论文标题
PROG-QAOA：通过经典程序进行资源有效量子优化的框架
Prog-QAOA: Framework for resource-efficient quantum optimization through classical programs
论文作者
论文摘要
当前的最新量子优化算法需要将原始问题表示为二进制优化问题，然后将其转换为适合量子设备的同等成本汉密尔顿。分别实施汉密尔顿的每个术语通常会导致高冗余，从而大大增加所需的资源。取而代之的是，我们建议设计用于计算目标函数并认证约束的经典程序，然后将其编译为量子电路，从而消除了对二进制优化问题表示的依赖。这导致了量子近似优化算法（QAOA）的新变体，我们将其命名为基于程序的QAOA（PROG-QAOA）。我们利用这一想法来优化诸如旅行推销员问题和最大$ k $ cut之类的任务，并获得有关所有相关成本度量（例如，量子，门和电路深度的数量）几乎最佳的电路。虽然我们仅在一组特定的范式问题上证明PROG-QAOA的力量，但我们的方法便方便地适用于通用优化问题。
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing each term of the cost Hamiltonian separately often results in high redundancy, significantly increasing the resources required. Instead, we propose to design classical programs for computing the objective function and certifying the constraints, and later compile them to quantum circuits, eliminating the reliance on the binary optimization problem representation. This results in a new variant of the Quantum Approximate Optimization Algorithm (QAOA), which we name the Program-based QAOA (Prog-QAOA). We exploit this idea for optimization tasks like the Travelling Salesman Problem and Max-$K$-Cut and obtain circuits that are near-optimal with respect to all relevant cost measures, e.g., number of qubits, gates, and circuit depth. While we demonstrate the power of Prog-QAOA only for a particular set of paradigmatic problems, our approach is conveniently applicable to generic optimization problems.
