  Quantum walks are the quantum mechanical analogue of classical random walks
and an extremely powerful tool in quantum simulations, quantum search
algorithms, and even for universal quantum computing. In our work, we have
designed and fabricated an 8x8 two-dimensional square superconducting qubit
array composed of 62 functional qubits. We used this device to demonstrate high
fidelity single and two particle quantum walks. Furthermore, with the high
programmability of the quantum processor, we implemented a Mach-Zehnder
interferometer where the quantum walker coherently traverses in two paths
before interfering and exiting. By tuning the disorders on the evolution paths,
we observed interference fringes with single and double walkers. Our work is an
essential milestone in the field, brings future larger scale quantum
applications closer to realization on these noisy intermediate-scale quantum
processors.
