Detecting Quantum Phase Transitions using Classical Noises

Stephen Inglis, Jason Iaconis, Ann B. Kallin +1 more

Michael Kruse, H. G. Miller, Angelo Plastino +1 more

DR, MKP

We demonstrate that the O-HAT operator robustly detects quantum-to-classical phase transitions in a Mach-Zehnder interferometer across three noise regimes: NumPy ideal (d=40.0, p=4.65e-260), AerSimulator IBM-realistic (d=37.0, p=1.10e-75), and artificial T2=1ns sensitivity bound (d=43.0, p=1.87e-79). All regimes achieve d > 35 with 30 trials each. White noise negative control confirms |dH| > 5 in <0.2% of trials. Signal survives realistic superconducting qubit noise (T1=150us, T2=100us, gate error 0.03%, readout error 2%) with only 7.5% attenuation. Repository includes full Qiskit MZI simulation script and three-layer results data. GitHub: https://github.com/MMDR10/ohat-quantum

Anis Omidniaee, Keyvan Barati, Ali Farmani +2 more

Measurement-induced phase transitions are a central paradigm in non-unitary quantum dynamics, arising from the interplay between unitary evolution and projective measurements. In this study, we analyze the robustness of measurement-induced Ising order under combined coherent rotation errors and stochastic measurement noise, using echo-protected quantum circuits simulated for system sizes .Our results show that magnetization remains above 0.8 for measurement noise up to in the largest system, demonstrating a substantial enhancement compared to unprotected circuits where the same threshold drops below 0.12. Finite-size scaling confirms consistent crossing of magnetization curves at the critical noise , independent of system size within numerical resolution. Fidelity analysis further reveals that global quantum coherence is more sensitive: decreases to 0.5 near , while magnetization still exceeds 0.7, emphasizing the difference between classical order and quantum state integrity.The derivative of fidelity with respect to measurement noise, exhibits a sharp peak around for , providing a clear numerical indicator of the critical point. The robustness metric highlights an operationally useful ordered phase that persists for quantifying the combined effect of classical correlations and state fidelity. Overall, echo protection improves the threshold by more than 50% compared to unprotected dynamics and stabilizes both classical and quantum observables under realistic noise.These findings demonstrate quantitatively that coherent error mitigation, combined with fidelity-based diagnostics, significantly enhances the stability and detectability of measurement-induced phases on near-term quantum devices

Ming‐Liang Hu, Heng Fan

Victor Kasatkin, Evgeny Mozgunov, Nic Ezzell +1 more

The detection of quantum and classical phase transitions in the absence of an order parameter is possible using the Fisher information metric (FIM), also known as fidelity susceptibility. Here, we propose and investigate an unsupervised machine learning (ML) task: estimating the FIM given limited samples from a multivariate probability distribution of measurements made throughout the phase diagram. We utilize an unsupervised ML method called ClassiFIM (developed in a companion paper) to solve this task and demonstrate its empirical effectiveness in detecting both quantum and classical phase transitions using a variety of spin and fermionic models, for which we generate several publicly available datasets with accompanying ground-truth FIM. We find that ClassiFIM reliably detects both topological (e.g., XXZ chain) and dynamical (e.g., metal-insulator transition in Hubbard model) quantum phase transitions. We perform a detailed quantitative comparison with prior unsupervised ML methods for detecting quantum phase transitions. We demonstrate that ClassiFIM is competitive with these prior methods in terms of appropriate accuracy metrics while requiring significantly less resource-intensive training data compared to the original formulation of the prior methods. In particular, ClassiFIM only requires classical (single-basis) measurements. As part of our methodology development, we prove several theorems connecting the classical and quantum fidelity susceptibilities through equalities or bounds. We also significantly expand the existence conditions of the fidelity susceptibility, e.g., by relaxing standard differentiability conditions. These results may be of independent interest to the mathematical physics community.