This paper investigates the issue of "barren plateaus" in the training landscapes of quantum neural networks. It shows that for a wide class of parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. This is related to the 2-design characteristic of random circuits, and solutions to this problem must be studied. The paper discusses the use of hybrid quantum-classical algorithms for quantum simulation, optimization, and machine learning. These algorithms rely on optimizing a parameterized quantum circuit with a classical optimization loop. The resilience of these approaches to certain types of errors and flexibility with respect to coherence time and gate requirements make them especially attractive for NISQ implementations. The paper also discusses the use of random circuits as initial guesses for exploring the space of quantum states. While random circuits are often proposed as initial guesses due to their simplicity and hardware efficiency, the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. The paper presents results related to random quantum circuits in the context of the exponential dimension of Hilbert space and gradient-based hybrid quantum-classical algorithms. It shows that for a large class of random circuits, the average value of the gradient of the objective function is zero, and the probability that any given instance of such a random circuit deviates from this average value by a small constant ε is exponentially small in the number of qubits. The paper also discusses the contrast between gradients in classical deep networks and quantum circuits. In classical deep networks, gradients can vanish exponentially in the number of layers, while in quantum circuits, gradients are exponentially small in the number of qubits. This difference is due to the different scaling of the vanishing gradient and the complexity of computing expected values. The paper concludes that gradients in modest-sized random circuits tend to vanish without additional mitigating steps. This has implications for the design of ansätze for scaling to larger experiments. The paper suggests that structured initial guesses or pre-training segment by segment may be necessary to avoid these barren plateaus in the quantum setting.This paper investigates the issue of "barren plateaus" in the training landscapes of quantum neural networks. It shows that for a wide class of parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. This is related to the 2-design characteristic of random circuits, and solutions to this problem must be studied. The paper discusses the use of hybrid quantum-classical algorithms for quantum simulation, optimization, and machine learning. These algorithms rely on optimizing a parameterized quantum circuit with a classical optimization loop. The resilience of these approaches to certain types of errors and flexibility with respect to coherence time and gate requirements make them especially attractive for NISQ implementations. The paper also discusses the use of random circuits as initial guesses for exploring the space of quantum states. While random circuits are often proposed as initial guesses due to their simplicity and hardware efficiency, the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. The paper presents results related to random quantum circuits in the context of the exponential dimension of Hilbert space and gradient-based hybrid quantum-classical algorithms. It shows that for a large class of random circuits, the average value of the gradient of the objective function is zero, and the probability that any given instance of such a random circuit deviates from this average value by a small constant ε is exponentially small in the number of qubits. The paper also discusses the contrast between gradients in classical deep networks and quantum circuits. In classical deep networks, gradients can vanish exponentially in the number of layers, while in quantum circuits, gradients are exponentially small in the number of qubits. This difference is due to the different scaling of the vanishing gradient and the complexity of computing expected values. The paper concludes that gradients in modest-sized random circuits tend to vanish without additional mitigating steps. This has implications for the design of ansätze for scaling to larger experiments. The paper suggests that structured initial guesses or pre-training segment by segment may be necessary to avoid these barren plateaus in the quantum setting.