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SUMMARY:Two results on the stabiliser formalism - Nadish de Silva
DTSTART:20230801T131500Z
DTEND:20230801T141500Z
UID:TALK203587@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION:I will sketch two recent results to do with i) stabiliser stat
 e geometry and ii) efficient gate teleporatation of qudit gates.\n\ni) Arb
 itrary quantum states admit many stabiliser decompositions: ways of being 
 expressed as asuperposition of stabiliser states. Understanding of the str
 ucture of stabiliser decompositions has applications in simulating and ver
 ifying near-term quantum computers.\nWe introduce and study the vector spa
 ce of linear dependencies of n-qubit stabiliser states.  These spaces have
  canonical bases containing vectors whose size grows exponentially in n. W
 e construct elegant bases of dependencies of constant size three.\n\n\nii)
  Third-level gates are those that can be most easily implemented fault-tol
 erantly\nusing magic states. Those that are semi-Clifford can be implement
 ed with far more efficient use of resources.\nWe prove that every third-le
 vel gate of up to two qudits is semi-Clifford.  Our proof introduces techn
 iques from algebraic geometry which can be applied more widely within quan
 tum information.
LOCATION:MR14
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