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.

翻译：我们考虑一个代理，该代理希望利用从一组通过量子网络连接的量子计算机（QC）租赁的资源来执行给定的量子电路。为此，代理需要做出以下四个关键决策：（i）从每个量子计算机租赁多少量子比特，（ii）在不同时间槽将不同电路量子比特存储在哪些量子计算机上，（iii）在哪个量子计算机执行电路中的每个量子门，以及（iv）如何在量子计算机之间移动量子比特，选择迁移或隐形传态。我们将该代理面临的问题称为量子比特租赁与量子电路分布联合优化（JQLQCD）问题，并为其提供了一种全面的整数线性规划（ILP）公式。我们证明了JQLQCD问题是NP完全的。接着，我们识别了若干特殊情况，在这些情况下，该问题可以通过闭式解或多项式时间算法得到最优解。此外，我们提出了一种结合局部搜索优化的贪心算法，以求解一般JQLQCD问题的大规模实例。最后，我们通过大量数值计算评估了所提贪心算法的性能。