Reduction of unitary operators, quantum graphs and quantum channels

TL;DR

This paper introduces a method for reducing unitary operators, quantum graphs, and quantum channels, enabling the construction of complex quantum systems from simpler components and providing explicit implementations for certain reductions.

Contribution

It defines the reduction of unitary operators and quantum channels, discusses their application to quantum graphs, and provides explicit implementations for reduced quantum channels.

Findings

Reduction of unitary operators enables assembling complex quantum graphs.

Explicit implementations are provided for reduced quantum channels.

The approach facilitates constructing quantum systems from simpler building blocks.

Abstract

Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices of new quantum graphs from assembling of simpler graphs. The reduction of quantum channels is also defined. The implementation of the quantum gates corresponding to the reduced unitary operator is investigated, although no explicit construction is presented. The situation is different for the reduction of quantum channels for which explicit implementations are given.