相关论文: Parent Lindbladians for Matrix Product Density Ope…
Matrix product density operators (MPDOs) are an important class of states with interesting properties. Consequently, it is important to understand how to prepare these states experimentally. One possible way to do this is to design an open…
We study whether one can write a Matrix Product Density Operator (MPDO) as the Gibbs state of a quasi-local parent Hamiltonian. We conjecture this is the case for generic MPDO and give supporting evidences. To investigate the locality of…
Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for…
Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…
We propose a tensor network approach known as the locally purified density operator (LPDO) to investigate the classification and characterization of symmetry-protected topological (SPT) phases in open quantum systems. We extend the concept…
Matrix product density operator (MPDO) provides an efficient tensor network representation of mixed states on one-dimensional quantum many-body systems. We study a real-space renormalization group transformation of MPDOs represented by a…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally…
We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple $\mathbb{Z}_2$ graded algebras, which are physically distinguished by…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
In the Fock representation, we propose a framework to construct the generalized matrix product states (MPS) for topological phases with $\mathbb{ Z}_{p}$ parafermions. Unlike the $\mathbb{Z}_{2}$ Majorana fermions, the $% \mathbb{Z}_{p}$…
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…
An important open question for the current generation of highly controllable quantum devices is understanding which phases can be realized as stable steady-states under local quantum dynamics. In this work, we show how robust steady-state…
Simulating open quantum systems is essential for exploring novel quantum phenomena and evaluating noisy quantum circuits. In this Letter, we address the problem of whether mixed states generated from noisy quantum circuits can be…
The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…
We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state…
We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and…
Existence of Anderson localization is considered a manifestation of coherence of classical and quantum waves in disordered systems. Signatures of localization have been observed in condensed matter and cold atomic systems where the coupling…
Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and…
Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum…