PNNL

Abstract

Elementary quantum mechanics teaches that a closed physical system always evolves in a reversible manner. However, control and readout imply coupling the quantum system to the outside world, making it subject to relaxation and decoherence. Therefore, system-environment interactions must be included in the simulation of physically important theories. To study a broad range of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED, bosonic degrees of freedom, such as phonons, photons, and gluons, need to be included in optimized fermion algorithms for near-future quantum simulations. Specifically, given a quantum system surrounded by an external environment, its basic physics can usually be abstracted as a fermionic system interacting with bosonic modes. The accurate and efficient quantum simulation of these interacting models requires (1) a proper fermion/boson-to-qubit mapping scheme, (2) the construction of an effective Hamiltonian, and (3) error analysis of the introduced approximation. In this paper, we first provide a pedagogical overview of the qubitization and quantum simulation of boson-related Hamiltonians and the construction of their effective forms. We then focus on a formal error analysis of truncating bosonic modes in the quantum simulations of fermion-boson interacting Hamiltonians. Our aim is to offer a practical tutorial and technical guide in this emerging field of quantum computing.