  Modular quantum computing architectures are a promising alternative to
monolithic QPU (Quantum Processing Unit) designs for scaling up quantum
devices. They refer to a set of interconnected QPUs or cores consisting of
tightly coupled quantum bits that can communicate via quantum-coherent and
classical links. In multi-core architectures, it is crucial to minimize the
amount of communication between cores when executing an algorithm. Therefore,
mapping a quantum circuit onto a modular architecture involves finding an
optimal assignment of logical qubits (qubits in the quantum circuit) to
different cores with the aim to minimize the number of expensive inter-core
operations while adhering to given hardware constraints. In this paper, we
propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO)
technique to encode the problem and the solution for both qubit allocation and
inter-core communication costs in binary decision variables. To this end, the
quantum circuit is split into slices, and qubit assignment is formulated as a
graph partitioning problem for each circuit slice. The costly inter-core
communication is reduced by penalizing inter-core qubit communications. The
final solution is obtained by minimizing the overall cost across all circuit
slices. To evaluate the effectiveness of our approach, we conduct a detailed
analysis using a representative set of benchmarks having a high number of
qubits on two different multi-core architectures. Our method showed promising
results and performed exceptionally well with very dense and
highly-parallelized circuits that require on average 0.78 inter-core
communications per two-qubit gate.
