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SUMMARY:Mattie Ji: A K-theoretic Approach to Quantum Cellular Automata
DTSTART:20261015T121500Z
DTEND:20261015T131500Z
DTSTAMP:20261003T031600Z
UID:indico-event-249@indico.zdv.uni-mainz.de
DESCRIPTION:Speakers: Mattie Ji\n\nA K-theoretic Approach to Quantum Cellu
 lar AutomataAlgebraic K-theory\, on a very high level\, studies how to bre
 ak and assemble objects apart linearly\, which makes the field amenable to
  classification questions. In this work\, we apply this methodology to stu
 dy the classification of quantum cellular automata (QCA)\, which are model
 s for the dynamics of many-particle quantum systems. Although QCAs are tra
 ditionally studied over the complex numbers\, their underlying locality an
 d tensor-product structures make sense over arbitrary commutative rings.We
  first develop an algebraic theory of QCA over any commutative rings. Over
  a general space X and an arbitrary commutative ring R\, we then use algeb
 raic K-theory to construct a space of QCA whose deformation classes either
  are or refine the QCA classification groups. Furthermore\, we show that t
 he spaces of QCA on Euclidean lattices assemble to an $\\Omega$-spectrum i
 ndexed by the dimension. As a corollary\, we also obtain a non-connective 
 delooping of the K-theory of Azumaya R-algebras\, so the QCA classificatio
 n groups may be viewed as a multiplicative version of negative K-theory. T
 his talk is based on joint work with Bowen Yang.\n \n\nhttps://indico.zdv
 .uni-mainz.de/event/249/
LOCATION:Hilbertraum (Mainz)
URL:https://indico.zdv.uni-mainz.de/event/249/
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