# Error-detection-based quantum fault tolerance against discrete Pauli noise

### Benjamin W. Reichardt

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-157

November 22, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-157.pdf

A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the major hurdle in building such a computer is overcoming noise.

Developed over the last couple of years, new schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3-6% noise per gate -- an order of magnitude better than previous procedures. But proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all.

With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates ("noise thresholds") for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.

**Advisor:** Umesh Vazirani

BibTeX citation:

@phdthesis{Reichardt:EECS-2006-157, Author = {Reichardt, Benjamin W.}, Title = {Error-detection-based quantum fault tolerance against discrete Pauli noise}, School = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {Nov}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-157.html}, Number = {UCB/EECS-2006-157}, Abstract = {A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the major hurdle in building such a computer is overcoming noise. Developed over the last couple of years, new schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3-6% noise per gate -- an order of magnitude better than previous procedures. But proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all. With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates ("noise thresholds") for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.} }

EndNote citation:

%0 Thesis %A Reichardt, Benjamin W. %T Error-detection-based quantum fault tolerance against discrete Pauli noise %I EECS Department, University of California, Berkeley %D 2006 %8 November 22 %@ UCB/EECS-2006-157 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-157.html %F Reichardt:EECS-2006-157