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Machine learning techniques are increasingly being used in fundamentalresearch to solve various challenging problems. Here we explore one suchtechnique to address an important problem in quantum communication scenario.While transferring quantum information through a noisy quantum channel, theutility of the channel is characterized by its quantum capacity. Quantumchannels, however, display an intriguing property called super-additivity ofcoherent information. This makes the calculation of quantum capacity a hardcomputational problem involving optimization over an exponentially increasingsearch space. In this work, we first utilize a neural network ansatz torepresent quantum states and then apply an evolutionary optimization scheme toaddress this problem. We find regions in the three-parameter space of qubitPauli channels where coherent information exhibits this super-additivityfeature. We characterised the quantum codes that achieves high coherentinformation, finding several non-trivial quantum codes that outperforms therepetition codes for some Pauli channels. For some Pauli channels, these codesdisplays very high super-additivity of the order of 0.01, much higher than theobserved values in other well studied quantum channels. We further compared thelearning performance of the Neural Network ansatz with the raw ansatz to findthat in the three-shot case, the neural network ansatz outperforms the rawrepresentation in finding quantum codes of high coherent information. We alsocompared the learning performance of the evolutionary algorithm with a simpleParticle Swarm Optimisation scheme and show empirical results indicatingcomparable performance, suggesting that the Neural Network ansatz coupled withthe evolutionary scheme is indeed a promising approach to finding non-trivialquantum codes of high coherent information.

Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms