  Quantum optimization as a field has largely been restricted by the
constraints of current quantum computing hardware, as limitations on size,
performance, and fidelity mean most non-trivial problem instances won't fit on
quantum devices. Even proposed solutions such as distributed quantum computing
systems may struggle to achieve scale due to the high cost of inter-device
communication. To address these concerns, we propose Deferred Constraint
Quantum Divide and Conquer Algorithm (DC-QDCA), a method for constructing
quantum circuits which greatly reduces inter-device communication costs for
some quantum graph optimization algorithms. This is achieved by identifying a
set of vertices whose removal partitions the input graph, known as a separator;
by manipulating the placement of constraints associated with the vertices in
the separator, we can greatly simplify the topology of the optimization
circuit, reducing the number of required inter-device operations. Furthermore,
we introduce an iterative algorithm which builds on these techniques to find
solutions for problems with potentially thousands of variables. Our
experimental results using quantum simulators have shown that we can construct
tractable circuits nearly three times the size of previous QDCA methods while
retaining a similar or greater level of quality.
