Mixed-state dynamics in one-dimensional quantum lattice systems: A time-dependent superoperator renormalization algorithm
Michael Zwolak,Guifre Vidal +1 more
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TLDR
An algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems with a superoperator renormalization scheme to efficiently describe the state and the time evolving block decimation technique to efficiently update the state during a time evolution is presented.Abstract:
We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension.read more
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The density-matrix renormalization group in the age of matrix product states
TL;DR: This paper gives a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of D MRG algorithms in exclusively MPS terms transparent.
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The density-matrix renormalization group in the age of matrix product states
TL;DR: The density matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems as mentioned in this paper.
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The density-matrix renormalization group
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Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
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References
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Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.