Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits' quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve $131$ benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to $18$ qubits or over $100$ quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.

中文翻译：

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用于精确量子位重新排序的具有隐式 SWAP 门计数的多项式大小模型

由于量子计算背后的物理原理，量子电路设计人员必须遵守量子位有限相互作用距离所带来的约束。因此，现有电路需要通过插入 SWAP 门来修改，这通过交换两个量子位的量子状态的位置来改变量子位顺序。我们考虑线性阵列上的最近邻合规问题，其中所需的 SWAP 门的数量要最小化。我们介绍了问题的整数线性规划模型，该模型的大小在量子位和门的数量上呈多项式缩放。此外，我们使用商业求解器 CPLEX 将 131 美元的基准实例求解为最优。与之前使用精确方法评估的那些相比，基准实例要大得多。最大的电路包含高达 18 美元的量子比特或超过 100 美元的量子门。这种公式似乎也适用于开发启发式方法，因为在搜索过程中可以快速发现（接近）最优解。