Simulating Effective QED on Quantum Computers

by Torin Stetina (University of Washington)

Monday 19 Jul 2021, 14:00 → 15:00 US/Eastern

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, and additionally examine qubitization methods. 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 MRCISD states in effective QED which provide a reasonable initial guess for the groundstate.