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.
The researchers showed 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, they have provided a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. They proposed concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 1013 non-Clifford operations and also provided a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED with a reasonable initial guess for the ground state. Finally, they estimated the planewave cutoffs needed to accurately simulate heavy elements such as gold.
