To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system’s size grows large. In this work, we introduce a self-learning tomographic scheme based on the variational hybrid quantum-classical method. The key part of the scheme is a learning procedure, in which we learn a control sequence capable of driving the unknown target state coherently to a simple fiducial state, so that the target state can be directly reconstructed by applying the control sequence reversely. In this manner, the state tomography problem is converted to a state-to-state transfer problem. To solve the latter problem, we use the closed-loop learning control approach. Our scheme is further experimentally tested using techniques of a 4-qubit nuclear magnetic resonance. \red{Experimental results indicate that the proposed tomographic scheme can handle a broad class of states including entangled states in quantum information, as well as dynamical states of quantum many-body systems common to condensed matter physics.

中文翻译：

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变分混合量子经典方法的量子纯态层析成像

为了获得对量子系统的完整描述，通常使用标准的量子态层析成像技术，然而，这需要进行指数级的测量，因此在系统尺寸变大时是不切实际的。在这项工作中，我们介绍了一种基于变分混合量子经典方法的自学层析成像方案。该方案的关键部分是学习过程，其中我们学习能够将未知目标状态连贯地驱动到简单基准状态的控制序列，从而可以通过反向应用控制序列来直接重建目标状态。以这种方式，状态断层摄影问题被转换为状态到状态转移问题。为了解决后一个问题，我们使用闭环学习控制方法。我们的方案使用4量子位核磁共振技术进行了进一步的实验测试。\ red {实验结果表明，拟议的层析成像方案可以处理多种状态，包括量子信息中的纠缠态以及凝聚态物理学中常见的量子多体系统的动力学态。