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SUMMARY:Spacetime Spins: Statistical mechanics for error correction with s
 tabilizer circuits - Cory Aitchison\, Centre for Quantum Information and F
 oundations\, Department of Applied Maths and Theoretical Physics\, Univers
 ity of Cambridge
DTSTART:20260210T110000Z
DTEND:20260210T115000Z
UID:TALK243652@talks.cam.ac.uk
CONTACT:Cory Aitchison
DESCRIPTION:This paper is available at https://arxiv.org/abs/2512.21991\n\
 nAbstract:\nA powerful method for analyzing quantum error-correcting codes
  is to map them onto classical statistical mechanics models. Such mappings
  have thus far mostly focused on static codes\, possibly subject to repeat
 ed syndrome measurements. Recent progress in quantum error correction\, ho
 wever\, has prompted new paradigms where codes emerge from stabilizer circ
 uits in spacetime -- a unifying perspective encompassing syndrome extracti
 on circuits of static codes\, dynamically generated codes\, and logical op
 erations. We show how to construct statistical mechanical models for stabi
 lizer circuits subject to independent Pauli errors\, by mapping logical eq
 uivalence class probabilities of errors to partition functions using the s
 pacetime subsystem code formalism. We also introduce a modular language of
  spin diagrams for constructing the spin Hamiltonians\, which we describe 
 in detail focusing on independent circuit-level X-Z error channels. With t
 he repetition and toric codes as examples\, we use our approach to analyti
 cally rank logical error rates and thresholds between code implementations
  with standard and dynamic syndrome extraction circuits\, describe the eff
 ect of transversal logical Clifford gates on logical error rates\, and per
 form Monte Carlo simulations to estimate maximum likelihood thresholds. Ou
 r framework offers a universal prescription to analyze\, simulate\, and co
 mpare the decoding properties of any stabilizer circuit\, while revealing 
 the innate connections between dynamical quantum systems and noise-resilie
 nt phases of matter. 
LOCATION:Computer Laboratory\, William Gates Building\, Room FW11
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