On the Pauli group on 2-qubits in dynamical systems with pseudofermions

TL;DR

This paper explores how Pauli groups on 2-qubits can emerge in dynamical systems with non self-adjoint Hamiltonians and can be represented using pseudofermionic operators, extending their relevance beyond quantum computing.

Contribution

It demonstrates the appearance of Pauli groups in non-Hermitian dynamical systems and introduces their representation via pseudofermionic operators.

Findings

Pauli groups appear in non-Hermitian dynamical systems

Representation of Pauli groups with pseudofermionic operators

Extension beyond quantum computing contexts

Abstract

The group of matrices $P_1$ of Pauli is a finite 2-group of order 16 and plays a fundamental role in quantum information theory, since it is related to the quantum information on the 1-qubit. Here we show that both $P_1$ and the Pauli 2-group $P_2$ of order 64 on 2-qubits, other than in quantum computing, can also appear in dynamical systems which are described by non self-adjoint Hamiltonians. This will allow us to represent $P_1$ and $P_2$ in terms of pseudofermionic operators.