Speaker
Description
Physics-informed neural networks (PINNs) are a versatile methodology that integrates deep learning techniques with the solution of dynamics governed by differential equations, with applications across multiple areas of physics. In this work, we design and optimize a PINN-based control scheme that, instead of directly solving the dynamics of the system, uses the integration of the evolution equation as a physical constraint to learn and predict coherent control functions [1], for implementing quantum logic gates through hamiltonian dynamics. For doing so, we consider the single-qubit Hadamard gate and the two-qubit CNOT gate as coherent transformation objectives, to be implemented in neutral atom and superconducting-like platforms. To achieve this, the loss function is formulated such that the expected operation is considered to be effectively applied at a specific time (the final time). We calculate the fidelity between the quantum state obtained using the PINN scheme and the ideal state expected at the end of the evolution. As preliminary results, after training the PINN with a set of initial states suitable for each target gate, we obtain an average fidelity over that set of states of $99.99\%$ in the implementation of Hadamard and CNOT operations. We also calculate the effects on such dynamics under the influence of pure dephasing and amplitude damping noises, finding that Hadamard is more affected by the pure dephasing than amplitude damping noise in contrast to the case of CNOT. As a next step, average fidelity on a set of states different from the one set used in the training process will be evaluated and optimized for then to make some comparison with other control techniques.
References
[1] Ariel Norambuena, Marios Mattheakis, Francisco J. González and Raúl Coto. Physics-Informed Neural Networks for Quantum Control. Phys. Rev. Lett. 132, 010801 (2024).
Keywords: Physics-informed neural networks, quantum gates, quantum control.