The paper presents two techniques to mitigate errors and decoherence in short-depth quantum circuits, which are crucial for near-term quantum applications such as quantum simulations and approximate optimization algorithms. The first technique, **Extrapolation to the Zero Noise Limit**, uses Richardson's deferred approach to cancel higher-order terms of the noise perturbations, improving the accuracy of expectation values. The second technique, **Probabilistic Error Cancellation**, represents the ideal circuit as a quasi-probabilistic mixture of noisy circuits, allowing for efficient estimation of expectation values with high precision. Both methods do not require additional qubit resources and are designed to be practical for current quantum experiments. The paper also discusses the conditions under which these techniques can be applied and provides numerical examples to demonstrate their effectiveness.The paper presents two techniques to mitigate errors and decoherence in short-depth quantum circuits, which are crucial for near-term quantum applications such as quantum simulations and approximate optimization algorithms. The first technique, **Extrapolation to the Zero Noise Limit**, uses Richardson's deferred approach to cancel higher-order terms of the noise perturbations, improving the accuracy of expectation values. The second technique, **Probabilistic Error Cancellation**, represents the ideal circuit as a quasi-probabilistic mixture of noisy circuits, allowing for efficient estimation of expectation values with high precision. Both methods do not require additional qubit resources and are designed to be practical for current quantum experiments. The paper also discusses the conditions under which these techniques can be applied and provides numerical examples to demonstrate their effectiveness.