Quantum Information Approach to Bosonization of Supersymmetric Yang-Mills Fields

TL;DR

This paper develops a quantum information framework for bosonizing supersymmetric Yang-Mills fields, constructing representations suitable for quantum computing, and identifying symmetries in supersymmetric systems.

Contribution

It introduces a novel bosonization method for SUSY systems, constructs irreducible representations across sectors, and connects these to quantum computing implementations.

Findings

Constructed a minimal bosonization of SUSY with one bosonic and two fermionic degrees of freedom.

Identified an osp(2|2) symmetry in the constructed system.

Developed representations in terms of qubit operators for quantum information applications.

Abstract

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.