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Experimental Observation of Measurement-Induced Phase Transitions on NISQ Processors via Feedback-Stabilized Criticality

Angel Jose Toranzo Portela

Published Jan 18, 2026• 0 citations
Publisher

Abstract

Measurement-induced phase transitions (MIPT) offer a novel paradigm for exploring quantum criticality, yet their experimental observation remains stifled by the "post-selection problem"—the exponential cost of resolving quantum trajectories. Here, we propose a scalable protocol to observe feedback-stabilized criticality on current Noisy Intermediate-Scale Quantum (NISQ) processors, eliminating the need for post-selection. By coupling local measurements to real-time unitary feedback, we demonstrate that a many-body quantum system can be steered toward the universal 1/e information horizon, effectively turning the measurement back-action from a source of decoherence into a resource for complexity. Extensive numerical simulations incorporating realistic depolarizing noise reveal a robust stability plateau extending to gate error rates of p ≈ 10⁻², compatible with state-of-the-art superconducting architectures such as IBM Heron. Furthermore, we introduce a verification scheme based on classical shadows to efficiently estimate the Schmidt concentration ⟨K_c⟩ without full tomography. Our results establish that thermodynamic error correction is achievable in the NISQ era, providing a blueprint for the first experimental observation of a feedback-induced phase transition at the mesoscopic scale (N ~ 100).

DOI
10.5281/zenodo.18294210

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Measurement-induced phase transitions (MIPT) offer a novel paradigm for exploring quantum criticality, yet their experimental observation remains stifled by the "post-selection problem"—the exponential cost of resolving quantum trajectories. Here, we propose a scalable protocol to observe feedback-stabilized criticality on current Noisy Intermediate-Scale Quantum (NISQ) processors, eliminating the need for post-selection. By coupling local measurements to real-time unitary feedback, we demonstrate that a many-body quantum system can be steered toward the universal 1/e information horizon, effectively turning the measurement back-action from a source of decoherence into a resource for complexity. Extensive numerical simulations incorporating realistic depolarizing noise reveal a robust stability plateau extending to gate error rates of p ≈ 10⁻², compatible with state-of-the-art superconducting architectures such as IBM Heron. Furthermore, we introduce a verification scheme based on classical shadows to efficiently estimate the Schmidt concentration ⟨K_c⟩ without full tomography. Our results establish that thermodynamic error correction is achievable in the NISQ era, providing a blueprint for the first experimental observation of a feedback-induced phase transition at the mesoscopic scale (N ~ 100).
Abstract: Measurement-based feedback control is a foundational tool in quantum engineering, quantum thermodynamics, and quantum information processing. While feedback is known to stabilize small quantum systems, its scalability to larger systems remains poorly characterized. In this work, we identify a fundamental measurement–coherence scaling barrier for full-state feedback control in open quantum systems. We show that for generic n-qubit states the measurement resources required for real-time state reconstruction scale exponentially with system size, while the available coherence window remains finite. As a result, beyond a system-size threshold ncrit, the time required to acquire sufficient state information exceeds the decoherence time, preventing closure of the feedback loop. We derive an explicit closed-form expression for ncrit in terms of three hardware parameters—coherence time, single-shot measurement time, and reconstruction accuracy—and show that under realistic device conditions this threshold is typically in the range 2–7 qubits. This provides a quantitative information-theoretic explanation for why full- state tomographic feedback has only been demonstrated at very small scales. Importantly, the barrier is architectural rather than fundamental: syndrome-based control, stabilizer tracking, and measurement-efficient protocols such as classical shadows evade it by exploiting structure and extracting only operationally relevant information. Our results formalize a design principle for scalable quantum control and clarify the operational boundaries of feedback in noisy intermediate-scale quantum (NISQ) devices.
We present matrix product state (MPS) simulations of feedback-stabilized quantum criticality, extending system sizes to N = 100 qubits—over six times larger than accessible via exact diagonalization. Building on the recent identification of the 1/e information horizon as a universal quantum-classical boundary, we develop an adaptive bond dimension strategy that preserves critical correlations during time evolution despite truncation errors. Random quantum circuits with measurement rates adjusted via real-time feedback successfully stabilize the Schmidt concentration across N ∈ {20, 40, 60, 80, 100} qubits. For the largest system (N = 100), ensemble-averaged results yield ⟨Kc⟩ = 0.363±0.003, consistent with the theoretical prediction 1/e = 0.368 within 1.2% (t-test p = 0.15), demonstrating successful crossing of the psychological 100-qubit barrier. The observed non-monotonic scaling reflects oscillatory finite-size convergence characteristic of second-order critical points. All system sizes remain within ±5% of target, with variance decreasing for larger N, demonstrating robustness across correlation length regimes. Our adaptive MPS protocol enables simulation of volume-law entanglement phases at unprecedented mesoscopic scales, establishing computational feasibility for near-term experimental platforms.
Monitored many-body quantum systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling dynamical phases. Proposed approaches to study the MIPT experimentally typically rely on a classical decoding process, but the complexity of this decoding generally grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome this difficulty in the context of tree-shaped quantum circuits. We construct a hybrid circuit with Haar-random unitary operators, and we show that the MIPT can be detected without postselection using a simple decoding process whose complexity grows linearly with the number of qubits. The tree structure also enables a complete theoretical description of the MIPT and all its critical properties. We experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation. To overcome the exponential complexity of measurement induced phase transition (MIPT), the authors propose a protocol which can detect MIPT easily on a tree-like quantum circuit. They experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation.
Mid-circuit measurements and feedback operations conditioned on the measurement outcomes are essential for implementing quantum error-correction on quantum hardware. When integrated in quantum many-body dynamics, they can give rise to novel non-equilibrium phase transitions both at the level of each individual quantum trajectory and the averaged quantum channel. Experimentally resolving both transitions on realistic devices has been challenging due to limitations on the fidelity and the significant latency for performing mid-circuit measurements and feedback operations in real time. Here, we develop a superconducting quantum processor that enables global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and fast conditional feedback with a 200 ns real-time decision latency. Using this platform, we demonstrate the coexistence of an absorbing-state transition in the quantum channel and a measurement-induced entanglement transition at the level of individual quantum trajectories. For the absorbing-state transition, we experimentally extract a set of critical exponents at the transition point, which is in excellent agreement with the directed percolation universality class. Crucially, the two transitions occur at distinct values of the tuning parameter. Our results demonstrate that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics.
Measurement-induced phase transitions (MIPTs) epitomize new intellectual pursuits inspired by the advent of quantum hardware and the emergence of discrete and programmable circuit dynamics. Nevertheless, experimentally observing this transition is challenging, often requiring non-scalable protocols, such as post-selecting measurement trajectories or relying on classical simulations. We introduce a scalable data-centric approach using Quantum Attention Networks (QuAN) to detect MIPTs without requiring post-selection or classical simulation. Applying QuAN to dynamics generated by Haar random unitaries and weak measurements, we first demonstrate that it can pinpoint MIPTs using their interpretation as "learnability" transitions, where it becomes possible to distinguish two different initial states from the measurement record, locating a phase boundary consistent with exact results. Motivated by sample efficiency, we consider an alternative "phase recognition" task-classifying weak- and strong-monitoring data generated from a single initial state. We find QuAN can provide an efficient and noise-tolerant upper bound on the MIPT based on measurement data alone by coupling Born-distribution-level (inter-trajectory) and dynamical (temporal) attention. In particular, our inspection of the inter-trajectory scores of the model trained with minimal sample size processing test data confirmed that QuAN paid special attention to the tail of the distribution of the Born probabilities at early times. This reassuring interpretation of QuAN's learning implies the phase-recognition approach can meaningfully signal MIPT in an experimentally accessible manner. Our results lay the groundwork for observing MIPT on near-term quantum hardware and highlight attention-based architectures as powerful tools for learning complex quantum dynamics.
Measurement-induced phase transition (MIPT) describes the nonanalytical change of the entanglement entropy resulting from the interplay between measurement and unitary evolution. In this paper, we investigate the relaxation critical dynamics near the MIPT for different initial states in a one-dimensional quantum circuit. Specifically, when the initial state is in the volume-law phase with vanishing measurement probability, we find that the half-chain entanglement entropy SSS decays as S∝t−1S\propto t^{-1}S∝t−1 with the coefficients proportional to the size of the system in the short-time stage; In contrast, when the initial state is the product state, SSS increases with time as S∝ln⁡tS\propto \ln{t}S∝lnt, consistent with previous studies. Despite these contrasting behaviors, we develop a unified scaling form to describe these scaling behaviors for different initial states where the off-critical-point effects can also be incorporated. This framework offers significant advantages for experimental MIPT detection. Our novel scheme, leveraging relaxation dynamical scaling, drastically reduces post-selection overhead, and can eliminate it completely with trackable classical simulation.