  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. This paves the way for several important
studies, including quantum simulation of nonequilibrium dynamics and braiding
of quasiparticles in quantum Hall states.
