Quantum simulation from quantum chemistry to quantum field theory

Quantum simulation proposes using future quantum computers to calculate the properties of quantum systems. In the context of chemistry, the focus is the problem of electronic structure: determining the electronic energy given the nuclear coordinates of a molecule. Quantum computing approaches to quantum chemistry problems have become a central focus of academic and commercial efforts to build a quantum computer. I will give an introduction to quantum algorithms in this field as well as progress and prospects for experimental implementations. It is natural to wonder whether lessons learned from chemistry can be applied to other areas of physics. Simulating quantum field theories, by any means, is challenging, as are quantum algorithms for fundamental physics problems. We will show that the light front formulation of quantum field theory is particularly useful in this regard. We analyze a simple 1 1D theory and show how the calculation of quantities of interest in this theory is analogous to the quantum algorithms for chemistry that we understand in detail.

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