Neural-network quantum state tomography in four-photon entanglement systems

Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla +3 more

Lucas Rantz

Quantum photonic circuits began growing in research interest due to the long coherence times of photonic qubits, allowing for potential long-range quantum communication. To miniaturize these photonic circuits, much research has been done into integrating these systems into a chip-architecture, commonly known as an integrated photonic circuit. Due to the collapse postulate of quantum mechanics, information encoded into photons must be extracted from measurement distributions, formally known as quantum state tomography. This thesis examines the use of neural networks in quantum state tomography, compared to the commonly used maximum likelihood estimation method in a two-qubit system, in the presence of errors typically found in integrated photonic circuits. It is shown in simulation, that by altering the training of a neural network to incorporate errors, the state reconstruction infidelity can be greatly decreased and far surpass the maximum likelihood estimation. Networks are also shown with low bit-precisions, allowing for the potential future use of ultra-fast optical processors to create the neural network. From this work, it can be concluded that neural networks are able to not only complete the task of quantum state tomography, but are able to withstand errors and create more faithful reconstructions for the outputs of integrated quantum photonic circuits.

Joe Yoshimoto, Hikaru Shimizu, Kazufumi Tanji +5 more

Victor Wei, W. A. Coish, Pooya Ronagh +1 more

Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct the quantum state via a neural network ansatz, is often implemented via a basis-dependent cross-entropy loss function. State-of-the-art implementations of NNQST are often restricted to characterizing a particular subclass of states, to avoid an exponential growth in the number of required measurement settings. To provide a more broadly applicable method for efficient state reconstruction, we present “neural-shadow quantum state tomography” (NSQST)—an alternative neural network-based QST protocol that uses infidelity as the loss function. The infidelity is estimated using the classical shadows of the target state. Infidelity is a natural choice for training loss, benefiting from the proven measurement sample efficiency of the classical shadow formalism. Furthermore, NSQST is robust against various types of noise without any error mitigation. We numerically demonstrate the advantage of NSQST over NNQST at learning the relative phases of three target quantum states of practical interest, as well as the advantage over direct shadow estimation. NSQST greatly extends the practical reach of NNQST and provides a novel route to effective quantum state tomography. Published by the American Physical Society 2024

Marcel Neugebauer, Laurin E. Fischer, Alexander Jäger +4 more

We study the performance of efficient quantum state tomography methods based on neural-network quantum states using measured data from a two-photon experiment. Machine-learning-inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e., to positive semidefinite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.

Joanna Wiśniewska, Marek Sawerwain