Quantum Property Learning for NISQ Networks: Universal Quantum Witness Machines

The learning of fundamental quantum properties—namely coherence, discord, and entanglement—benchmarks the security, computational, and metrological capability of noisy intermediate-scale quantum (NISQ) communication, computing, and sensing networks. The current learning techniques vary widely for these fundamental quantum properties, including standard tomographic procedures that involve exhaustive optimization. Fortunately, the fundamentally distinct quantum properties feature an intricate connection. In this paper, we put forth the concept of universal quantum witness machines (UQWMs) to develop a unified framework for quantum property learning (QPL) of a quantum system. We first formulate the certification and quantification of quantum properties based on quantum witnesses. The witness-based certification method is experimentally accessible and resource-efficient but lacks reliability and generality. To universalize the scope and circumvent the unreliability, we transform the certification task into a classification task by employing UQWMs with classical machine learning to construct quantum property classifiers. This formalism offers a unifying perspective on the certification, quantification, and classification of these enigmatically linked fundamental quantum properties. To demonstrate our UQWM approach, we provide a comparative numerical analysis of quantum property quantification with quantum witnesses and classification performance analysis of quantum property classification with convolutional neural networks, specifically for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> quantum systems.