aiqbench analysis
This research presents a novel method for reconstructing topological invariants in monitored quantum circuits by eliminating the need for exponentially costly postselection. By utilizing randomized symmetry eigenstates and an offline decoder, the study achieves exact finite-time response identities that are polynomially scalable under Gaussian limits. This advancement significantly reduces experimental sampling bottlenecks while enabling precise diagnostics of symmetry-protected-topological phases through joint-sector spectroscopy.
Postselection-Free Reconstruction of Monitored SPT Flux-Charge Responses
arXiv:2608.15477v1 Announce Type: new Abstract: A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.
Abstract:A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2608.15477 [quant-ph]
(or arXiv:2608.15477v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.15477 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
Monitored_SPT_code/README.md
Monitored_SPT_code/core.py
Monitored_SPT_code/error_budget_validation.py
Monitored_SPT_code/extended_validation.py
Monitored_SPT_code/joint_path_validation.py
Monitored_SPT_code/make_figures.py
Monitored_SPT_code/requirements.txt
Monitored_SPT_code/validate_exact_gaussian_decoder.py
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Full text under the publisher's open licence · 258 words
