Simulating Effective QED on Quantum Computers

Journal Article · 18 January 2022 · Quantum

DOI: https://doi.org/10.22331/q-2022-01-18-622 · OSTI ID:1840816

Stetina, Torin F. ^[1]; Ciavarella, Anthony ^[2]; Li, Xiaosong ^[3]; Wiebe, Nathan ^[4]

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1. Department of Chemistry, University of Washington, Seattle, Washington, USA, Simons Institute for the Theory of Computation, University of California, Berkeley, California, USA
2. Institute for Nuclear Theory, University of Washington, Seattle, Washington, USA, Department of Physics, University of Washington, Seattle, Washington, USA
3. Department of Chemistry, University of Washington, Seattle, Washington, USA
4. Department of Physics, University of Washington, Seattle, Washington, USA, Pacific Northwest National Laboratory, Richland, Washington, USA, Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, Challenge Institute for Quantum Computation, University of Washington, Seattle, Washington, USA

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 fermionic 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 $O(n_s^3/ϵ{)}^{1+o\left(1\right)}$ in the thermodynamic limit for position basis simulations and $O(n_s^{4+2/3}/ϵ{)}^{1+o\left(1\right)}$ in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of $\tilde{O}\left(n_s^{2+2/3}/ϵ\right)$ for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of $\tilde{O}\left(n_s^{5+2/3}/ϵ\right)$ . 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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-76RL01830; FG02-00ER41132
• OSTI ID: 1840816
• Report Number(s): PNNL-SA-165105; 622
• Journal Information: Quantum, Journal Name: Quantum Vol. 6; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement
• Country of Publication: Austria
• Language: English