Quantum Measurement Drives Phase Transitions and Emergent Symmetries in Circuits.

Unitary evolution and measurements compete to influence quantum systems, inducing phase transitions. Researchers map this evolution onto classical spin problems, analytically examining random circuit models and deriving a minimum measurement range for a fully scrambled state. Emergent continuous symmetries appear in larger systems, mirroring spin dynamics.

The behaviour of quantum systems under the combined influence of unitary evolution – the natural progression dictated by quantum mechanics – and measurement, presents a complex challenge to physicists. Recent research illuminates how measurement, often considered a disruptive process that collapses quantum states, can surprisingly induce phase transitions and even generate emergent symmetries within these systems. Haifeng Tang from Stanford Institute for Theoretical Physics, Stanford University, Hong-Yi Wang from Princeton Quantum Initiative, Princeton University, Zhong Wang from Institute for Advanced Study, Tsinghua University, and Xiao-Liang Qi, also from Stanford Institute for Theoretical Physics, Stanford University, explore this phenomenon in their article, “Measurement induced scrambling and emergent symmetries in random circuits”. Their work maps the evolution of quantum systems subject to both unitary processes and measurements onto a classical spin problem, providing analytical insights into various random circuit models and establishing a lower bound for measurement range required to achieve a globally scrambled quantum state. Furthermore, they demonstrate the appearance of continuous symmetries, such as U(1) and SU(2), in certain random measurement models as the system’s dimensionality increases, suggesting parallels between spin dynamics and the behaviour of these complex quantum circuits.

Continuous quantum measurement exerts a substantial influence on the behaviour of quantum systems, inducing phase transitions and the emergence of previously unobserved states of matter. This departs from the conventional understanding of quantum dynamics, typically governed by unitary evolution, where a system evolves predictably without external intervention. Unitary evolution preserves the total probability of a system, but measurement introduces a non-unitary element, altering the system’s state.

Researchers now demonstrate a successful correspondence between the effects of these quantum measurements and established classical spin models. Spin models, used extensively in statistical mechanics, describe systems with interacting magnetic moments, providing a framework for analysing complex behaviours. This mapping allows for analytical treatment of quantum phenomena that would otherwise be intractable. Specifically, the research focuses on applying this correspondence to random quantum circuits, complex quantum algorithms where quantum gates are applied in a random order.

Entanglement, a quantum mechanical phenomenon where two or more particles become linked and share the same fate, irrespective of distance, serves as a crucial indicator of these transitions. The degree of entanglement within the system directly correlates with the changes induced by continuous measurement. Increased entanglement often signals a shift in the system’s behaviour, indicating the emergence of a new phase.

Verification of these findings relies heavily on tensor network methods, a class of numerical techniques used to efficiently simulate quantum many-body systems. These methods provide accurate approximations of the system’s behaviour, allowing researchers to confirm the predictions derived from the classical mapping. The computational demands of simulating quantum systems are significant, and tensor networks offer a viable approach to overcome these challenges.

In certain instances, continuous measurement reveals emergent continuous symmetries within the quantum system. Symmetries describe transformations that leave a system unchanged, and their emergence suggests a fundamental restructuring of the system’s properties. These emergent symmetries are not present in the initial Hamiltonian, the mathematical description of the system’s energy, but arise as a consequence of the measurement process itself. This suggests that measurement not only alters the system’s state but also its underlying structure.