Quantum walks, in virtue of the coherent superposition and quantum
interference, possess the exponential superiority over its classical
counterpart in applications of quantum searching and quantum simulation. A
straitforward physical implementation involving merely photonic source, linear
evolution network and detection make it very appealing, in light of the
stringent requirements of universal quantum computing. The quantum enhanced
power is highly related to the state space of quantum walks, which can be
expanded by enlarging the dimension of evolution network and/or photon number.
Increasing photon number is considerably challenging due to probabilistic
generation of single photons and multiplicative loss. Here we demonstrate a
two-dimensional continuous-time quantum walk by using the external geometry of
photonic waveguide arrays, rather than inner the degree of freedom of photons.
Using femtosecond laser direct writing, we construct a large-scale
three-dimensional structure which forms a two-dimensional lattice with up to
49X49 nodes on a photonic chip. We demonstrate the quantum transport properties
via observing the ballistic evolution pattern and the variance profile, which
agree well with simulation results for quantum walks. We further reveal the
transient nature of the walk from our implementation, suggesting a higher
dimension. An architecture that allows free evolvement in all directions and
large scale, combing with defect and disorder control, may bring up powerful
and versatile quantum walk machines for classically intractable problems.