Unveiling a Hidden Percolation Transition in Monitored Clifford Circuits: Inroads from ZX-Calculus
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arXiv
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| Natura: | Preprint |
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2025
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| author | Buznach, Einat Chowdhury, Debanjan Ruhman, Jonathan |
| author_facet | Buznach, Einat Chowdhury, Debanjan Ruhman, Jonathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unveiling a Hidden Percolation Transition in Monitored Clifford Circuits: Inroads from ZX-Calculus Buznach, Einat Chowdhury, Debanjan Ruhman, Jonathan Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons 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. |
| title | Unveiling a Hidden Percolation Transition in Monitored Clifford Circuits: Inroads from ZX-Calculus |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2502.13211 |