Examples

Here, we provide examples demonstrating how QICS can be used to solve a variety of semidefinite and quantum relative entropy programs, with an emphasis on applications arising in quantum informaiton theory.

It is recommended that beginners first read Getting started and Representing matrices to better understand the example code provided in these pages.

Semidefinite programming

Max cut

Semidefinite relaxation of the max cut problem and its complex counterpart.

sdp/maxcut.html

Block diagonal

How block-diagonal structure in a semidefinite program can be exploited.

sdp/product.html

Quantum information

Suite of semidefinite programs arising in quantum information theory.

sdp/quantum.html

Quantum relative entropy programming

Quantum key distribution

How to compute the quantum key rate for a given quantum cryptographic protocol.

qrep/qkd.html

Nearest matrix

Finding the closest matrix to a given matrix in the quantum relative entropy sense.

qrep/nearest.html

Quantum channels

Explores the fundamental limits of communication with quantum resources.

qrep/channel.html

Noncommutative perspective

Some examples involving operator relative entropies and weighted geometric means.

qrep/opper.html

Renyi entropies

Some examples involving minimizing Renyi entropies and sandwiched Renyi entropies.

qrep/renyi.html