Tree tensor network approach to simulating Shor's algorithm
Abstract
Constructively simulating quantum systems furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this paper, we directly simulate and explore the entanglement structure present in the paradigmatic example for exponential quantum speedups: Shor's algorithm. To perform our simulation, we construct a dynamic tree tensor network which manifestly captures two salient circuit features for modular exponentiation. These are the natural two-register bipartition and the invariance of entanglement with respect to permutations of the top-register qubits. Our construction help identify the entanglement entropy properties, which we summarize by a scaling relation. Further, the tree network is efficiently projected onto a matrix product state from which we efficiently execute the quantum Fourier transform. In conclusion, future simulation of quantum information states with tensor networks exploiting circuit symmetries is discussed.
- Authors:
-
[1]
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1414718
- Alternate Identifier(s):
- OSTI ID: 1414322
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Dumitrescu, Eugene F. Tree tensor network approach to simulating Shor's algorithm. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.96.062322.
Dumitrescu, Eugene F. Tree tensor network approach to simulating Shor's algorithm. United States. https://doi.org/10.1103/PhysRevA.96.062322
Dumitrescu, Eugene F. Wed .
"Tree tensor network approach to simulating Shor's algorithm". United States. https://doi.org/10.1103/PhysRevA.96.062322. https://www.osti.gov/servlets/purl/1414718.
@article{osti_1414718,
title = {Tree tensor network approach to simulating Shor's algorithm},
author = {Dumitrescu, Eugene F.},
abstractNote = {Constructively simulating quantum systems furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this paper, we directly simulate and explore the entanglement structure present in the paradigmatic example for exponential quantum speedups: Shor's algorithm. To perform our simulation, we construct a dynamic tree tensor network which manifestly captures two salient circuit features for modular exponentiation. These are the natural two-register bipartition and the invariance of entanglement with respect to permutations of the top-register qubits. Our construction help identify the entanglement entropy properties, which we summarize by a scaling relation. Further, the tree network is efficiently projected onto a matrix product state from which we efficiently execute the quantum Fourier transform. In conclusion, future simulation of quantum information states with tensor networks exploiting circuit symmetries is discussed.},
doi = {10.1103/PhysRevA.96.062322},
journal = {Physical Review A},
number = 6,
volume = 96,
place = {United States},
year = {Wed Dec 20 00:00:00 EST 2017},
month = {Wed Dec 20 00:00:00 EST 2017}
}
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Works referencing / citing this record:
Validating quantum-classical programming models with tensor network simulations
journal, December 2018
- McCaskey, Alexander; Dumitrescu, Eugene; Chen, Mengsu
- PLOS ONE, Vol. 13, Issue 12
Benchmarking treewidth as a practical component of tensor network simulations
journal, December 2018
- Dumitrescu, Eugene F.; Fisher, Allison L.; Goodrich, Timothy D.
- PLOS ONE, Vol. 13, Issue 12
Optimising Matrix Product State Simulations of Shor's Algorithm
journal, January 2019
- Dang, Aidan; Hill, Charles D.; Hollenberg, Lloyd C. L.
- Quantum, Vol. 3
Optimising Matrix Product State Simulations of Shor's Algorithm
text, January 2017
- Dang, Aidan; Hill, Charles D.; Hollenberg, Lloyd C. L.
- arXiv