We formulate the control over quantum matter, so as to perform arbitrary quantum computation, as an optimization problem. We then provide a schematic machine learning algorithm for its solution. Imagine a long strip of ‘quantum stuff’, endowed with certain assumed physical properties, and equipped with regularly spaced wires to provide input settings and to read off outcomes. After showing how the corresponding map from settings to outcomes can be construed as a quantum circuit, we provide a machine learning framework to tomographically ‘learn’ which settings implement the members of a universal gate set. To that end, we devise a loss function measuring how badly a proposed encoding has failed to implement a given circuit, and prove the existence of ‘tomographically complete’ circuit sets: should a given encoding minimize the loss function for each member of such a set, it also will for an arbitrary circuit. At optimum, arbitrary quantum gates, and thus arbitrary quantum programs, can be implemented using the stuff.

我们制定了对量子物质的控制，以执行任意量子计算，作为一个优化问题。然后，我们为其解决方案提供了一种示意性机器学习算法。想象一长条“量子物质”，具有某些假定的物理特性，并配备有规律间隔的导线以提供输入设置并读取结果。在显示了从设置到结果的对应映射如何被解释为量子电路之后，我们提供了一种机器学习框架，以断层摄影术“学习”哪些设置实现了通用门集的成员。为此，我们设计了一个损耗函数，用于测量所提议的编码未能实现给定电路的严重程度，并证明“断层完整”电路集的存在：如果给定的编码使该集合中每个成员的损耗函数最小化，那么对于任意电路也是如此。在最佳状态下，可以使用填充物来实现任意量子门，从而实现任意量子程序。