A Multilevel Framework for Partitioning Quantum Circuits

Abstract

Executing quantum algorithms over dis tributed quantum systems requires quan tum circuits to be divided into sub-circuits which communicate via entanglement based teleportation. Naively mapping cir cuits to qubits over multiple quantum pro cessing units (QPUs) results in large com munication overhead, increasing both exe cution time and noise. This can be min imised by optimising the assignment of qubits to QPUs and the methods used for covering non-local operations. Formu lations that are general enough to cap ture the spectrum of teleportation possi bilities lead to complex problem instances which can be difficult to solve effectively. This highlights a need to exploit the wide range of heuristic techniques used in the graph partitioning literature. This pa per formalises and extends existing con structions for graphical quantum circuit partitioning and designs a new objective function that captures further possibilities for non-local operations via nested state teleportation. We adapt the well-known Fiduccia-Mattheyses heuristic to the con straints and problem objective and explore multilevel techniques that coarsen hyper graphs and partition at multiple levels of granularity. We find that this reduces run time and improves solution quality of stan dard partitioning. We place these tech niques within a larger framework, through which we can extract full distributed quan tum circuits including teleportation in structions. We compare the entanglement requirements and runtimes with state-of the-art methods, finding that we achieve the lowest entanglement costs in most cases. Averaging over a wide range of circuits, we reduce the entanglement re quirements by 35% compared with the next best-performing method. We also f ind that our techniques can scale to much larger circuit sizes than competing meth ods, provided the number of partitions is not too large.