Optimal Hamiltonian of Fermion Flows

TL;DR

This paper formulates Fermion flows within quantum stochastic calculus and determines the Hamiltonian coefficients that minimize a quadratic performance functional, extending previous Boson flow results.

Contribution

It introduces a general Fermion flow framework and derives optimal Hamiltonian coefficients for minimizing a quadratic functional, advancing quantum control theory.

Findings

Derived explicit Hamiltonian coefficients for Fermion flows

Extended Boson flow results to Fermion flows

Optimized quadratic performance functional for Fermion systems

Abstract

After providing a general formulation of Fermion flows within the context of Hudson-Parthasarathy quantum stochastic calculus, we consider the problem of determining the noise coefficients of the Hamiltonian associated with a Fermion flow so as to minimize a naturally associated quadratic performance functional. This extends to Fermion flows results of the authors previously obtained for Boson flows .