The interplay of entanglement, measurement, and noise in near-term quantum devices may lead to novel emergent phenomena. This work presents a theoretical framework to understand collective effects in the dynamics of quantum entanglement and information, using the tools of statistical mechanics. The new effective description of generic quantum circuits lends insight into a measurement-induced phase transition in the information content of the system and points toward novel schemes to identify this transition in experiments.
The interplay of entanglement, measurement, and noise in near-term quantum devices may lead to novel emergent phenomena. This work presents a theoretical framework to understand collective effects in the dynamics of quantum entanglement and information, using the tools of statistical mechanics. The new effective description of generic quantum circuits lends insight into a measurement-induced phase transition in the information content of the system and points toward novel schemes to identify this transition in experiments.
The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and midcircuit measurements. The quantum noises with a size-independent occurring probability can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities $q=p/{L}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as p increases when $\ensuremath{\alpha}=1$. With the help of an effective statistical model, we reveal that the phase transition is of first order arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture further deepens the understanding of the connection between entanglement behavior and the capacity of information protection. When $\ensuremath{\alpha}\ensuremath{\ne}1$, one spin configuration always dominates regardless of p and thus the phase transition disappears. Moreover, we highlight the difference between the effects of size-dependent bulk noise and boundary noises. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations.
Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.
Random quantum circuits provide a framework for probing universal dynamical phenomena in chaotic quantum many-body systems, by circumventing the microscopic details of Hamiltonian evolution. Bipartite entanglement measures can be used to characterize the dynamical phases that emerge in these systems. Typically, under random unitary evolution, bipartite entanglement entropies exhibit a linear growth, and attain steady-state values that scale extensively with the system volume. However, when local projective measurements are introduced, a suppression of steady-state bipartite entropies occurs, leading to a sub-extensive scaling with the system volume. This class of entanglement scaling transitions, from an extensive to a sub-extensive scaling regime, has sparked interest in a broader class of measurement-induced phase transitions, with a potential to further our understanding of fault-tolerance in quantum computing, and in realizing synthetic quantum phases on digital quantum simulators. In this work, we characterize entanglement scaling transitions in one-dimensional random quantum circuits composed of q-level systems, with the local Hilbert space dimension q ≥ 2. This predominantly numerical study employs generalizations of the stabilizer formalism and the Clifford group to higher-dimensional Hilbert spaces to simulate the measurement-induced transitions. We find that the nature of the entanglement scaling transition remains invariant under changes in the local Hilbert space dimension. However, the critical measurement rate inducing the transition increases with q, asymptotically approaching 1/2 in the limit q → ∞. To further explore this classical limit, we develop a minimal dynamical model that captures entanglement structures under unitary evolution. We analyze the entanglement structures in thermal stabilizer states using this model, and propose an approach for incorporating measurements within this framework.
This is a conference proceeding in the framework of workshop “OpenQMBP2023” * at Institute Pascal (Orsay, France) and associated with the lecture given by Prof. Ehud Altman. We provide a comprehensive analysis of recent results in the context of measurement-induced phase transitions (MIPT) in quantum systems, with a particular focus on hybrid quantum circuits as a model system in one-dimension. Recent resutls, demonstrate how varying the rate of projective measurements can induce phase transitions, resulting in abrupt changes in the properties of the entanglement. The interplay between unitary evolution and measurement processes can be investigated, through mappings to classical statistical models and the application of replica field theory techniques. Starting from a low-entangled state, there can be three regimes characterized by different dynamics of bipartite entanglement entropies for a portion of the system: high-rate measurements leading to rapid entanglement saturation (area law), low-rate measurements allowing linear entanglement growth (up to volume law), and a critical rate at which entanglement grows logarithmically. Finally, we present results on the non-local effects of local measurements by ex-amining the field theory of critical ground states in Tomonaga-Luttinger liquids.
Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos, and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are postselected to satisfy the global TR invariance of each quantum trajectory. We confirm these predictions numerically and find, for both generic and Clifford-based evolutions, critical exponents in the case of “strong,” i.e., global TR invariance where each quantum trajectory is TR invariant.
Quantum-induced phase transitions are a fascinating area of research, offering potential for novel technological applications. This paper explores the use of entanglement propagation as a method for identifying and quantifying these transitions within quantum systems. We propose a new framework that models the transition as a network of entangled particles, where the propagation of entanglement directly dictates the rate of the transition. This approach offers a dynamic and potentially more insightful understanding of phase transitions compared to traditional static models. The core mechanism involves quantifying the entanglement propagation as a key indicator of the transition. The goal is to provide a robust and quantitative tool for characterizing these phenomena. This work directly addresses the limitations of current phase transition theories by embracing entanglement as a fundamental driver.