Kitaev Model Study Reveals Volume-Law Phase and Tunable Entanglement with Single and Multi-Qubit Checks

The pursuit of stable quantum states with topological protection represents a major goal in modern physics, and recent advances explore how to create and control these states using engineered quantum circuits. Tushya Kalpada, Aayush Vijayvargia, Ezra Day-Roberts, and Onur Erten, all from Arizona State University, investigate the behaviour of a specific quantum system, the measurement-only Kitaev model, and demonstrate how carefully chosen measurements can dramatically alter its quantum phases. Their work reveals that adding new measurement terms to the model allows scientists to tune between different phases, including those exhibiting both short-range order and long-range topological memory. Crucially, the team identifies specific measurement operators that either stabilise or promote the emergence of these phases, offering a pathway towards designing circuits with enhanced quantum coherence and potentially useful for quantum information storage and processing.

Measurements Drive Topological Phase Transitions

This research investigates measurement-induced phase transitions, topological order, and entanglement in monitored quantum systems, focusing on variations of the Kitaev model. Scientists explore how continuous quantum measurements can drive transitions between different states of matter, unlike traditional transitions caused by temperature or external fields. The research centers on understanding if these measurements can stabilize topological order, a crucial property for building robust quantum computers, and how measurements affect the entanglement within the system. The team analyzes how entanglement grows and spreads within the monitored systems, looking for signatures of different phases, such as those with limited or extensive entanglement.

They utilize the Kitaev model, a solvable model of interacting spins, as a platform to study these phenomena, exploring variations through different types of measurements, introducing disorder, and considering various system geometries. A key question driving the research is whether measurements can create or stabilize qubits protected from errors within the monitored system. The research demonstrates that, under specific conditions, continuous measurements can stabilize topological order in the Kitaev model, suggesting the possibility of measurement-based quantum error correction. Scientists show that certain types of measurements protect the topological code from decoherence, the loss of quantum information.

The team maps out the phase diagrams of the monitored Kitaev model, revealing how the system’s behavior changes as the measurement rate varies, identifying different phases characterized by distinct entanglement properties and topological order. They also find evidence that measurements can dynamically generate logical qubits within the monitored system, emerging as collective excitations. The analysis of entanglement structure reveals signatures of criticality at the phase transitions, showing how entanglement grows and spreads as the system approaches a critical point. Scientists establish a connection between the monitored Kitaev model and loop models, simpler models that capture the essential physics, allowing them to classify the different phases based on their symmetry properties.

Extensions of the Kitaev model, including altermagnets and bilayer systems, are explored, revealing new and interesting phases. The research also investigates the emergence of Majorana liquid phases, exotic states of matter with potential applications in topological quantum computing. This research is significant because it provides new insights into measurement-based quantum error correction, a crucial step towards building fault-tolerant quantum computers. It sheds light on the emergence of topological order and Majorana liquid phases, essential for topological quantum computers. The work contributes to the broader understanding of measurement-induced phase transitions, a relatively new area of research in condensed matter physics. It provides a theoretical framework for understanding the dynamics of entanglement and information scrambling in monitored quantum systems, and establishes connections between different areas of physics.

Mapping Kitaev Model Phases with Mutual Information

Scientists engineered a new method to investigate the phase diagram of the monitored Kitaev model, expanding its capabilities with new measurement terms. The research pioneered a technique using stabilizer simulations, coupled with tripartite mutual information and entropy measures, to precisely locate phase boundaries within the system. Researchers implemented a four-qubit plaquette operator, simultaneously measuring two opposite bonds on a plaquette, to generate a distinct volume-law phase while preserving topological order. This innovative approach allows for the exploration of non-equilibrium phases inaccessible in traditional equilibrium systems.

The research team meticulously mapped the system’s evolution by introducing a single-qubit term and a three-qubit operator that commutes with the flux operators. Experiments employed finite-size scaling of the tripartite mutual information to determine the critical points separating different phases. The single-qubit term induced a transition from a critical-law phase to a volume-law phase, and ultimately to a trivial product state, revealing a genuinely non-equilibrium feature. Conversely, the three-qubit operator stabilized the critical-law phase, promoting longer loops and faster diffusion of loop endpoints.

Scientists further quantified the system’s behavior by tracking the fraction of plaquettes spanned by the stabilizer generators, providing a direct measure of flux conservation. Data analysis revealed a decrease in this fraction as the single-qubit term increased, indicating a disruption of flux conservation and a transition towards the trivial phase. This study demonstrates that the interplay between bond measurements and single-site measurements governs the system’s dynamics, allowing for precise control over measurement rates and exploration of novel non-equilibrium phases.

Entanglement Phases and Measurement-Driven Transitions

Scientists have achieved a detailed understanding of entanglement phases within a monitored quantum system based on the Kitaev model. This work explores how adding specific measurement operators to the system influences the resulting entanglement, revealing a rich phase diagram with distinct behaviors. The research team meticulously mapped out these phases using stabilizer simulations alongside measurements of tripartite mutual information and entanglement entropy. Experiments revealed that introducing a single-qubit operator drives the system towards a trivial state at high field strengths, but unexpectedly generates an intermediate volume-law phase characterized by extensive entanglement.

Conversely, a three-qubit operator effectively stabilizes the critical-law phase, preventing its transition to a more conventional area-law entangled state. This stabilization is a key finding, demonstrating a method to preserve exotic entanglement properties. Further investigations involved a four-qubit operator that simultaneously measures bonds on a hexagonal plaquette, a process that preserves topological order. Results demonstrate this operator generates a distinct volume-law phase, allowing for extensive entanglement to coexist with conserved flux memory, a characteristic of topological systems.

The team quantitatively located the boundaries between these phases, providing precise measurements of the conditions under which each phase emerges. These findings highlight the crucial role of operator algebra in organizing the observed entanglement phases. The research demonstrates that carefully chosen measurement operators can not only induce new phases but also stabilize and preserve existing topological order, opening avenues for exploring and controlling entanglement in quantum systems.