A fractional quantum Hall factory on quantum processors: constant-depth preparation of clustered non-Abelian states

This study investigates the computational cost of preparing various fractional quantum Hall (FQH) states on digital quantum processors. Specifically, the authors seek to understand what determines the circuit depth required to construct these many-body wavefunctions and whether a unified framework can prepare a wide catalog of FQH states at scale.

The researchers developed a systematic framework to map FQH trial wavefunctions to parent Hamiltonians, which are then translated into quantum circuits. By analyzing the "pattern of zeros"—a mathematical description of how particles cluster in FQH states—they identified a "clustering dichotomy." They tested this framework by preparing 18 different families of FQH states, including non-Abelian Read-Rezayi and Moore-Read states, on IBM Heron quantum processors, reaching up to 156 qubits.

The study reveals that the circuit depth is fundamentally tied to the clustering properties of the FQH state. States with clustered particles (where particles are kept apart in specific patterns) allow for parallel circuit execution, resulting in a constant two-qubit depth regardless of the number of qubits. In contrast, the Abelian Laughlin state requires a sequential, chained circuit structure that grows linearly with system size. The authors successfully demonstrated this by preparing the Read-Rezayi $\mathbb{Z}_3$ state at a constant depth of three across a range of 8 to 118 qubits, and verified the results through fractional charge measurements and interferometric braiding of non-Abelian quasiholes.

This work establishes a scalable, systematic route for simulating exotic topological matter on near-term quantum hardware. By demonstrating that more complex, non-Abelian states are often cheaper to prepare than simpler Abelian ones, the authors provide a new perspective on the computational complexity of topological phases. This opens the door to studying non-Abelian anyons and other elusive quantum phenomena on programmable processors, bypassing the limitations of conventional experimental platforms.