Kavli Affiliate: Debanjan Chowdhury
| First 5 Authors: Einat Buznach, Debanjan Chowdhury, Jonathan Ruhman, ,
| Summary:
We revisit the measurement-induced phase transition (MPT) in Clifford
circuits, which are both classically simulable and exhibit critical behavior
widely believed to be distinct from classical percolation theory, using
ZX-calculus. We analyze the MPT in a dynamical model composed of CNOT, SWAP,
identity gates, and Bell-pair measurements, respectively, arranged randomly in
a brickwork pattern. Our circuits exhibit a transition that is seemingly
distinct from classical percolation based on standard arguments, that is in
line with the prevailing understanding in the field. In contrast, by employing
ZX-calculus based simplification techniques, we unveil a hidden percolation
transition within the circuit structure. Over a range of parameters tied to the
probabilities for applying different gates, we demonstrate that the classical
percolation transition in the ZX-simplified network coincides with the MPT
observed through mutual information. Our findings suggest that the MPT in
Clifford circuits is, in fact, controlled by a classical percolation transition
in disguise.
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