Fractional Chern insulators (FCIs) are lattice analogs of fractional quantum Hall systems, where the interplay of strong interactions with a frustrated tunnelling kinetics leads to the emergence of a gapped ground state with long-range entanglement and anyonic excitations. The highly correlated nature of such systems makes their adiabatic preparation challenging already beyond the minimal system size of two particles. Considering Floquet implementations of the bosonic Harper-Hofstadter-Hubbard model of few photons in superconducting circuits, we design protocols for the driven-dissipative stabilization of its FCI ground state at half filling via quantum bath engineering. Dissipation control is achieved through the coupling to driven leaky cavity modes, which realize a tuneable artificial environment having the Floquet-FCI as its approximate fixed point. For systems of two, three and six particles, we show numerically how the flexibility of the control scheme further allows for the detection of fractional quantum Hall signatures in the stabilized steady states, including bulk incompressibility, Hall response and the trapping of fractional charges. Our results provide a concrete pathway to dissipation-assisted preparation of strongly correlated states in quantum simulators.
Fractional quantum Hall (FQH) states are a central paradigm of strongly correlated quantum matter and a key platform for topological quantum computation. Here, we propose a purely dissipative protocol based on local loss and pump channels for preparing Laughlin-like states at filling
1/3, with a possible extension to other
1/M filling states. We show that the Laughlin-like state is the exact unique steady state of the Lindbladian under open boundary conditions. Finite-size analysis of the Lindbladian gap suggests efficient dissipative preparation over the system sizes and parameter regime considered. We further demonstrate adiabatic pumping of a Laughlin-like state through slow modulation of the pump channels during the evolution. Our work opens a feasible route to preparing and manipulating FQH states on near-term quantum simulators.
We present numerical evidence of an interaction-driven quantum Hall plateau transition between a
∣C∣>1 Chern Insulator (CI) and a
ν=1/3 Laughlin state in the Harper-Hofstadter model. We study the model at flux densities
p/q, where the lowest Landau level (LLL) manifold comprises
p magnetic sub-bands. For weak interactions, the model realises integer CIs corresponding to filled sub-bands, while strongly interacting candidate states include fractional quantum Hall (FQH) states at LLL filling fractions
ν=r/t. These phases may compete at the same particle density when
p=t. As a concrete example, we numerically explore the physics at flux density
nϕ=3/11, where we show evidence that a direct transition occurs between a CI and a
ν=1/3 Laughlin state, which we characterise in terms of its critical, topological and entanglement properties. We also show that strong interactions generically stabilise a
ν=1/3 Laughlin state even when the LLL is split into multiple bands, and introduce a powerful methodology to extract its topological entanglement entropy by exploiting the scaling of magnetic length with
nϕ.
Engineered dissipation can be employed to prepare interesting quantum many-body states in a nonequilibrium fashion. The basic idea is to obtain the state of interest as the unique steady state of a quantum master equation, irrespective of the initial state. Due to a fundamental competition of topology and locality, the dissipative preparation of gapped topological phases with a nonvanishing Chern number has so far remained elusive. Here, we study the open quantum system dynamics of fermions on a two-dimensional lattice in the framework of a Lindblad master equation. In particular, we discover a mechanism to dissipatively prepare a topological steady state with nonzero Chern number by means of short-range system bath interaction. Quite remarkably, this gives rise to a stable topological phase in a nonequilibrium phase diagram. We demonstrate how our theoretical construction can be implemented in a microscopic model that is experimentally feasible with cold atoms in optical lattices.
Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states, hosting topological order and fractionalized anyonic excitations. Their realization poses a demanding target for quantum simulation. Here, we realize a bosonic FCI on an IBM Nighthawk superconducting quantum processor using classically optimized variational circuits. We target a Laughlin-like state that is an exact zero-energy ground state of a long-range parent Hamiltonian on a torus, eliminating physical edges and providing a favorable geometry for accessing fractional quantum Hall physics in a small system. On a
4×4 qubit lattice, we prepare both the four-boson FCI ground state and a three-boson state hosting two quasiholes. Measurements of particle densities and correlations reproduce the characteristic structure of the target states, while reconstructed chiral magnetization currents resolve the circulating current pattern associated with the quasiholes. The preparation of these strongly correlated topological states with shallow circuits establishes a route toward the digital simulation and manipulation of fractionalized excitations, including measurements of topological invariants and anyonic braiding.
Engineered dissipation can be employed to prepare interesting quantum many body states in a non-equilibrium fashion. The basic idea is to obtain the state of interest as the unique steady state of a quantum master equation, irrespective of the initial state. Due to a fundamental competition of topology and locality, the dissipative preparation of gapped topological phases with a non-vanishing Chern number has so far remained elusive. Here, we study the open quantum system dynamics of fermions on a two-dimensional lattice in the framework of a Lindblad master equation. In particular, we discover a mechanism to dissipatively prepare a topological steady state with non-zero Chern number by means of short-range system bath interaction. Quite remarkably, this gives rise to a stable topological phase in a non-equilibrium phase diagram. We demonstrate how our theoretical construction can be implemented in a microscopic model that is experimentally feasible with cold atoms in optical lattices.