Researchers have made a significant breakthrough in understanding the origins of finite entanglement scaling, a fundamental concept in the tensor network ecosystem. By resolving an open problem, they have determined the actual perturbations induced by matrix product state approximations of critical systems, which deviate from the predictions of conformal field theory1. This discovery has far-reaching implications for the development of quantum computing and its potential impact on cryptography. The study demonstrates that the approximations used in matrix product states can lead to distinct perturbations, challenging the conventional understanding of entanglement scaling. This finding is crucial for the advancement of quantum computing, as it rewrites assumptions about computation and cryptography. The research has the potential to influence the design of quantum algorithms and the development of quantum-resistant cryptographic protocols, so understanding the origins of finite entanglement scaling is essential for practitioners seeking to harness the power of quantum computing securely.