tag:blogger.com,1999:blog-6703779.post115921431875876565..comments2014-11-20T10:20:14.824+00:00Comments on scrofulous: unglorious problems in quantum informationaram harrowhttp://www.blogger.com/profile/01272118188252697149noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6703779.post-75560658189076302672007-05-05T11:19:00.000+01:002007-05-05T11:19:00.000+01:00I solved problem #1 and will post the (not terribl...I solved problem #1 and will post the (not terribly exciting) solution on the arxiv in probably a few months. Email me if you want me to send it to you before then.aram harrowhttp://www.blogger.com/profile/01272118188252697149noreply@blogger.comtag:blogger.com,1999:blog-6703779.post-1159369393207375332006-09-27T16:03:00.000+01:002006-09-27T16:03:00.000+01:00Good point. Actually this construction was the bes...<I>Good point. Actually this construction was the best we found in quant-ph/0207072, and it's no more than 5 times the optimal number of uses of V.</I><BR/><BR/>When I wrote up my thesis I found a slightly better way to do it, and the construction is now optimal.Chrisnoreply@blogger.comtag:blogger.com,1999:blog-6703779.post-1159268159602015022006-09-26T11:55:00.000+01:002006-09-26T11:55:00.000+01:00I worked on the first problem all day yesterday wi...I worked on the first problem all day yesterday with no success. It is really unbelievable that this problem is open. <BR/><BR/>I thought I had almost solved it using some techniques from a Hamiltonian simulation paper that I wrote with Dave, but then I realised that I can't multiply by -1 properly.mickhttp://quantumbiodiscs.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-6703779.post-1159226305342859922006-09-26T00:18:00.000+01:002006-09-26T00:18:00.000+01:00Good point. Actually this construction was the be...Good point. Actually this construction was the best we found in <A HREF="http://uk.arxiv.org/abs/quant-ph/0207072" REL="nofollow">quant-ph/0207072</A>, and it's no more than 5 times the optimal number of uses of V.<BR/><BR/>So it's only the d>2 case that's open.aram harrowhttp://www.blogger.com/profile/01272118188252697149noreply@blogger.comtag:blogger.com,1999:blog-6703779.post-1159225960763041142006-09-26T00:12:00.000+01:002006-09-26T00:12:00.000+01:001 is true for d=2, right?a) Canonically decompose ...1 is true for d=2, right?<BR/><BR/>a) Canonically decompose V=exp(i ( a XX + b YY + c ZZ)), by appropriate pre and post local unitaries<BR/>b) Conjugate V by XI to generate (XI)V(XI)=exp(i ( a XX - b YY - c ZZ))<BR/>c) Similarly construct exp(i ( -a XX + b YY - c ZZ)) and exp(i ( -a XX - b YY + c ZZ)) by appropriate conjugations<BR/>d) Use all three of these to together to generate exp(-i(a XX+b YY + c ZZ)) which is V^{-1}<BR/><BR/>(Probably an easier way to get this, but oh well.)Dave Baconhttp://dabacon.org/pontiffnoreply@blogger.com