Adiabatic quantum computation is polynomially equivalent to standard quantum computation. This result shows that any quantum algorithm can be efficiently simulated by an adiabatic computation, and vice versa. The adiabatic model, which involves slowly evolving a quantum system from an initial Hamiltonian to a final Hamiltonian, is shown to be as powerful as the standard quantum circuit model. The equivalence holds even when considering physically realistic scenarios with particles on a two-dimensional grid and nearest neighbor interactions. This result has implications for the design of quantum algorithms and the construction of fault-tolerant quantum computers. The key insight is that the computational power of adiabatic computation can be characterized in terms of the spectral gaps of sparse matrices, making it accessible to a broader scientific audience. The paper also addresses the practical feasibility of adiabatic computation, showing that it can be implemented with two-local Hamiltonians on a two-dimensional grid, which is more realistic for experimental realization. The results demonstrate that adiabatic computation can simulate any quantum computation efficiently, and that the model is robust against certain types of noise. The paper also highlights the importance of spectral gaps in determining the efficiency of adiabatic algorithms and raises open questions about the potential of adiabatic computation in quantum computing.Adiabatic quantum computation is polynomially equivalent to standard quantum computation. This result shows that any quantum algorithm can be efficiently simulated by an adiabatic computation, and vice versa. The adiabatic model, which involves slowly evolving a quantum system from an initial Hamiltonian to a final Hamiltonian, is shown to be as powerful as the standard quantum circuit model. The equivalence holds even when considering physically realistic scenarios with particles on a two-dimensional grid and nearest neighbor interactions. This result has implications for the design of quantum algorithms and the construction of fault-tolerant quantum computers. The key insight is that the computational power of adiabatic computation can be characterized in terms of the spectral gaps of sparse matrices, making it accessible to a broader scientific audience. The paper also addresses the practical feasibility of adiabatic computation, showing that it can be implemented with two-local Hamiltonians on a two-dimensional grid, which is more realistic for experimental realization. The results demonstrate that adiabatic computation can simulate any quantum computation efficiently, and that the model is robust against certain types of noise. The paper also highlights the importance of spectral gaps in determining the efficiency of adiabatic algorithms and raises open questions about the potential of adiabatic computation in quantum computing.