  Integrated quantum optics has drastically reduced the size of table-top
optical experiments to the chip-scale, allowing for demonstrations of
large-scale quantum information processing and quantum simulation. However,
despite these advances, practical implementations of quantum photonic circuits
remain limited because they consist of large networks of waveguide
interferometers that path encode information which do not easily scale.
Increasing the dimensionality of current quantum systems using higher degrees
of freedom such as transverse spatial field distribution, polarization, time,
and frequency to encode more information per carrier will enable scalability by
simplifying quantum computational architectures, increasing security and noise
tolerance in quantum communication channels, and simulating richer quantum
phenomena. Here we demonstrate a scalable platform for photonic quantum
information processing using waveguide quantum circuit building blocks based on
the transverse spatial mode degree of freedom: mode multiplexers and mode
beamsplitters. A multimode waveguide is inherently a densely packed system of
spatial and polarization modes that can be coupled by perturbations to the
waveguide. We design a multimode waveguide consisting of three spatial modes
(per polarization) and a nanoscale grating beamsplitter to show tunable quantum
interference between pairs of photons in different transverse spatial modes. We
also cascade these structures and demonstrate NOON state interferometry within
a multimode waveguide. These devices have potential to perform transformations
on more modes and be integrated with existing architectures, providing a
scalable path to higher-dimensional Hilbert spaces and entanglement.
