  A major hurdle for building a large-scale quantum computer is to scale up the
number of qubits while maintaining connectivity between them. In trapped-ion
devices, this connectivity can be provided by physically moving subregisters
consisting of a few ions across the processor. The topology of the connectivity
is given by the layout of the ion trap where one-dimensional and
two-dimensional arrangements are possible. Here, we focus on an architecture
based on a rectangular two-dimensional lattice, where each lattice site
contains a subregister with a linear string of ions. We refer to this
architecture as the Quantum Spring Array (QSA). Subregisters placed in
neighboring lattice sites can be coupled by bringing the respective ion strings
close to each other while avoiding merging them into a single trapping
potential. Control of the separation of subregisters along one axis of the
lattice, known as the axial direction, uses quasi-static voltages, while the
second axis, the radial, requires control of radio frequency signals. In this
work, we investigate key elements of the 2D lattice quantum computation
architecture along both axes: We show that the coupling rate between
neighboring lattice sites increases with the number of ions per site and the
motion of the coupled system can be resilient to noise. The coherence of the
coupling is assessed, and an entangled state of qubits in separate trapping
regions along the radial axis is demonstrated. Moreover, we demonstrate control
over radio frequency signals to adjust radial separation between strings, and
thus tune their coupling rate. We further map the 2D lattice architecture to
code primitives for fault-tolerant quantum error correction, providing a step
towards a quantum processor architecture that is optimized for large-scale
fault-tolerant operation.
