Individuals' privacy and legal regulations demand genomic data be handled and studied with highly secure privacy-preserving techniques. In this work, we propose a feasible Secure Multiparty Computation (SMC) system assisted with quantum cryptographic protocols that is designed to compute a phylogenetic tree from a set of private genome sequences. This system significantly improves the privacy and security of the computation thanks to three quantum cryptographic protocols that provide enhanced

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... curity against quantum computer attacks. This system adapts several distance-based methods (Unweighted Pair Group Method with Arithmetic mean, Neighbour-Joining, Fitch-Margoliash) into a private setting where the sequences owned by each party are not disclosed to the other members present in the protocol. We theoretically evaluate the performance and privacy guarantees of the system through a complexity analysis and security proof and give an extensive explanation about the implementation details and cryptographic protocols. We also implement a quantum-assisted secure phylogenetic tree computation based on the Libscapi implementation of the Yao, the PHYLIP library and simulated keys of two quantum systems: Quantum Oblivious Key Distribution and Quantum Key Distribution. This demonstrates its effectiveness and practicality. We benchmark this implementation against a classical-only solution and we conclude that both approaches render similar execution times, the only difference being the time overhead taken by the oblivious key management system of the quantum-assisted approach.