The paper discusses the application of quantum mechanics to decision trees, which are used to solve computational problems. The authors introduce a quantum algorithm that evolves a state through the tree, starting from the root node. They prove that if a classical algorithm can reach the $n$-th level in polynomial time, then the quantum algorithm can do so as well. However, they also provide examples where the classical algorithm requires exponential time, while the quantum algorithm can solve the problem in polynomial time. The paper further explores the construction of the Hilbert space and the Hamiltonian for quantum evolution through decision trees, showing that it aligns with conventional quantum computation. The authors conclude by discussing a specific family of trees that is quantum penetrable but not classically penetrable, highlighting the potential advantages of quantum algorithms in certain scenarios.The paper discusses the application of quantum mechanics to decision trees, which are used to solve computational problems. The authors introduce a quantum algorithm that evolves a state through the tree, starting from the root node. They prove that if a classical algorithm can reach the $n$-th level in polynomial time, then the quantum algorithm can do so as well. However, they also provide examples where the classical algorithm requires exponential time, while the quantum algorithm can solve the problem in polynomial time. The paper further explores the construction of the Hilbert space and the Hamiltonian for quantum evolution through decision trees, showing that it aligns with conventional quantum computation. The authors conclude by discussing a specific family of trees that is quantum penetrable but not classically penetrable, highlighting the potential advantages of quantum algorithms in certain scenarios.