相关论文: Lecture Notes: Introduction to random unitary circ…

Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the dynamics toward an absorbing state, we…

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling…

Dissipation is inevitable in realistic quantum circuits. We examine the effects of dissipation on a class of monitored random circuits that exhibit a measurement-induced entanglement phase transition. This transition has previously been…

The rise of programmable quantum devices has motivated the exploration of circuit models which could realize novel physics. A promising candidate is a class of hybrid circuits, where entangling unitary dynamics compete with disentangling…

These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

These notes are from a series of lectures given at the Universidad de Los Andes in Bogot\'a, Colombia on some topics of current interest in quantum information. While they aim to be self-contained, they are necessarily incomplete and…

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…

Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper,…

Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by…

The evolution of a quantum system subject to measurements can be described by stochastic quantum trajectories of pure states. Instead, the ensemble average over trajectories is a mixed state evolving via a master equation. Both descriptions…

These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.

We introduce a new measure called reduced entropy of sublattice to quantify entanglement in spin, electron and boson systems. By analyzing this quantity, we reveal an intriguing connection between quantum entanglement and quantum phase…

A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase…

This is a conference proceeding in the framework of workshop "OpenQMBP2023" at Institute Pascal (Orsay, France) and associated to the lecture given by Prof. Ehud Altman. We provide a comprehensive analysis of recent results in the context…

We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements in addition to random unitary dynamics. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT),…

We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary…

This is a collection of the lecture notes of the three authors for a first-year graduate course on control system theory and design (ECE 515 , formerly ECE 415) at the ECE Department of the University of Illinois at Urbana-Champaign. This…

The intensely studied measurement-induced entanglement phase transition has become a hallmark of non-unitary quantum many-body dynamics. Usually, such a transition only shows up at the level of each individual quantum trajectory, and is…

The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range…