This paper investigates the feasibility of achieving quantum supremacy using near-term quantum devices without error correction. The authors argue that sampling from the output distributions of random quantum circuits is a computationally hard task for classical computers, as it requires exponential time in the number of qubits. They study the convergence of output distributions to the Porter-Thomas distribution, characteristic of quantum chaos, using simulations of up to 42 qubits. They introduce cross entropy as a benchmark for quantum circuits, which measures the similarity between experimental samples and ideal circuit outputs. The cross entropy is closely related to circuit fidelity and can be efficiently measured when circuit simulations are available. The authors argue that quantum supremacy can be achieved with approximately fifty superconducting qubits, as chaotic states are sensitive to errors but can still produce results that are exponentially harder for classical computers to simulate. They also discuss the computational hardness of classical sampling problems, showing that they require exponential resources in the number of qubits. The paper concludes that quantum supremacy is achievable in the near-term with current technology, as the cross entropy difference between experimental and ideal circuits can be used to define a practical test of quantum supremacy.This paper investigates the feasibility of achieving quantum supremacy using near-term quantum devices without error correction. The authors argue that sampling from the output distributions of random quantum circuits is a computationally hard task for classical computers, as it requires exponential time in the number of qubits. They study the convergence of output distributions to the Porter-Thomas distribution, characteristic of quantum chaos, using simulations of up to 42 qubits. They introduce cross entropy as a benchmark for quantum circuits, which measures the similarity between experimental samples and ideal circuit outputs. The cross entropy is closely related to circuit fidelity and can be efficiently measured when circuit simulations are available. The authors argue that quantum supremacy can be achieved with approximately fifty superconducting qubits, as chaotic states are sensitive to errors but can still produce results that are exponentially harder for classical computers to simulate. They also discuss the computational hardness of classical sampling problems, showing that they require exponential resources in the number of qubits. The paper concludes that quantum supremacy is achievable in the near-term with current technology, as the cross entropy difference between experimental and ideal circuits can be used to define a practical test of quantum supremacy.