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SUMMARY:Fault Tolerance by Construction - Benjamin Rodatz\, Department of 
 Computer Science\, University of Oxford
DTSTART:20260224T110000Z
DTEND:20260224T115000Z
UID:TALK244294@talks.cam.ac.uk
CONTACT:Lia Yeh
DESCRIPTION:This paper is available at https://arxiv.org/abs/2506.17181\n\
 nAbstract:\n\nA key challenge in fault-tolerant quantum computing is synth
 esising and optimising circuits in a noisy environment\, as traditional te
 chniques often fail to account for the effect of noise on circuits. In thi
 s work\, we propose a framework for designing fault-tolerant quantum circu
 its that are correct by construction. The framework starts with idealised 
 specifications of fault-tolerant gadgets and refines them using provably s
 ound basic transformations.\n\nTo reason about manipulating circuits while
  preserving their error correction properties\, we define fault equivalenc
 e\; two circuits are considered fault-equivalent if all undetectable fault
 s on one circuit have a corresponding fault on the other. This guarantees 
 that the effect of undetectable faults on both circuits is the same. We ar
 gue that fault equivalence is a concept that is already implicitly present
  in the literature. Many problems\, such as state preparation and syndrome
  extraction\, can be naturally expressed as finding an implementable circu
 it that is fault-equivalent to an idealised specification.\n\nTo utilise f
 ault equivalence in a computationally tractable manner\, we adapt the ZX c
 alculus\, a diagrammatic language for quantum computing. We restrict its r
 ewrite system to not only preserve the underlying linear map but also faul
 t equivalence\, i.e. the circuit's behaviour under noise. Enabled by our f
 ramework\, we verify\, optimise and synthesise new and efficient circuits 
 for syndrome extraction and cat state preparation. We confirm the improved
  performance of our optimised circuits in simulation. We anticipate that f
 ault equivalence can capture and unify different approaches in fault-toler
 ant quantum computing\, paving the way for an end-to-end circuit compilati
 on framework.
LOCATION:Computer Laboratory\, William Gates Building\, Room FW11
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