Boson Sampling as Canonical Transformation: A semiclassical approach in Fock space

TL;DR

This paper presents a semiclassical framework for boson sampling using canonical transformations in Fock space, linking quantum interference with classical scattering theory to improve understanding and computation of many-body quantum processes.

Contribution

It introduces a novel semiclassical approach that models complex many-body scattering as canonical transformations, offering new representations for transition probabilities in boson sampling.

Findings

Derived exact relations for scattering processes.

Connected quantum interference with classical transformations.

Provided new tools for analyzing boson sampling complexity.

Abstract

We show that a theory of complex scattering between many-body (Fock) states can be constructed such that its classical limit is a canonical transformation thus encoding quantum interference in the semiclassical form of the associated unitary operator. Based on this idea, we study the different coherent effects expected under different choices of the many-body states and provide different representations of the associated transition probabilities. In this way, we derive exact relations and representations of the scattering process that can be used to attack timely problems related with Boson Sampling.