  With the increasing crossover between quantum information and machine
learning, quantum simulation of neural networks has drawn unprecedentedly
strong attention, especially for the simulation of associative memory in
Hopfield neural networks due to their wide applications and relatively simple
structures that allow for easier mapping to the quantum regime. Quantum
stochastic walk, a strikingly powerful tool to analyze quantum dynamics, has
been recently proposed to simulate the firing pattern and associative memory
with a dependence on Hamming Distance. We successfully map the theoretical
scheme into a three-dimensional photonic quantum chip and realize quantum
stochastic walk evolution through well-controlled detunings of the propagation
constant. We demonstrate a good match rate of the associative memory between
the experimental quantum scheme and the expected result for Hopfield neural
networks. The ability of quantum simulation for an important feature of a
neural network, combined with the scalability of our approach through low-loss
integrated chip and straightforward Hamiltonian engineering, provides a primary
but steady step towards photonic artificial intelligence devices for
optimization and computation tasks of greatly improved efficiencies.
