CENTER FOR COMPUTATION & TECHNOLOGY

Simulating the Hamiltonian dynamics of quantum systems is one of the most promising applications of digital quantum computers. In this talk, I will discuss how to speed up digital quantum simulation by using randomness. In the first part, I will use randomness to improve the product-formula algorithm, a straight-forward approach to quantum simulation that has been demonstrated by several experimental groups. I will show that by randomizing how the Hamiltonian terms are ordered, one can prove stronger bounds on the quality of approximation for product formulas, and thereby give more efficient simulations. I will provide further numerical evidence suggesting that the randomized approach has better empirical performance as well. In the second part, I will describe a randomized approach to time-dependent Hamiltonian simulation. I will show that this approach can simulate Hamiltonians with $L^1$-norm scaling, whereas the best previous results scale with the $L^\infty$ norm. Our approach thus provides an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly, such as in the semi-classical simulations of scattering processes in quantum chemistry.