Optimal Control Policies for Distributed Quantum Computing with Quantum Walks

Distributed quantum computing (DQC) is a key application of quantum networks. It enables interconnected quantum computers to virtually implement a powerful quantum machine that uses entanglement to solve problems that cannot be addressed by individual computers alone. One of the key capabilities that quantum networks must support to DQC is the execution of quantum controlled gates among qubits residing in geographically separated quantum computers. In order to perform such control, we describe a quantum walk network control plane protocol that captures the logic operations needed for the execution of remotely controlled quantum gates. The quantum walk protocol provides multiple ways to distribute a given quantum circuit in a network. The multitude of valid distribution schemes for the same circuit naturally leads to the definition of a combinatorial optimization problem that captures the optimal way to use the network for circuit execution. In this context, we define an integer programming formulation to compute network policies to implement a given quantum circuit minimizing network resource utilization, i.e the number of channel uses necessary to implement the circuit. The formulation determines both the assignment of qubits described by a logical description of the circuit tophysical qubits in the network, and how to route quantum control information with quantum walks.