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Unveiling a Hidden Percolation Transition in Monitored Clifford Circuits: Inroads from ZX Calculus.

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This summary is machine-generated.

Measurement-induced phase transitions in Clifford circuits are revealed to be a disguised classical percolation transition. This discovery challenges previous assumptions by showing a hidden percolation phenomenon within the circuit structure.

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Area of Science:

  • Quantum Information Science
  • Complex Systems

Background:

  • Measurement-induced phase transitions (MPTs) in quantum circuits are a key area of research.
  • Clifford circuits are classically simulable, yet exhibit critical behavior.
  • Prevailing understanding suggests MPTs in Clifford circuits differ from classical percolation.

Purpose of the Study:

  • To re-examine the nature of MPTs in Clifford circuits.
  • To investigate the relationship between MPTs and classical percolation theory.
  • To utilize ZX calculus for circuit analysis.

Main Methods:

  • Analysis of a dynamical model with controlled not (CNOT) gates, SWAP gates, identity gates, and Bell-pair measurements in a brickwork pattern.
  • Application of ZX-calculus based simplification techniques.
  • Observation of MPT via mutual information.

Main Results:

  • Standard analysis suggested the MPT was distinct from classical percolation.
  • ZX-calculus simplification unveiled a hidden classical percolation transition.
  • The identified percolation transition coincided with the MPT observed through mutual information.

Conclusions:

  • The measurement-induced phase transition in Clifford circuits is controlled by an underlying classical percolation transition.
  • ZX calculus provides a powerful tool for uncovering hidden structures in quantum circuits.
  • This finding recontextualizes the understanding of critical phenomena in classically simulable quantum systems.