Quantum Approximate Optimization Algorithm (QAOA) is one of the leading candidates for demonstrating the quantum advantage using near-term quantum computers. Unfortunately, high device error rates limit us from reliably running QAOA circuits for problems with more than a few qubits. In QAOA, the problem graph is translated into a quantum circuit such that every edge corresponds to two 2-qubit CNOT operations in each layer of the circuit. As CNOTs are extremely error-prone, the fidelity of QAOA circuits is dictated by the number of edges in the problem graph. We observe that majority of graphs corresponding to real-world applications follow the ``power-law`` distribution, where some hotspot nodes have significantly higher number of connections. We leverage this insight and propose ``FrozenQubits`` that freezes the hotspot nodes or qubits and intelligently partitions the state-space of the given problem into several smaller sub-spaces which are then solved independently. The corresponding QAOA sub-circuits are significantly less vulnerable to gate and decoherence errors due to the reduced number of CNOT operations in each sub-circuit. Unlike prior circuit-cutting approaches, FrozenQubits does not require any exponentially complex post-processing step. Our evaluations with 5,300 QAOA circuits on eight different quantum computers from IBM shows that FrozenQubits can improve the quality of solutions by 8.73x on average (and by up to 57x), albeit utilizing 2x more quantum resources.

翻译：量子近似优化算法（QAOA）是利用近期量子计算机展示量子优越性的主要候选算法之一。然而，高设备错误率限制了我们在大规模问题上可靠运行QAOA电路的能力。在QAOA中，问题图被转化为量子电路，使得每条边对应电路每层中的两个双量子比特CNOT操作。由于CNOT操作极易出错，QAOA电路的保真度取决于问题图中边的数量。我们观察到，大多数现实应用对应的图遵循"幂律"分布，其中某些热点节点具有显著更多的连接。基于这一洞察，我们提出"FrozenQubits"方法，该方法冻结热点节点或量子比特，智能地将给定问题的状态空间划分为若干更小的子空间，并分别求解。相应的QAOA子电路由于每个子电路中CNOT操作数量的减少，对门错误和退相干错误的敏感性显著降低。与先前的电路切割方法不同，FrozenQubits不需要任何指数复杂度的后处理步骤。我们在IBM的八台不同量子计算机上对5,300个QAOA电路的评估表明，尽管使用了2倍的量子资源，FrozenQubits能够将解的质量平均提升8.73倍（最高可达57倍）。