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June 2, 20260 citationsOpen Access

Gauge-Theoretic Defect Representation of Quantum States: A Dimensional Threshold for Classical Simulatability

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PParcex-studio

Key Points

  • This research aims to develop a geometric framework for representing quantum states based on Z8 gauge theory.
  • Introduced a geometric representation using Z8 gauge theory with topological defects.
  • Computed expectation values of local observables in O(n) time using an 8×8 transfer matrix.
  • Implemented a 1D algorithm with accompanying code to validate linear scaling.
  • The expectation values of local observables were accurately computed in O(n) time.
  • The implemented code confirmed linear scaling for quantum state representation in one dimension.
  • Higher-dimensional theory aspects were discussed but not implemented in the code.

Abstract

This paper introduces a geometric representation of quantum states using Z8 gauge theory with topological defects. Clifford gates correspond to gauge transformations; T‑gates correspond to inserting defects. In one dimension, expectation values of local observables are computed in O(n) time using an 8×8 transfer matrix. The accompanying code implements the 1D algorithm and confirms linear scaling. Higher‑dimensional theory is discussed in the paper but not implemented in the code.

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Cite This Study

Parcex-studio (2026) studied this question.

synapsesocial.com/papers/6a1e732830b38c64201b66aahttps://doi.org/10.5281/zenodo.20475388
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