Even Newer Approaches to Quantum Simulation of Systems

In keeping with the tradition of always giving a talk on “New Approaches to Quantum Simulation” that I have kept for the last five years, I’ll be talking about even newer approaches to quantum simulation. In particular, here I will talk about recent developments of methods that hybridize existing approaches to quantum simulations such as QDrift, Qubitization and Trotter formulas, We will show that these methods can, in certain cases, improve the scaling of existing quantum algorithms. Next, I will talk about ways that constant factors can be improved by hybridizing compilation methods with quantum simulation to break up a Hamiltonian into a sum of fragments that can be inexpensively simulated through the greedy introduction of artificial terms into the Hamiltonian. Then I will discuss recent approaches that borrow ideas from error mitigation to show how low order Trotter formulas can be extrapolated to give error scaling that rivals that of linear combinations of unitaries methods for energy estimation. Lastly, I will discuss how quantum forces can be computed in simulation and show how quantum and classical dynamics can be hybridized to improve the performance polynomially with respect to the best known approaches for molecular dynamics by incorporating the classical simulation within the quantum computer. Finally, I will conclude by discussing the prospective methods that I may talk about in my similarly titled talk at next years conference.