We demonstrate characterizing quantum evolutions via matrix factorization algorithm, a particular type of the recommender system (RS). A system undergoing a quantum evolution can be characterized in several ways. Here we choose (i) quantum correlations quantified by measures such as entropy, negativity, or discord, and (ii) state-fidelity. Using quantum registers with up to 10 qubits, we demonstrate that an RS can efficiently characterize both unitary and nonunitary evolutions. After carrying out a detailed performance analysis of the RS in two qubits, we show that it can be used to distinguish a clean database of quantum correlations from a noisy or a fake one. Moreover, we find that the RS brings about a significant computational advantage for building a large database of quantum discord, for which no simple closed-form expression exists. Also, RS can efficiently characterize systems undergoing nonunitary evolutions in terms of quantum discord reduction as well as state-fidelity. Finally, we utilize RS for the construction of discord phase space in a nonlinear quantum system.

中文翻译：

---

通过推荐系统有效表征量子演化

我们演示了通过矩阵分解算法（一种特定类型的推荐系统 (RS)）表征量子演化。经历量子演化的系统可以通过多种方式表征。在这里，我们选择 (i) 由熵、负性或不和谐等度量量化的量子相关性，以及 (ii) 状态保真度。使用多达 10 个量子位的量子寄存器，我们证明了 RS 可以有效地表征酉和非酉演化。在对两个量子位中的 RS 进行详细的性能分析后，我们表明它可用于区分干净的量子相关性数据库与嘈杂或虚假的数据库。此外，我们发现 RS 为构建大型量子不和谐数据库带来了显着的计算优势，其中不存在简单的封闭形式表达式。还，RS 可以在量子不和谐减少和状态保真度方面有效地表征经历非幺正演化的系统。最后，我们利用 RS 在非线性量子系统中构建不和谐相空间。