  Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a
promising platform for quantum information processing. In DPQA, atomic qubits
are selectively loaded into arrays of optical traps that can be reconfigured
during the computation itself. Leveraging qubit transport and parallel,
entangling quantum operations, different pairs of qubits, even those initially
far away, can be entangled at different stages of the quantum program
execution. Such reconfigurability and non-local connectivity present new
challenges for compilation, especially in the layout synthesis step which
places and routes the qubits and schedules the gates. In this paper, we
consider a DPQA architecture that contains multiple arrays and supports 2D
array movements, representing cutting-edge experimental platforms. Within this
architecture, we discretize the state space and formulate layout synthesis as a
satisfiability modulo theories problem, which can be solved by existing solvers
optimally in terms of circuit depth. For a set of benchmark circuits generated
by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces
the number of two-qubit entangling gates on small problem instances by 1.7x
compared to optimal compilation results on a fixed planar architecture. To
further improve scalability and practicality of the method, we introduce a
greedy heuristic inspired by the iterative peeling approach in classical
integrated circuit routing. Using a hybrid approach that combined the greedy
and optimal methods, we demonstrate that our DPQA-based compiled circuits
feature reduced scaling overhead compared to a grid fixed architecture,
resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These
methods enable programmable, complex quantum circuits with neutral atom quantum
computers, as well as informing both future compilers and future hardware
choices.
