Abstract
Perhaps the earliest application of quantum computing in learning theory was in the field of neural networks. The quantum perceptron shows theoretical bounds on what is possible by a single unitary transformation and a subsequent measurement. This pattern repeats in other applications of quantum neural networks: as the unitary evolution of quantum systems is linear, the nonlinear characteristic of artificial neurons is introduced through measurements. Feedforward networks envision alternating classical and quantum components. A quantum associative memory—the quantum variant of Hopfield networks—follows a different path, keeping all states in a quantum superposition. Some experimental results are already available on a small scale, including technology with nuclear magnetic resonance and also with quantum dots.
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