The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the $\textit{gate decomposition cost}$.

中文翻译：

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变分算法中的量子经典权衡和多控量子门分解


近期量子计算机的计算能力受到门操作的嘈杂执行和有限数量的物理量子比特的限制。混合变分算法非常适合近期量子设备，因为它们允许在用于解决问题的量子资源和经典资源数量之间进行广泛的权衡。本文通过研究一个特定案例——将量子近似优化算法 （QAOA） 应用于最大独立集 （MIS） 问题的实例，研究了算法和硬件级别可用的权衡。我们考虑了 QAOA 的三种变体，它们在算法层面上提供了不同的权衡，包括它们所需的经典参数数量、量子门和所需的经典优化的迭代。由于 MIS 是一个约束组合优化问题，因此 QAOA 必须遵守问题约束。这可以通过使用许多多控制门操作来实现，这些操作必须分解为目标硬件可执行的门。我们研究了这个硬件级别可用的权衡，将不同原生门集的门保真度和分解效率组合成一个称为 $\textit{门分解成本}$ 的指标。