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

Mapping quantum circuits to modular architectures with QUBO