Reinforcement learning and numerical methods applied to some quantum information problems

This thesis explores diverse aspects of quantum information processing, addressing challenges in quantum communication, error correction, and metrology. The study begins with a study of a variational quantum algorithm designed to enhance quantum error correction techniques. Employing an unconventional distance to overcome the issue of barren plateaus, the algorithm showcases improved scalability and performance. This novel distance is the Quantum Wasserstein distance of order 1, which lacks a very common property, the unitary invariance. This property will be crucial to tame the barren plateaus phenomenon. Moving forward, this work includes an extensive analysis of the Dolinar receiver. We proposed a generalization to the Quantum State Discrimination problem, in which we relaxed one of its hypotheses, proposing then a solution to this generalized counterpart. The investigation provides a theoretical foundation for improving the discrimination capabilities of quantum states, with potential applications in quantum communication protocols. In particular, this new set of hypotheses can be extremely useful for quantum communication over very noisy optical quantum channels, and can also help in the problem of phase locking. Furthermore, the thesis introduces a general methodology grounded in reinforcement learning principles to tackle experimental design challenges in quantum metrology. This approach is manifested in the form of a Python library built on TensorFlow, facilitating the optimization of quantum measurements for enhanced precision and accuracy. The proposed framework offers a versatile tool for researchers and experimentalists working in quantum metrology, streamlining the process of designing experiments tailored to specific quantum systems. In summary, this thesis addresses some challenges in quantum information using numerical methods and provides innovative solutions that contribute to the ongoing development of the field.