and optimal control corrections, enabling it to generalise to unseen device configurations.

Detailed analysis of the optimised pulses revealed that the deep reinforcement learning component focused on correcting for subtle parameter drifts, rather than attempting to redesign the entire pulse sequence. This suggests that the reinforcement learning agent is effectively learning to compensate for systematic errors in the device, rather than trying to overcome fundamental limitations in the control hardware. Qudits, unlike conventional qubits which represent information as 0 or 1, utilise multiple energy levels, allowing for denser data encoding and potentially faster processing. A qubit has a two-dimensional Hilbert space, while a qutrit occupies a three-dimensional space. This increased dimensionality allows a single qutrit to store more information than a single qubit. The number 3 is significant as it represents the number of energy levels naturally accessed by superconducting transmons, making them attractive qutrit candidates. Superconducting transmons are artificial atoms fabricated on microchips, and their energy levels can be precisely controlled using microwave pulses. The inherent three-level structure of these devices simplifies the implementation of qutrit-based quantum computation. This offers potential advantages in computational speed and data density compared to qubit-based systems, potentially enabling the solution of complex problems that are intractable for classical computers.

Robust controlled-phase gate calibration advances multi-level qudit quantum computation

Calibration of qudits, quantum systems using more than two energy levels, is now underway to build more powerful and efficient computers. The development of reliable calibration techniques is a critical step towards realising the full potential of qudit-based quantum computation. While this hybrid approach, combining established optimal control with adaptive deep reinforcement learning, shows promise, the work focuses exclusively on controlled-phase gates. The controlled-phase gate is a fundamental building block for many quantum algorithms, but a complete quantum computer requires a universal set of gates, including single-qubit rotations and other two-qubit interactions. Whether this calibration technique can be generalised to other, equally important, gate types needed for complex quantum algorithms remains to be seen. Generalising this approach to other gate types will require careful consideration of the specific control challenges associated with each gate and may necessitate modifications to the reinforcement learning algorithm.

Establishing robust calibration for a single gate type within a qudit system provides a key methodology for further development. The successful demonstration of robust calibration for the controlled-phase gate provides a valuable proof-of-concept and establishes a framework for calibrating other gate types. Utilising quantum systems with three or more energy levels moves beyond the limitations of standard two-level qubits. The increased dimensionality of qudits allows for more efficient encoding of quantum information and potentially enables the development of more powerful quantum algorithms. The achievement of robust controlled-phase gates was enabled by integrating optimal control with deep reinforcement learning. This hybrid approach doesn’t redesign control pulses entirely, but instead subtly corrects for imperfections arising from manufacturing variations in physical hardware, demonstrating an efficient use of computational resources and paving the way for scalable quantum computation. By focusing on correcting for small deviations from ideal behaviour, the reinforcement learning agent can significantly improve gate fidelity without requiring extensive retraining or redesign of the control system. This efficiency is crucial for scaling up to larger quantum systems with many qudits.

Researchers successfully demonstrated robust controlled-phase gates using two qutrits, a system utilising three energy levels rather than the standard two of qubits. This matters because it addresses a key challenge in building larger quantum computers: maintaining accuracy when physical components aren’t perfect. The team achieved this by combining optimal control techniques with deep reinforcement learning to calibrate the gates, improving performance despite variations in device parameters. The authors note that further work is needed to extend this calibration method to other essential gate types for more complex quantum algorithms.