New method finds hidden order in quantum systems

Researchers have developed a new method to map quantum phase transitions using the vector field of the reduced fidelity susceptibility (RFS), a technique that requires no prior knowledge of the system’s order parameters. Nicola Mariella of IBM Research – Dublin and colleagues applied this approach to three distinct quantum models, the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms, demonstrating its versatility beyond single systems.

The work, published in Quantum volume 10, page 2217 (2026), reveals phase boundaries and stable phases through the divergence and convergence of arrows within the RFS vector field. This framework offers a unified approach to phase characterization and order-parameter discovery relying only on reduced density matrices of small subsystems.

Reduced Fidelity Susceptibility (RFS) Vector Field for Phase Diagrams

This approach bypasses the need to predefine what researchers are looking for, automatically revealing observables that function as order parameters, critical elements defining the transition itself. Validation of these discovered order parameters used eigendecomposition and finite-size scaling analysis, confirming alignment with expected universality classes for each model tested. The RFS vector field reveals phase boundaries as divergence points in the vector field, and stable phases as convergence points toward reference states, providing a visual map of quantum behavior.

The research, detailed in Quantum volume 10, builds upon earlier work exploring fidelity susceptibility as a tool for identifying critical phenomena. Previous studies, such as one published in Physical Review X in 2015, laid groundwork for understanding how fidelity can be used to detect quantum phase transitions, but the current work expands this by focusing on the vector field itself as a source of information.

The authors state their method’s practical application and verification process. The team’s work also acknowledges the historical context of quantum phase transition studies, referencing foundational papers dating back to 1926 and 1976, demonstrating a clear lineage of thought within the field. The implications extend beyond simply locating phase transitions; the RFS vector field provides a unified framework that requires no prior knowledge of symmetry or transition type.

This is particularly valuable when investigating complex quantum systems where the underlying order parameters are unknown or difficult to predict. The method’s reliance on readily accessible reduced density matrices further enhances its practicality, making it a potentially powerful tool for researchers exploring the intricacies of quantum many-body systems and seeking to understand the fundamental principles governing their behavior.

Order Parameter Discovery Without Prior Symmetry Knowledge

The vector field of reduced fidelity susceptibility (RFS) now enables the construction of phase diagrams without pre-existing knowledge of a system’s symmetries, a departure from conventional methods. This approach, detailed in a recent publication in Quantum volume 10, allows researchers to map quantum phase transitions and to identify the underlying order parameters that define them, automatically. This versatility signifies a move beyond tailoring analysis to specific systems. The RFS vector field isn’t limited to a single, pre-defined scenario.

The researchers make their data available through a Zenodo repository, linking to a “qupytex” dataset with DOI 10. 5281/zenodo. 21776634, promoting reproducibility and further investigation.

Validation via Eigendecomposition and Finite-Size Scaling

Researchers verified that the discovered order parameters exhibited behavior consistent with established universality classes, confirming the method’s reliability in characterizing diverse quantum systems. Analysis of the ANNNI model, known for its complex phase diagram and potential for multiple commensurate phases, revealed the expected transitions and associated order parameters. Similarly, the cluster state model, a cornerstone of measurement-based quantum computation, yielded results consistent with its known topological properties.

The Rydberg atom chain, a promising platform for realizing programmable quantum systems, also displayed predictable behavior, further bolstering confidence in the method’s broad applicability. By analyzing how the eigenvalues of the density matrices changed with system size, the researchers could confirm the expected critical exponents and universality classes associated with each phase transition.

RFS Application to ANNNI, Cluster, and Rydberg Models

This validation extends beyond simply locating known transitions. The RFS approach automatically identified the underlying order parameters defining each phase without prior assumptions about symmetry or transition type. Recent advances in Rydberg atom control have highlighted their potential for hardware-efficient, fault-tolerant quantum computation and the RFS method accurately mapped their phase behavior.

Unlike earlier techniques, this framework doesn’t rely on tailoring adjustments to specific models, offering a more generalized solution for characterizing quantum systems. This broad applicability extends beyond theoretical models to encompass physically realizable systems, including those built with Rydberg atoms, a promising platform for quantum simulation.

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