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arXiv:2311.00058 · Physical Review X

Observing Quantum Measurement Collapse as a Learnability Phase Transition

Utkarsh Agrawal, Javier Lopez-Piqueres, Romain Vasseur, Sarang Gopalakrishnan, Andrew C. Potter

Published Oct 15, 2024• 22 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevx.14.041012

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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
Monitored quantum dynamics—unitary evolution interspersed with measurements—has recently emerged as a rich domain for phase structure in quantum many-body systems away from equilibrium. Here we study monitored dynamics from the point of view of an eavesdropper who has access to the classical measurement outcomes, but not to the quantum many-body system. We show that a measure of information flow from the quantum system to the classical measurement record—the —undergoes a phase transition in correspondence with the measurement-induced phase transition (MIPT). This transition determines the eavesdropper’s (in)ability to learn properties of an unknown initial quantum state of the system, given a complete classical description of the monitored dynamics and arbitrary classical computational resources. We make this learnability transition concrete by defining classical shadow protocols that the eavesdropper may apply to this problem, and show that the MIPT manifests as a transition in the sample complexity of various shadow-estimation tasks, which become harder in the low-measurement phase. We focus on three applications of interest: Pauli expectation values (where we find the MIPT appears as a point of optimal learnability for typical Pauli operators), many-body fidelity, and global charge in U ( 1 ) -symmetric dynamics. Our work unifies different manifestations of the MIPT under the umbrella of and gives this notion a general operational meaning via classical shadows. Published by the American Physical Society 2024
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.
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 transitions (MIPTs) in monitored quantum circuits are usually characterized by preparing steady states at different uniform measurement probabilities. Here we introduce a spatial realization of the MIPT by imposing a deterministic measurement gradient in a single monitored Clifford chain. The resulting steady state contains coexisting volume-law, critical, and area-law regions, with the point p(x)=pcp(x)=p_cp(x)=pc​ acting as a spatial critical cut. By scanning entanglement observables across this profile, we show that the transition is organized by a spatial scaling form. Although this structure is analogous to finite-time scaling in temporally driven MIPT, the spatial protocol has no Kibble-Zurek dynamics. Instead, the physical bounds 0≤p≤10\le p\le 10≤p≤1 impose a finite linear window, producing cutoff-controlled asymptotic regimes whose fitted exponents provide direct access to the correlation-length exponent ννν. Our results establish spatially inhomogeneous measurements as a controlled route to engineer and probe measurement-induced criticality within a single steady state.
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.
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).