Optimal Policies for Distributed Quantum Computing with Quantum Walk Control Plane Protocol

Distributed quantum computing is a promising application of quantum networks as it leverages the power of interconnected small quantum computers to perform generic quantum operations that cannot be tackled by single computers alone. The key question in distributed quantum computing using quantum networks is applying a quantum gate on qubits that are geographically separated. In this work, we propose an optimization framework to describe distributed control policies that implement a quantum circuit with gates acting on qubits located in distinct nodes. The distributed control operations throughout the quantum network can be described by a logical control plane quantum walk protocol. We then investigate the problem of assigning logical qubits in a circuit description to physical qubits in the network, with the objective of minimizing the amount of quantum control information exchanged between nodes. We present an integer programming formulation for the problem that determines both qubit assignment and network paths for the transmission of quantum control information. Our formulation restricts to circuits with 2-qubit controlled gates and highlights the difficulty of the problem in terms of complexity. Our formulation can be used to analyze the demand for network resources in terms of the number of channel uses with respect to node capacity and circuit width.