4.6 Article

Simulating Effective QED on Quantum Computers

Journal

QUANTUM
Volume 6, Issue -, Pages 1-44

Publisher

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
DOI: 10.22331/q-2022-01-18-622

Keywords

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Funding

  1. Google Quantum AI
  2. NSF
  3. Pacific Northwest National Laboratory LDRD program
  4. Embedding Quantum Computing into Many-Body Frameworks for Strongly Correlated Molecular and Materials Systems project by US Department of Energy (DOE)
  5. INT's U.S. Department of Energy [DE-FG02-00ER41132]
  6. U.S. Depart-ment of Energy [DE-SC0019478]
  7. U.S. Department of Energy, Office of Science, Basic Energy Sciences, in the Heavy-Element Chemistry program [DE-SC0021100]
  8. Molecular Sciences Software Institute under NSF [OAC-1547580]
  9. U.S. Department of Energy (DOE) [DE-SC0019478] Funding Source: U.S. Department of Energy (DOE)

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In recent years, quantum computing has emerged as a preeminent application in the simulations of chemistry and condensed materials, offering exponential speedup for solving the electronic structure of certain strongly correlated electronic systems. This study shows that effective quantum electrodynamics (QED), equivalent to QED to second order in perturbation theory, can be simulated on a quantum computer in polynomial time while properly treating all four components of the wavefunction. The authors provide a detailed analysis of such simulations in position and momentum bases using Trotter-Suzuki formulas and discuss their findings on gate counts for simulating relativistic versions of the uniform electron gas.
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the ferrnionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T-gates needed to perform such simulations on a 3D lattice of n(s) sites scales at worst as O(n(s)(3)/epsilon)(1+o(1)) in the thermodynamic limit for position basis simulations and O(n(s)(4+2/3)/epsilon)(1+o(1)) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of (O) over tilde (n(s)(2+2/3)/epsilon ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of (O) over tilde (n(s)(5+2/3)/epsilon). We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 10(13) non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

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