Models on Quantum Computers
Abstract
We formulate a discretization of σ models suitable for simulation by quantum computers. Space is substituted with a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the “fuzzy sphere”, a construction well known from noncommutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact O(3) symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum model. That would allow for continuum results to be obtained for very rough discretizations of the target space as long as the space discretization is made fine enough. The cost of performing time evolution, measured as the number of controlled-not operations necessary, is 12LT/Δt, where L is the number of spatial sites, T the maximum time extent, and Δt the time spacing.
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States); George Washington Univ., Washington, DC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- Contributing Org.:
- NuQS Collaboration
- OSTI Identifier:
- 1559079
- Alternate Identifier(s):
- OSTI ID: 1610232
- Grant/Contract Number:
- FG02-95ER40907; FG02-93ER40762
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 123 Journal Issue: 9; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; physics; lattice field theory; lattice gauge theory; quantum computation; quantum simulation
Citation Formats
Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, Lawrence, Scott, and NuQS Collaboration. σ Models on Quantum Computers. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.090501.
Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, Lawrence, Scott, & NuQS Collaboration. σ Models on Quantum Computers. United States. https://doi.org/10.1103/PhysRevLett.123.090501
Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, Lawrence, Scott, and NuQS Collaboration. Wed .
"σ Models on Quantum Computers". United States. https://doi.org/10.1103/PhysRevLett.123.090501.
@article{osti_1559079,
title = {σ Models on Quantum Computers},
author = {Alexandru, Andrei and Bedaque, Paulo F. and Lamm, Henry and Lawrence, Scott and NuQS Collaboration},
abstractNote = {We formulate a discretization of σ models suitable for simulation by quantum computers. Space is substituted with a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the “fuzzy sphere”, a construction well known from noncommutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact O(3) symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum model. That would allow for continuum results to be obtained for very rough discretizations of the target space as long as the space discretization is made fine enough. The cost of performing time evolution, measured as the number of controlled-not operations necessary, is 12LT/Δt, where L is the number of spatial sites, T the maximum time extent, and Δt the time spacing.},
doi = {10.1103/PhysRevLett.123.090501},
journal = {Physical Review Letters},
number = 9,
volume = 123,
place = {United States},
year = {Wed Aug 28 00:00:00 EDT 2019},
month = {Wed Aug 28 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevLett.123.090501
https://doi.org/10.1103/PhysRevLett.123.090501
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Cited by: 43 works
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Figures / Tables:
FIG. 1: Circuit implementing the time evolution. Starting from the left, we display the kinetic term exp[−$iΔt\mathcal{H}^0$] (for two sites) and the link terms: exp[−$iΔtH^{I1}$(1, 0)] , exp[−$iΔtH^{I2}$ 1, 0)] , and exp[−$iΔtH^{I3}$(1,0)] . The notation for the gates used here is standard in the quantum computing literature.
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