Quantum algorithms for disordered physics
Abstract
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudorandom number generator directly into the time evolution circuit. This technique is applied to quantum simulation of fewbody disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metalinsulator transition on a threedimensional lattice. Additionally, we demonstrate the algorithm on a onedimensional lattice, using physical quantum processors.
 Authors:

 George Washington Univ., Washington, DC (United States); Univ. of Maryland, College Park, MD (United States). Dept. of Physics
 Univ. of Maryland, College Park, MD (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Univ. of Maryland, College Park, MD (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 OSTI Identifier:
 1605403
 Alternate Identifier(s):
 OSTI ID: 1605500
 Grant/Contract Number:
 FG0293ER40762; FG0295ER40907
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 3; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Bedaque, Paulo, Alexandru, Andrei, and Lawrence, Scott. Quantum algorithms for disordered physics. United States: N. p., 2020.
Web. doi:10.1103/PhysRevA.101.032325.
Bedaque, Paulo, Alexandru, Andrei, & Lawrence, Scott. Quantum algorithms for disordered physics. United States. https://doi.org/10.1103/PhysRevA.101.032325
Bedaque, Paulo, Alexandru, Andrei, and Lawrence, Scott. Thu .
"Quantum algorithms for disordered physics". United States. https://doi.org/10.1103/PhysRevA.101.032325. https://www.osti.gov/servlets/purl/1605403.
@article{osti_1605403,
title = {Quantum algorithms for disordered physics},
author = {Bedaque, Paulo and Alexandru, Andrei and Lawrence, Scott},
abstractNote = {We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudorandom number generator directly into the time evolution circuit. This technique is applied to quantum simulation of fewbody disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metalinsulator transition on a threedimensional lattice. Additionally, we demonstrate the algorithm on a onedimensional lattice, using physical quantum processors.},
doi = {10.1103/PhysRevA.101.032325},
journal = {Physical Review A},
number = 3,
volume = 101,
place = {United States},
year = {2020},
month = {3}
}
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