  We present a method to split quantum circuits of variational quantum
algorithms (VQAs) to allow for parallel training and execution, that maximally
exploits the limited number of qubits in hardware to solve large problem
instances. We apply this specifically to combinatorial optimization problems,
where inherent structures from the problem can be identified, thus directly
informing how to create these parallelized quantum circuits, which we call
slices. We test our method by creating a parallelized version of the Quantum
Approximate Optimization Algorithm, which we call pQAOA, and explain how our
methods apply to other quantum algorithms like the Variational Quantum
Eigensolver and quantum annealing. We show that not only can our method address
larger problems, but that it is also possible to run full VQA models while
training parameters using only one slice. These results show that the loss of
information induced by splitting does not necessarily affect the training of
parameters in quantum circuits for optimization. This implies that
combinatorial optimization problems are encoded with redundant information in
quantum circuits of current VQAs. Therefore, to attain quantum advantage for
combinatorial optimization, future quantum algorithms should be designed to
incorporate information that is free of such redundancies.
