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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-martin-stefanak-0
SUMMARY:Algebraic Graph Theory-Martin Štefaňák
CLASS:PUBLIC
DESCRIPTION:TITLE: Recurrence of unitary and stochastic quantum walks\n\nS
 PEAKER:\n Martin Štefaňák\n\nAFFILIATION: \n\nCzech Technical Universit
 y in Prague\n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\
 nABSTRACT: Recurrence means a return of the dynamical system to its\ninit
 ial state. Classical result of Polya [1] from 1920’s shows that\na rando
 m walk on a line and a 2D grid returns to the origin with\ncertainty\, whi
 le it is transient on higher-dimensional lattices. For\nquantum walks\, de
 tection of recurrence requires partial measurement\nafter each step\, yiel
 ding a conditional quantum dynamic. We review the\nmethod to study quantum
  recurrence based on generating functions [2]\,\nfocusing on the quantum w
 alk on a line. Combination of measurement\ninduced effects and faster spre
 ading implies that a quantum walk on a\nline can escape to infinity withou
 t ever returning to the origin.\nFinally\, we present a recent extension o
 f the study of recurrence to\nquantum stochastic walks [3]\, which interpo
 lates between quantum and\nclassical walk dynamics [4]. Surprisingly\, we 
 find that introducing\nclassical randomness can reduce the recurrence prob
 ability --- despite\nthe fact that the classical random walk returns with 
 certainty --- and\nwe identify the conditions under which this intriguing 
 phenomenon\noccurs.\n\n[1] G. Pólya\, Math. Ann. 84\, 149 (1921) \n[2] F.
  A. Grünbaum\, et al.\, Commun. Math. Phys. 320\, 543 (2013) \n[3] F. A. 
 Grünbaum and L. Velázquez\, Advances Math. 326\, 352 (2018) \n[4] M. Št
 efaňák\, et al.\, arXiv:2501.08674
DTSTAMP:20260402T165738Z
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