相关论文: Quantum Barcodes: Persistent Homology for Quantum …
Quantum phase transitions are highly remarkable phenomena manifesting in quantum many-body systems. However, their precise identifications in equilibrium systems pose significant theoretical and experimental challenges. Thus far, dynamical…
Distinguishing non-local orders, including global and topological orders of states through solely local measurements and classical communications (LOCC) is a highly non-trivial and challenging task since the topology of states is determined…
We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
The 1-form symmetries in two-dimensional topological systems are ``shadowed'' as global symmetries in their one-dimensional quantum transfer matrices. In this work, we introduce a distinct shadow effect arising from the pair-creation of…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying…
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always…
We propose a dual-architecture quantum simulation framework for modeling morphisms and stability conditions in the bounded derived category $\mathbf{D}^b(\mathrm{Coh}(X))$, with applications to D-brane physics on K\"ahler and non-K\"ahler…
The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought new concepts that revolutionized the way we understand many-body systems. Recently, through the discovery of symmetry protected topological…
We describe a novel tool for the quantum characterization of optical devices. The experimental setup involves a stable reference state that undergoes an unknown quantum transformation and is then revealed by balanced homodyne detection.…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…
Barcoding photons can provide a host of functionalities that could benefit future quantum communication systems and networks beyond today's imagination. As a significant application of barcoding photons, we introduce code division…
Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by…
Quantum self-oscillatory phases are ubiquitous in driven-dissipative systems. Classically, each phase is defined by its flow pattern and how stationary sets organize phase space (e.g. fixed points and limit cycles), with transitions…
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
In standard persistent homology, a persistent cycle born and dying with a persistence interval (bar) associates the bar with a concrete topological representative, which provides means to effectively navigate back from the barcode to the…
Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among…