Quantifying Majorana Bound State Locality in Interacting Systems Enables Robust Qubit Protection

Protecting quantum information from environmental noise represents a fundamental hurdle in the development of practical quantum computers. William Samuelson of Lund University, Juan Daniel Torres Luna and Sebastian Miles from Delft University of Technology, along with colleagues, now demonstrates how the robustness of Majorana bound states, promising building blocks for topological qubits, directly relates to their physical separation within a material. The team rigorously establishes the connection between the locality of these states and their protection from external disturbances, a crucial step for realising stable quantum computation. By defining Majorana bound states from the ground state of interacting systems, they quantify how their spatial separation constrains environmental coupling, ultimately determining the feasibility of performing the complex manipulations needed for quantum processing.

Local perturbations represent a central challenge in quantum computing. Topological superconductors, featuring separated Majorana bound states (MBSs), provide a robust form of protection that depends solely on the locality of perturbations. Researchers address this by defining MBSs from many-body ground states and demonstrating how their locality constrains their coupling to an environment, quantifying the protection of the energy degeneracy.

Braiding Majorana Zero Modes for Qubits

Scientists are making significant progress in harnessing Majorana zero modes (MZMs) for building robust quantum computers. These exotic quasiparticles offer inherent protection against computational errors. The research focuses on simplifying the complex interactions between MZMs and establishing a clear understanding of how to manipulate them through braiding to perform reliable quantum calculations. The work centers on an effective Hamiltonian and how to simplify it to facilitate braiding operations. By carefully choosing a mathematical framework, or gauge, researchers can minimize unwanted couplings between MZMs and improve the overall stability of the quantum system, reducing the strength of interactions that could lead to errors.

Key to this approach is understanding the relationships between the components of the Hamiltonian. Researchers define coefficients describing the strength of these interactions and derive bounds on their values, crucial for ensuring robustness by limiting the influence of environmental noise. The team proves these coefficients are directly related to the norms of operators describing the MZMs, providing a quantifiable measure of their stability. The research highlights the importance of choosing a gauge that minimizes the distinguishability of the two ground states. This led to the development of a generalized Majorana polarization, a metric for assessing the quality of MBSs and optimizing qubit design, contributing to the development of topological quantum computation.

Locality Protects Qubits From Decoherence

Scientists have achieved a breakthrough in understanding how to protect qubits from environmental disturbances. The research rigorously defines Majorana bound states (MBSs), offering inherent protection against decoherence, and quantifies the conditions necessary for reliable quantum computation. The team demonstrated that the locality of these MBSs directly constrains their susceptibility to external perturbations, establishing a crucial link between physical separation and quantum information preservation. Experiments revealed that the strength of environmental coupling to MBSs is limited by the size of the interaction region, meaning that only local interactions significantly affect qubit stability.

This finding is captured mathematically through bounds on effective operators, demonstrating that the norms of these operators, which dictate the magnitude of environmental influence, are directly proportional to the norms of the reduced MBSs. Specifically, the team proved that the norms of operators representing coupling to the environment are constrained by the Frobenius norm, achieving saturation when the environmental interaction precisely matches the ground state of the system. Further analysis established a critical inequality connecting the protection of the energy spectrum to the localization of the ground-state MBSs. Researchers derived a bound on the energy splitting between quantum states, demonstrating that this splitting is limited by the norms of the coupling operators and the localization of the MBSs, particularly robust when considering a large number of states in the environment. To optimize qubit protection, scientists explored the impact of gauge choice on the derived bounds. They discovered that minimizing a quantity related to the distinguishability of the two ground states yields the strongest protection, leading to the development of a generalized Majorana polarization, a metric for assessing the quality of MBSs and providing a framework for optimizing qubit design and performance.

Robust Majorana Protection With Imperfect Coupling

This research establishes a new framework for understanding the protection of Majorana bound states, crucial components in fault-tolerant quantum computing. Scientists developed a formalism applicable to both non-interacting and interacting systems, defining MBSs through the partial trace of ground-state wavefunctions. This approach allows researchers to assess the robustness of energy spectrums and the feasibility of non-abelian braiding, a key operation for manipulating quantum information. The team proved rigorous bounds on the protection offered by spatially separated Majorana bound states, demonstrating that even imperfect coupling does not necessarily ruin the protocol, provided operation times are adjusted accordingly.

They identified specific criteria, based on measurable quantities like Majorana polarization and local distinguishability, to determine a system’s suitability for braiding operations, relying solely on the ground states of the system for studying strongly interacting topological systems using computational techniques. Researchers acknowledge that their bounds involve quality measures warranting further investigation, particularly concerning the influence of entanglement between ground states on the properties of the Majorana bound states. Future work could explore these relationships in greater detail, furthering the development of robust topological quantum computers.