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CATEGORIES:CQIF Seminar
SUMMARY:Continuous groups of transversal gates for quantum
error correcting codes from finite clock referenc
e frames - Mischa Woods (ETH Zurich\, Swizerland)
DTSTART;TZID=Europe/London:20200220T141500
DTEND;TZID=Europe/London:20200220T151500
UID:TALK138997AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138997
DESCRIPTION:Preprint available at ArXiv 1902.07725. Also onlin
e talk at QIP 2020. Abstract is as follows.\n\nFol
lowing the recent introduction of the task of refe
rence frame error correction\, we show how\, by us
ing reference frame alignment with clocks\, one ca
n add a continuous Abelian group of transversal lo
gical gates to any error-correcting code. With thi
s we further explore a way of circumventing the no
-go theorem of Eastin and Knill\, which states tha
t if local errors are correctable\, the group of t
ransversal gates must be of finite order. We are a
ble to do this by introducing a small error on the
decoding procedure that decreases with the dimens
ion of the frames used. Furthermore\, we show that
there is a direct relationship between how small
this error can be and how accurate quantum clocks
can be: the more accurate the clock\, the smaller
the error\; and the no-go theorem would be violate
d if time could be measured perfectly in quantum m
echanics. The asymptotic scaling of the error is s
tudied under a number of scenarios of reference fr
ames and error models. The scheme is also extended
to errors at unknown locations\, and we show how
to achieve this by simple majority voting related
error correction schemes on the reference frames.
In the Outlook\, we discuss our results in relatio
n to the AdS/CFT correspondence and the Page-Woote
rs mechanism.
LOCATION:MR21\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:Johannes Bausch
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