论文标题
Wasserstein溶液质量和量子近似优化算法：投资组合优化案例研究
Wasserstein Solution Quality and the Quantum Approximate Optimization Algorithm: A Portfolio Optimization Case Study
论文作者
论文摘要
优化金融资产投资组合是一个关键的工业问题，可以使用适用于量子处理单元（QPU）的算法大致解决。我们使用量子近似优化算法（QAOA）基准了这种方法的成功；靶向门模型QPU的算法。我们的重点是由归一化和互补的Wasserstein距离（$η$）确定的解决方案的质量，我们以一种将QAOA作为概率转运蛋白暴露的方式提出。使用$η$作为应用程序性能的特定基准，我们将其作为QPU的选择作为QAOA电路深度$ P $的函数。在$ n = 2 $（2 QUAT）时，我们发现大多数系统的峰值解决方案质量为$ p = 5 $，对于$ n = 3 $，此峰值为$ p = 4 $，在被困的离子QPU上。还可以使用$ p $提高解决方案质量，使用更通用的量子交替运算符Ansätz的变体，$ p = 2 $，$ n = 2 $和$ 3 $，这尚未报道。在相同的测量值中，观察到$η$在超过有限镜头产生的噪声的水平下是可变的。这表明可变性本身应被视为给定应用程序的QPU性能基准。在研究QAOA的理想执行时，我们发现当投资组合预算$ b $接近$ n/2 $时，$ p = 1 $解决方案质量会降低，并且当$ b \ b \ 1 $或$ n-1 $时增加。这种趋势直接对应于二项系数$ NCB $，并且与最近报道的可及性缺陷现象有关。基于$ p = 1 $的$η$以外的$η$以超出$ p = 1 $的基础，将衍生品的和无衍生的经典优化器进行基准测试，以发现无衍生的优化器通常对给定的计算资源，问题大小和电路深度更有效。
Optimizing of a portfolio of financial assets is a critical industrial problem which can be approximately solved using algorithms suitable for quantum processing units (QPUs). We benchmark the success of this approach using the Quantum Approximate Optimization Algorithm (QAOA); an algorithm targeting gate-model QPUs. Our focus is on the quality of solutions achieved as determined by the Normalized and Complementary Wasserstein Distance, $η$, which we present in a manner to expose the QAOA as a transporter of probability. Using $η$ as an application specific benchmark of performance, we measure it on selection of QPUs as a function of QAOA circuit depth $p$. At $n = 2$ (2 qubits) we find peak solution quality at $p=5$ for most systems and for $n = 3$ this peak is at $p=4$ on a trapped ion QPU. Increasing solution quality with $p$ is also observed using variants of the more general Quantum Alternating Operator Ansätz at $p=2$ for $n = 2$ and $3$ which has not been previously reported. In identical measurements, $η$ is observed to be variable at a level exceeding the noise produced from the finite number of shots. This suggests that variability itself should be regarded as a QPU performance benchmark for given applications. While studying the ideal execution of QAOA, we find that $p=1$ solution quality degrades when the portfolio budget $B$ approaches $n/2$ and increases when $B \approx 1$ or $n-1$. This trend directly corresponds to the binomial coefficient $nCB$ and is connected with the recently reported phenomenon of reachability deficits. Derivative-requiring and derivative-free classical optimizers are benchmarked on the basis of the achieved $η$ beyond $p=1$ to find that derivative-free optimizers are generally more effective for the given computational resources, problem sizes and circuit depths.
