Constructing networks of quantum channels for state preparation
Creators: name: Bondarenko, Dmytro
Publisher: name: Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
Year: 2021
Subjects: subject: denoising
subject: state preparation
subject: open quantum systems
subject: quantum machine learning
subject: dissipative preparation
subject: quantum state engineering
subject: parent Lindbladians
subject: matrix product density operators
subject: quantum neural networks
subject: recurrent quantum neural networks
subject: quantum autoencoders
subject: quantum channels
subject: quantum state extrapolation
subject: Rauschunterdrückung
subject: Zustandspräparation
subject: offene Quantensysteme
subject: maschinelles Lernen auf Quantencomputern
subject: Quantendaten
subject: dissipative Zustandspräparation
subject: Design von Quantenzuständen
subject: erzeugende Lindbladoperatoren
subject: Matrixproduktdichteoperator
subject: Neuronale Netze auf Quantencomputern
subject: Quantenautoencoder
subject: Quantenkanäle
subject: Extrapolation von Quantenzuständen
subject: Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik

description: Entangled possibly mixed states are an essential resource for quantum computation, communication, metrology, and the simulation of many-body systems. It is important to develop and improve preparation protocols for such states. One possible way to prepare states of interest is to design an open system that evolves only towards the desired states. A Markovian evolution of a quantum system can be generally described by a Lindbladian. Tensor networks provide a framework to construct physically relevant entangled states. In particular, matrix product density operators (MPDOs) form an important variational class of states. MPDOs generalize matrix product states to mixed states, can represent thermal states of local one-dimensional Hamiltonians at sufficiently large temperatures, describe systems that satisfy the area law of entanglement, and form the basis of powerful numerical methods. In this work we develop an algorithm that determines for a given linear subspace of MPDOs whether this subspace can be the stable space of some frustration free k-local Lindbladian and, if so, outputs an appropriate Lindbladian. We proceed by using machine learning with networks of quantum channels, also known as quantum neural networks (QNNs), to train denoising post-processing devices for quantum sources. First, we show that QNNs can be trained on imperfect devices even when part of the training data is corrupted. Second, we show that QNNs can be trained to extrapolate quantum states to, e.g., lower temperatures. Third, we show how to denoise quantum states in an unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip, dephasing errors, and random unitary noise. Finally, we develop recurrent QNNs (RQNNs) for denoising that requires memory, such as combating drifts. RQNNs can be thought of as matrix product quantum channels with a quantum algorithm for training and are closely related to MPDOs. The proposed preparation and denoising protocols can be beneficial for various emergent quantum technologies and are within reach of present-day experiments.