Characterization and verification of quantum systems with neural networks

Abstract

Characterizing quantum systems and verifying their behaviours are central tasks in the fields of quantum information and quantum many-body physics, and serve as the foundation for numerous quantum technologies. However, these tasks are made extremely challenging by the exponential increase in the number of parameters needed to describe quantum states and processes when the size of the quantum system increases. Due to this exponential increase, conventional methods like quantum tomography become unviable for large quantum systems. Given the capabilities of deep neural networks in handling large datasets, a promising approach to the challenge is to apply deep neural networks to the characterization of quantum systems. The goal of this dissertation is to provide efficient new techniques for the characterization and verification of quantum states and processes, and to explore the interplay between quantum information tasks and ideas in classical machine learning. We start from the problem of characterizing quantum states from experimental data, introducing a flexible neural network capable of learning sets of quantum states. This network can be trained using classically simulated data from a set of fiducial states and measurements and then be used for characterizing quantum states that exhibit structural similarities with the fiducial states. We then expand our study to the characterization of quantum processes. Specifically, we consider the problem of predicting a quantum process's behavior when applied to an ensemble of input states. To tackle this problem, we develop a neural emulator that mimics the action of a quantum process, significantly reducing the quantum resources necessary for characterizing families of quantum processes with sufficiently regular structure.

After developing general-purpose techniques for state and process characterization, we consider the application of deep neural networks to quantum many-body physics. A challenging problem in quantum many-body physics is the identification of different phases of matter characterized by global parameters, that is, parameters involving a number of systems growing as the total system’s size. To address this problem, we introduce a multi-task neural network model, capable of accurate predicting multiple global properties of many-body quantum systems using limited measurement data obtained from a few neighboring sites. Remarkably, the model can perform unsupervised classification of quantum phases of matter and uncover unknown boundaries between different phases, even without any labeled data.

Finally, we address the task of quantum verification, which involves assessing whether two uncharacterized quantum devices exhibit the same behavior, and is significant for benchmarking near-term quantum computers and quantum simulators. We further introduce a machine learning algorithm based on convolutional neural networks for comparing unknown quantum states, working with limited and noisy data. Our approach achieves this by evaluating the similarity of quantum states through lower-dimensional representations constructed from measurement data by the proposed neural network. We show the versatility of our method by applying it to both discrete and continuous-variable quantum states. The model can even be applied to quantum states across diverse experimental platforms, each with its distinct set of achievable measurements. Furthermore, we demonstrate its effectiveness in experimentally testing the equivalence of two states up to Gaussian unitary transformations.