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SUMMARY:Continuous groups of transversal gates for quantum error correctin
 g codes from finite clock reference frames - Mischa Woods (ETH Zurich\, Sw
 izerland)
DTSTART:20200220T141500Z
DTEND:20200220T151500Z
UID:TALK138997@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:Preprint available at ArXiv 1902.07725. Also online talk at QI
 P 2020. Abstract is as follows.\n\nFollowing the recent introduction of th
 e task of reference frame error correction\, we show how\, by using refere
 nce frame alignment with clocks\, one can add a continuous Abelian group o
 f transversal logical gates to any error-correcting code. With this we fur
 ther explore a way of circumventing the no-go theorem of Eastin and Knill\
 , which states that if local errors are correctable\, the group of transve
 rsal gates must be of finite order. We are able to do this by introducing 
 a small error on the decoding procedure that decreases with the dimension 
 of the frames used. Furthermore\, we show that there is a direct relations
 hip between how small this error can be and how accurate quantum clocks ca
 n be: the more accurate the clock\, the smaller the error\; and the no-go 
 theorem would be violated if time could be measured perfectly in quantum m
 echanics. The asymptotic scaling of the error is studied under a number of
  scenarios of reference frames and error models. The scheme is also extend
 ed to errors at unknown locations\, and we show how to achieve this by sim
 ple majority voting related error correction schemes on the reference fram
 es. In the Outlook\, we discuss our results in relation to the AdS/CFT cor
 respondence and the Page-Wooters mechanism.
LOCATION:MR21\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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