Joint Optimization of Qubit Leasing and Quantum Circuit Distribution

We consider an agent, who would like to execute a given quantum circuit using resources leased from a set of quantum computers (QCs) connected by a quantum network. For this purpose, the agent needs to make the following four key decisions: (i) how many qubits to lease from each QC, (ii) at which QCs to store different circuit qubits in different time slots, (iii) at which QC to execute each gate in the circuit, and (iv) how to move qubits between QCs, choosing between migration and teleportation. We refer to this problem facing the agent as the joint qubit leasing and quantum circuit distribution (JQLQCD) problem, and provide a comprehensive integer linear programming (ILP) formulation for it. We show that the JQLQCD problem is NP-complete. Next, we identify several special cases in which the problem can be optimally solved in closed form or via polynomial-time algorithms. Also, we propose a greedy algorithm with local search refinement to solve large instances of the general JQLQCD problem. Finally, we evaluate the performance of the proposed greedy algorithm using extensive numerical computations.