This paper investigates the feasibility of universal quantum computation (UQC) using a model that includes only Clifford unitaries, the creation of the state |0⟩, and qubit measurements in the computational basis. Additionally, it allows the creation of a one-qubit ancilla in a mixed state ρ, which is a parameter of the model. The goal is to determine for which ρ UQC can be efficiently simulated. The authors construct purification protocols that consume several copies of ρ and produce a single output qubit with higher polarization. These protocols allow one to increase the polarization only along certain "magic" directions. If the polarization of ρ along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, called a magic state. The authors show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of their results with the Gottesman-Knill theorem is discussed. The paper discusses the theory of fault-tolerant quantum computation, which defines an important number called the error threshold. If the physical error rate is less than the threshold value δ, it is possible to stabilize computation by transforming the quantum circuit into a fault-tolerant form where errors can be detected and eliminated. However, if the error rate is above the threshold, errors begin to accumulate, resulting in rapid decoherence and rendering the output of the computation useless. The actual value of δ depends on the error correction scheme and the error model. The paper discusses the connection between the model and the Gottesman-Knill theorem, which states that operations from the Clifford group can only produce quantum states of a very special form called stabilizer states. The authors show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The paper also discusses the concept of magic states, which are special states that, when combined with Clifford group operations, allow for universal quantum computation. The authors construct two particular schemes of UQC simulation based on a method called magic states distillation. They prove that adaptive computation in the basis O allows one to simulate universal quantum computation whenever the fidelity between ρ and a T-type or H-type magic state exceeds certain thresholds. The authors also discuss the error analysis of their model, showing that the threshold error probability for the distillation of T-type and H-type magic states is approximately 0.173 and 0.927, respectively. The paper concludes with a discussion of the implications of their results for fault-tolerant quantum computation.This paper investigates the feasibility of universal quantum computation (UQC) using a model that includes only Clifford unitaries, the creation of the state |0⟩, and qubit measurements in the computational basis. Additionally, it allows the creation of a one-qubit ancilla in a mixed state ρ, which is a parameter of the model. The goal is to determine for which ρ UQC can be efficiently simulated. The authors construct purification protocols that consume several copies of ρ and produce a single output qubit with higher polarization. These protocols allow one to increase the polarization only along certain "magic" directions. If the polarization of ρ along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, called a magic state. The authors show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of their results with the Gottesman-Knill theorem is discussed. The paper discusses the theory of fault-tolerant quantum computation, which defines an important number called the error threshold. If the physical error rate is less than the threshold value δ, it is possible to stabilize computation by transforming the quantum circuit into a fault-tolerant form where errors can be detected and eliminated. However, if the error rate is above the threshold, errors begin to accumulate, resulting in rapid decoherence and rendering the output of the computation useless. The actual value of δ depends on the error correction scheme and the error model. The paper discusses the connection between the model and the Gottesman-Knill theorem, which states that operations from the Clifford group can only produce quantum states of a very special form called stabilizer states. The authors show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The paper also discusses the concept of magic states, which are special states that, when combined with Clifford group operations, allow for universal quantum computation. The authors construct two particular schemes of UQC simulation based on a method called magic states distillation. They prove that adaptive computation in the basis O allows one to simulate universal quantum computation whenever the fidelity between ρ and a T-type or H-type magic state exceeds certain thresholds. The authors also discuss the error analysis of their model, showing that the threshold error probability for the distillation of T-type and H-type magic states is approximately 0.173 and 0.927, respectively. The paper concludes with a discussion of the implications of their results for fault-tolerant quantum computation.