scholarly journals Matrix product state formulation of the multiconfiguration time-dependent Hartree theory

2018 ◽  
Vol 149 (19) ◽  
pp. 194114 ◽  
Author(s):  
Yuki Kurashige
Keyword(s):  
Time Dependent ◽  
Matrix Product ◽  
Product State ◽  
Matrix Product State

scholarly journals A new method to calculate ultrafast electron dynamics in molecules based on matrix product states

2019 ◽  
Vol 205 ◽  
pp. 03009
Author(s):  
Lars-Hendrik Frahm ◽  
Daniela Pfannkuche
Keyword(s):  
Wave Function ◽  
Time Dependent ◽  
New Method ◽  
Matrix Product ◽  
Product State ◽  
Electron Dynamics ◽  
Matrix Product States ◽  
Electronic Wave ◽  
Matrix Product State ◽  
Electronic Wave Function

We propose a new method to describe electron dynamics in molecules on the scale of femtoseconds. It is based on factorizing the electronic wave function into a matrix product state and using this factorization to solve the time dependent Schrodinger equation.

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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