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
Random unitaries scramble quantum information into highly nonlocal degrees of freedom, thereby providing protection from local noise. However, as demonstrated by Turkeshi and Sierant (Phys. Rev. Lett. 132, 140401, 2024 and arXiv:2603.00235), this protection may fail once local noise grows sufficiently strong. These works describe a phase transition in a noisy random encoding-decoding circuit model between an error-protecting phase, in which encoded information is recoverable, and an error-vulnerable phase, in which encoded information is lost, with the transition occurring at a critical coherent noise angle
αc≈1.14. Here, we present the first experimental observation of this transition, conducted on IBM's ibm_pittsburgh Heron r3 device for system sizes of up to
N=26 qubits. We detect this transition via three order parameters: fidelity, Rényi-2 entanglement entropy, and stabilizer Rényi-2 entropy. For the latter two, we employ randomized measurement protocols to construct estimators, and for all three, we rely on zero-noise extrapolation and M3 SPAM error mitigation. We then jointly model the finite-size scaling collapse across all three order parameters with a Gaussian process regression, yielding a critical angle
αc≈1.01, well below the theoretical value. Inputting noiseless simulated data into the same model yields
αc≈1.05, implying that the discrepancy between experiment and theory is due to our encoding circuits, which are not deep enough to be truly Haar-random. Finally, we observe that the same model cannot adequately identify critical behavior in unmitigated, raw experimental data. This indicates that error mitigation techniques are crucial for detecting the transition on hardware.
Abstract Monitored quantum circuits offer great perspectives for exploring the interplay of quantum information and complex quantum dynamics. These systems exhibit entanglement and purification phase transitions, along with various symmetry-enforced and ordered non-equilibrium phases. The central question is whether these phases can persist in real-world noisy devices. We study the fate of the symmetry-enforced absorbing state and charge-sharpening transitions in the presence of noise, and establish that noise results in coherent and incoherent symmetry-breaking effects. The coherent effects blur the distinction between phases, turning sharp transitions into crossovers, but states far from phase boundaries largely retain their essential character. We find, corrective feedback and postselected measurements can mitigate noise, stabilizing the absorbing and charge-sharp phases. Hence, if challenges like postselection are addressed, errors do not prevent the observation of symmetry-enforced phases in noisy intermediate-scale quantum (NISQ) devices. Additionally, we propose a symmetry-based method to characterize noise and gate fidelity.
We employ unsupervised learning tools to identify the dynamical phases and their measurement-induced transitions in quantum systems subject to the combined action of unitary evolution and stochastic local measurements. Specifically, we show that the principal component analysis and the intrinsic dimension estimation provide order parameters that directly locate the transition and the critical exponents in the classical encoding data space. Finally, we test our approach on stabilizer circuits as proof of principle, finding robust agreement with previous studies.
During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb + 171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.