  Distributed quantum computing (DQC) is a new paradigm aimed at scaling up
quantum computing via the interconnection of smaller quantum processing units
(QPUs). Shared entanglement allows teleportation of both states and gates
between QPUs. This leads to an attractive horizontal scaling of quantum
processing power, which comes at the expense of the additional time and noise
introduced by entanglement sharing protocols. Consequently, methods for
partitioning quantum circuits across multiple QPUs should aim to minimise the
amount of entanglement-based communication required between distributed QPUs.
Existing protocols tend to focus primarily on optimising entanglement costs for
gate teleportation or state teleportation to cover operations between QPUs,
rather than both at the same time. The most general form of the problem should
treat gate and state teleportation on the same footing, allowing minimal cost
circuit partitions through a combination of the two. This work introduces a
graph-based formulation which allows joint optimisation of gate and state
teleportation cost, including extensions of gate teleportation which group
gates together for distribution using common resources. The formulation permits
low e-bit cost for a variety of circuit types. Using a basic genetic algorithm,
improved performance over state-of-the-art methods is obtained in terms of both
average e-bit cost and time scaling.
