The paper presents a quantum algorithm for solving the satisfiability problem (SAT) using adiabatic evolution. The algorithm involves evolving a quantum state according to a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. The evolution time must be large enough to ensure the system reaches the desired final ground state. The required evolution time depends on the minimum energy difference between the lowest states of the interpolating Hamiltonian, which is generally difficult to estimate. The authors provide some special symmetric cases of SAT where the symmetry allows for estimating the gap and show that in these cases, the algorithm runs in polynomial time. They also discuss the limitations of the method, such as the requirement for the Hamiltonian to commute with certain operators to avoid level crossing. The paper includes detailed analyses of one-, two-, and three-qubit examples to illustrate the concepts and provides numerical evidence for the behavior of the minimum gap in various problems.The paper presents a quantum algorithm for solving the satisfiability problem (SAT) using adiabatic evolution. The algorithm involves evolving a quantum state according to a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. The evolution time must be large enough to ensure the system reaches the desired final ground state. The required evolution time depends on the minimum energy difference between the lowest states of the interpolating Hamiltonian, which is generally difficult to estimate. The authors provide some special symmetric cases of SAT where the symmetry allows for estimating the gap and show that in these cases, the algorithm runs in polynomial time. They also discuss the limitations of the method, such as the requirement for the Hamiltonian to commute with certain operators to avoid level crossing. The paper includes detailed analyses of one-, two-, and three-qubit examples to illustrate the concepts and provides numerical evidence for the behavior of the minimum gap in various problems.