Related papers: Quantum Barcodes: Persistent Homology for Quantum …
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcodes between the two different (dual) topological models of…
The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…
This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based…
Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…
Quantum convolutional neural networks (QCNNs) are quantum circuits for characterizing complex quantum states. They have been proposed for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter…
The technology of Quantum Computing (QC) is continuously evolving, as researchers explore new technologies and the public gains access to quantum computers with an increasing number of qubits. In addition, the research community and…
We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling information flow within and/or between clusters…
A topological approach to the study of genetic recombination, based on persistent homology, was introduced by Chan, Carlsson, and Rabad\'an in 2013. This associates a sequence of signatures called barcodes to genomic data sampled from an…
We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
Quantum computing promises a new approach to solving difficult computational problems, and the quest of building a quantum computer has started. While the first attempts on construction were succesful, scalability has never been achieved,…
How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs) which enable the…
Long-term quantum coherence constitutes one of the main challenges when engineering quantum devices. However, easily accessible means to quantify complex decoherence mechanisms are not readily available, nor are sufficiently stable systems.…
Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological…
We investigate a generic dynamical theory to characterize topological quantum phases by quantum quenches, and study the emergent topology of quantum dynamics when the quenches start from a deep or shallow trivial phase to topological…