Digital quantum computation of fermion-boson interacting systems

TL;DR

This paper presents a new quantum algorithm for simulating fermion-boson systems, enabling precise and scalable modeling of complex quantum interactions with potential applications in physics.

Contribution

The authors develop a discretization method for bosonic fields on qubits, extending existing fermion algorithms to include bosons and their interactions.

Findings

Algorithm scales polynomially with system size.

Successfully simulated a 2-site Holstein polaron with excellent accuracy.

Broad applicability to particle physics and condensed matter systems.

Abstract

We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the continuous theory thanks to the Nyquist-Shannon sampling theorem. The method makes the implementation of quantum algorithms for purely bosonic systems as well as fermion-boson interacting systems feasible. We present algorithmic circuits for computing the time evolution of these systems. The complexity of the algorithms scales polynomially with the system size. The algorithm is a natural extension of the existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to systems involving bosons and fermion-boson interactions and has a broad variety of potential applications in particle physics, condensed matter, etc. Due to the relatively small amount of additional resources required by the inclusion of bosons in our algorithm, the simulation of electron-phonon and similar systems can be placed in the same near-future reach as the simulation of interacting electron systems. We benchmark our algorithm by implementing it for a $2$-site Holstein polaron problem on an Atos Quantum Learning Machine (QLM) quantum simulator. The polaron quantum simulations are in excellent agreement with the results obtained by exact diagonalization.