An Introduction to Cartan's KAK Decomposition for QC Programmers

Details An Introduction to Cartan's KAK Decomposition for QC Programmers An Introduction to Cartan's KAK Decomposition for QC Programmers

2005-07-18

arxiv.org/abs/quant-ph/0507171v1

Physics

Quantum Physics

12 pages (20 files: 1 .tex, 1 .sty, 1 .esp, 14 .m, 1 .html, 1 .jpg, 1 .xxx)

Scientific paper

This paper presents no new results; its goals are purely pedagogical. A special case of the Cartan Decomposition has found much utility in the field of quantum computing, especially in its sub-field of quantum compiling. This special case allows one to factor a general 2-qubit operation (i.e., an element of U(4)) into local operations applied before and after a three parameter, non-local operation. In this paper, we give a complete and rigorous proof of this special case of Cartan's Decomposition. From the point of view of QC programmers who might not be familiar with the subtleties of Lie Group Theory, the proof given here has the virtues, that it is constructive in nature, and that it uses only Linear Algebra. The constructive proof presented in this paper is implemented in some Octave/Matlab m-files that are included with the paper. Thus, this paper serves as documentation for the attached m-files.

Affiliated with

Also associated with

No associations

Rating

An Introduction to Cartan's KAK Decomposition for QC Programmers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Introduction to Cartan's KAK Decomposition for QC Programmers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Introduction to Cartan's KAK Decomposition for QC Programmers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-188468