skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum algorithms for disordered physics

Abstract

We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body 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 metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional lattice, using physical quantum processors.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]
  1. George Washington Univ., Washington, DC (United States); Univ. of Maryland, College Park, MD (United States). Dept. of Physics
  2. 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:  
FG02-93ER40762; FG02-95ER40907
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 101; Journal Issue: 3; Journal ID: ISSN 2469-9926
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. doi:https://doi.org/10.1103/PhysRevA.101.032325
Bedaque, Paulo, Alexandru, Andrei, and Lawrence, Scott. Thu . "Quantum algorithms for disordered physics". United States. doi: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 pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body 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 metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional 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}
}

Works referenced in this record:

Absence of Diffusion in Certain Random Lattices
journal, March 1958


Anderson transitions
journal, October 2008


Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
journal, March 1979


Interactions and the Anderson transition
journal, March 1980


Anderson localization and interactions in one-dimensional metals
journal, January 1988


Quantum supremacy using a programmable superconducting processor
journal, October 2019


Universal Quantum Simulators
journal, August 1996


Digitization of scalar fields for quantum computing
journal, May 2019


Eliminating fermionic matter fields in lattice gauge theories
journal, August 2018


Formulation of lattice gauge theories for quantum simulations
journal, March 2015


Dynamic linear response quantum algorithm
journal, September 2019


Quantum Algorithms for Quantum Field Theories
journal, May 2012


General methods for digital quantum simulation of gauge theories
journal, August 2019


Quantum simulation of lattice gauge theories using Wilson fermions
journal, June 2018

  • Zache, T. V.; Hebenstreit, F.; Jendrzejewski, F.
  • Quantum Science and Technology, Vol. 3, Issue 3
  • DOI: 10.1088/2058-9565/aac33b

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016

  • Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp
  • Nature, Vol. 534, Issue 7608
  • DOI: 10.1038/nature18318

Scalar quantum field theories as a benchmark for near-term quantum computers
journal, March 2019

  • Yeter-Aydeniz, Kübra; Dumitrescu, Eugene F.; McCaskey, Alex J.
  • Physical Review A, Vol. 99, Issue 3
  • DOI: 10.1103/PhysRevA.99.032306

σ Models on Quantum Computers
journal, August 2019


Critical properties of the Anderson localization transition and the high-dimensional limit
journal, March 2017