We propose an Indirect Quantum Approximate Optimization Algorithm (referred to as IQAOA) where the Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the Hamiltonian describing the set of string vectors. This algorithm creates an efficient alternative to QAOA, where: 1) a Quantum parametrized circuit executed on a quantum machine models the set of string vectors; 2) a Classical meta-optimization loop executed on a classical machine; 3) an estimation of the average cost of each string vector computing, using a well know algorithm coming from the OR community that is problem dependent. The indirect encoding defined by dimensional string vector is mapped into a solution by an efficient coding/decoding mechanism. The main advantage is to obtain a quantum circuit with a strongly limited number of gates that could be executed on the noisy current quantum machines. The numerical experiments achieved with IQAOA permits to solve 8-customer instances TSP using the IBM simulator which are to the best of our knowledge the largest TSP ever solved using a QAOA based approach.

翻译：我们提出了一种间接量子近似优化算法（简称IQAOA），其中量子交替算子拟设考虑了泛参数化的酉算子族，以高效建模描述字符串向量集合的哈密顿量。该算法为QAOA提供了一种高效替代方案，其核心机制包括：1）在量子设备上执行的参数化量子电路用于建模字符串向量集合；2）在经典计算机上运行的经典元优化循环；3）利用运筹学领域中问题依赖的经典算法，估计每个字符串向量的平均成本。通过高效的编码/解码机制，由维度化字符串向量定义的间接编码被映射为具体解。该算法的主要优势在于获得的量子电路门数量极低，可在当前含噪量子设备上执行。基于IQAOA的数值实验利用IBM模拟器成功求解了8客户规模的旅行商问题（TSP），据我们所知，这是基于QAOA方法求解的最大规模旅行商问题实例。