This paper improves the Gottesman-Knill theorem, which states that stabilizer circuits—quantum circuits composed of CNOT, Hadamard, and phase gates—can be efficiently simulated on classical computers. The improvements include a faster simulation algorithm that reduces the time complexity for measurements from O(n³) to O(n²), at the cost of a factor-2 increase in the number of bits needed to represent a state. The algorithm is implemented in a program called CHP, which can simulate thousands of qubits efficiently. The paper also shows that simulating stabilizer circuits is complete for the classical complexity class ⊕L, indicating that stabilizer circuits are unlikely to be universal for classical computation. Efficient algorithms are provided for computing inner products between stabilizer states and for putting stabilizer circuits into a canonical form with O(n²/log n) gates. The simulation algorithm is extended to handle mixed states, limited non-stabilizer gates, and general tensor-product initial states. The results demonstrate that stabilizer circuits have practical applications in quantum computing and quantum error correction, and that classical simulation of these circuits is feasible for large numbers of qubits.This paper improves the Gottesman-Knill theorem, which states that stabilizer circuits—quantum circuits composed of CNOT, Hadamard, and phase gates—can be efficiently simulated on classical computers. The improvements include a faster simulation algorithm that reduces the time complexity for measurements from O(n³) to O(n²), at the cost of a factor-2 increase in the number of bits needed to represent a state. The algorithm is implemented in a program called CHP, which can simulate thousands of qubits efficiently. The paper also shows that simulating stabilizer circuits is complete for the classical complexity class ⊕L, indicating that stabilizer circuits are unlikely to be universal for classical computation. Efficient algorithms are provided for computing inner products between stabilizer states and for putting stabilizer circuits into a canonical form with O(n²/log n) gates. The simulation algorithm is extended to handle mixed states, limited non-stabilizer gates, and general tensor-product initial states. The results demonstrate that stabilizer circuits have practical applications in quantum computing and quantum error correction, and that classical simulation of these circuits is feasible for large numbers of qubits.