SWC Seminar - Quantum Computing Methods for the Simulation of Quantum Physical Systems | Shull Wollan Center
One of the main reasons to build a quantum computer is the simulation of the dynamics of quantum systems. Since the 90s, many quantum algorithms have been developed to this end. Such algorithms have vast applications in science, including quantum chemistry. Although it is well known that quantum computers can simulate spin (qubit) systems efficiently, several groups around the world are investigating new tools to significantly reduce the resources required for this problem. Additionally, quantum algorithms to simulate quantum systems of continuous variables are scarce.
In this talk, I will give an introduction to the simulation of quantum systems with quantum computers. I will then describe our new and simple quantum algorithm that implements an approximation to the Taylor series of the evolution operator. The cost of our algorithm, in contrast with those based on (Lie-Trotter) product formulas, is only logarithmic in the inverse of a precision parameter and can be shown to be optimal. In this way, we obtain an "exponential improvement”. I will also introduce the problem of the simulation of continuous-variable quantum systems, giving some emphasis on the quantum harmonic oscillator. I will show that in this case, a superpolynomial quantum speedup is indeed possible. Our result opens the door to discovering fast quantum algorithms for systems with infinite degrees of freedom.