Fractional Quantum Hall States Maintain Information Recovery above Critical Filling Factor, Enabling Robust Topological Computation

Fractional quantum Hall states represent a potentially revolutionary pathway towards robust quantum computation, as they inherently protect information within their unique electronic structure. Zijian Wang from the Institute for Advanced Study, Tsinghua University, and Ruihua Fan, Tianle Wang, Samuel J. Garratt, and Ehud Altman from the University of California, Berkeley, and Lawrence Berkeley National Laboratory, now demonstrate how these delicate states respond to realistic environmental noise. Their research investigates the impact of density decoherence, a common form of disruption, on the ability to reliably encode and retrieve quantum information within two prominent fractional Hall states, the Laughlin and Moore-Read states. The team identifies a critical threshold beyond which information remains fully recoverable, even with strong decoherence, and reveals that the Moore-Read state exhibits superior resilience, retaining its quantum information beyond the point at which the Laughlin state begins to degrade, thus bolstering the potential of non-Abelian fractional quantum Hall states for practical quantum technologies.

Fractional quantum Hall states are promising platforms for topological quantum computation due to their capacity to encode quantum information in topologically protected states and within the fusion space of non-Abelian anyons. This research investigates how density decoherence, a form of noise affecting local charge density, impacts information encoded in two prominent states, the Laughlin and Moore-Read states. The team identifies a critical filling factor, a specific condition relating to electron density, above which quantum information remains fully recoverable even with strong decoherence. Both the Laughlin and Moore-Read states operate within this stable range, demonstrating resilience to density noise. Below this critical filling factor, however, both states undergo a transition, losing their ability to reliably store quantum information.

Fractional Quantum Hall Effect and Topology

This extensive body of work covers a broad range of topics in condensed matter physics and quantum information, including the fractional quantum Hall effect and its associated topological order, alongside explorations of topological quantum computation and quantum error correction. Conformal field theory serves as a powerful mathematical tool for understanding these systems, while investigations into symmetry breaking and topological defects provide crucial insights into their behavior. Modern developments focus on the impact of open systems, measurement, and novel symmetry concepts on these states. Research highlights the foundational work of Laughlin and Moore and Read, establishing the principles of fractional quantum Hall physics.

Studies explore topological order and its application to quantum computation, leveraging anyons as building blocks for quantum gates. Investigations into symmetry breaking, as demonstrated by Berezinskii, Kosterlitz, and Thouless, reveal the underlying mechanisms governing these systems. Recent advancements focus on understanding these states in more realistic environments, where interactions with the surroundings are unavoidable, and exploring new types of topological order through engineered symmetries. This work demonstrates an increasing focus on open systems, the importance of symmetry, and a growing mathematical sophistication within the field.

Topological Quantum Information Survives Decoherence Thresholds

Scientists investigated the impact of density decoherence on quantum information encoded within the Laughlin and Moore-Read fractional quantum Hall states, revealing critical thresholds for information recovery. The work demonstrates that both states maintain fully recoverable information up to a specific filling factor, beyond which decoherence begins to degrade the encoded data. Experiments reveal a critical filling factor exists, above which information remains fully recoverable regardless of decoherence strength. Below this threshold, both states undergo a transition into a decohered phase, but their responses differ significantly.

Information within the Laughlin state degrades continuously with increasing decoherence, vanishing only with infinitely strong decoherence. However, the team discovered that quantum information encoded in the fusion space of non-Abelian anyons within the Moore-Read states remains fully recoverable even beyond this transition, demonstrating enhanced robustness. Measurements confirm that the Moore-Read state’s fusion space maintains integrity even under strong decoherence, surpassing the performance of the Laughlin state. The research establishes a crucial link between decoherence strength and information loss, quantifying the recoverable quantum information in these states. Scientists utilized quantum coherent information as a metric, identifying a sharp drop in this quantity as a signal for the breakdown of the state as a quantum memory. These findings support the potential of non-Abelian fractional Hall states for topological quantum computation and open avenues for developing error correction strategies tailored to these systems.

Critical Filling Factor Protects Quantum Information

Researchers have investigated the resilience of information encoded within the Laughlin and Moore-Read fractional quantum Hall states when subjected to density decoherence. Their work identifies a critical filling factor, a specific condition relating to electron density, above which information remains fully recoverable regardless of the strength of the decoherence. Both the Laughlin and Moore-Read states operate within this stable range. Below this critical point, both states undergo a transition into a decohered phase, but their responses differ significantly. Information encoded in the Laughlin state degrades gradually with increasing decoherence, diminishing but never entirely disappearing.

In contrast, the Moore-Read state demonstrates remarkable robustness, maintaining fully recoverable information even beyond this transition and under strong decoherence. These findings reinforce the potential of non-Abelian fractional Hall states as platforms for topological computation, where information is inherently protected from local disturbances. Future research will likely focus on developing methods to correct these errors and fully realize the promise of topological quantum computation.