Creating and manipulating a Laughlin-type $\nu=1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits

Understand

Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $\nu=1/3$ fractional quantum Hall state on a digitized quantum computer.

• Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture.
• We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer.
• We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state.