Matrix Product State, Quantum Entanglement, and Criticality in the One-Dimensional Dimerized Antiferromagnetic Heisenberg Model

2012 ◽  
Vol 58 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Guang-Hua Liu ◽  
Guang-Shan Tian
Keyword(s):  
Quantum Entanglement ◽  
Heisenberg Model ◽  
Matrix Product ◽  
Product State ◽  
One Dimensional ◽  
Matrix Product State ◽  
Antiferromagnetic Heisenberg Model ◽  
The One

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.

scholarly journals -exponents in the one-dimensional antiferromagnetic Heisenberg model with next-nearest-neighbour coupling

1997 ◽  
Vol 9 (16) ◽  
pp. 3435-3445 ◽  
Author(s):  
C Gerhardt ◽  
A Fledderjohann ◽  
E Aysal ◽  
K-H Mütter ◽  
J F Audet ◽  
...  
Keyword(s):  
Heisenberg Model ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
Antiferromagnetic Heisenberg Model ◽  
The One

scholarly journals Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

1996 ◽  
Vol 54 (10) ◽  
pp. 7168-7176 ◽  
Author(s):  
A. Fledderjohann ◽  
C. Gerhardt ◽  
K. H. Mütter ◽  
A. Schmitt ◽  
M. Karbach
Keyword(s):  
Heisenberg Model ◽  
Uniform Field ◽  
Critical Properties ◽  
One Dimensional ◽  
Antiferromagnetic Heisenberg Model ◽  
The One

Ground state of the one-dimensional antiferromagnetic Heisenberg model

1985 ◽  
Vol 31 (3) ◽  
pp. 1590-1599 ◽  
Author(s):  
J. Borysowicz ◽  
T. A. Kaplan ◽  
P. Horsch
Keyword(s):  
Ground State ◽  
Heisenberg Model ◽  
One Dimensional ◽  
Antiferromagnetic Heisenberg Model ◽  
The One
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