scholarly journals Matrix product state recursion methods for computing spectral functions of strongly correlated quantum systems

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Yifan Tian ◽  
Steven R. White
Keyword(s):  
Quantum Systems ◽  
Matrix Product ◽  
Strongly Correlated ◽  
Product State ◽  
Spectral Functions ◽  
Matrix Product State ◽  
Correlated Quantum Systems

scholarly journals Chebyshev matrix product state approach for spectral functions

2011 ◽  
Vol 83 (19) ◽  
Author(s):  
Andreas Holzner ◽  
Andreas Weichselbaum ◽  
Ian P. McCulloch ◽  
Ulrich Schollwöck ◽  
Jan von Delft
Keyword(s):  
Matrix Product ◽  
Product State ◽  
Spectral Functions ◽  
Matrix Product State

scholarly journals Numerical evaluation of two-time correlation functions in open quantum systems with matrix product state methods: a comparison

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Stefan Wolff ◽  
Ameneh Sheikhan ◽  
Corinna Kollath
Keyword(s):  
Correlation Functions ◽  
Open Quantum Systems ◽  
Time Correlation ◽  
Quantum Systems ◽  
Quantum Trajectories ◽  
Time Correlation Functions ◽  
Matrix Product ◽  
Product State ◽  
Open Quantum ◽  
Matrix Product State

We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach[1] and two approaches[2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.

scholarly journals Matrix product state representations

2007 ◽  
Vol 7 (5&6) ◽  
pp. 401-430 ◽  
Author(s):  
D. Perez-Garcia ◽  
F. Verstraete ◽  
M.M. Wolf ◽  
J.I. Cirac
Keyword(s):  
Quantum Systems ◽  
Quantum States ◽  
Matrix Product ◽  
Canonical Forms ◽  
Product State ◽  
Matrix Product State ◽  
Translation Symmetry

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

scholarly journals Geometric entanglement from matrix product state representations

2011 ◽  
Vol 13 (9) ◽  
pp. 093041 ◽  
Author(s):  
Bing-Quan Hu ◽  
Xi-Jing Liu ◽  
Jin-Hua Liu ◽  
Huan-Qiang Zhou
Keyword(s):  
Matrix Product ◽  
Product State ◽  
Matrix Product State

scholarly journals Optimising Matrix Product State Simulations of Shor's Algorithm

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 116 ◽  
Author(s):  
Aidan Dang ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Dimensional Structure ◽  
Matrix Product ◽  
Product State ◽  
One Dimensional ◽  
Matrix Product State ◽  
Shor's Algorithm ◽  
The One ◽  
High Level ◽  
Space Requirements ◽  
Factoring Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on r, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.

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