Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem in quantum many-body physics is the table-top generation and detection of emergent excitations analogous to gravitons -- the elusive mediators of gravitational force in a quantum theory of gravity. In solid-state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations. However, their direct observation remains an experimental challenge. Here, we generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.
Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem in quantum many-body physics is the table-top generation and detection of emergent excitations analogous to gravitons -- the elusive mediators of gravitational force in a quantum theory of gravity. In solid-state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations. However, their direct observation remains an experimental challenge. Here, we generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.
Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.
Synthetic quantum matter provides a highly tunable route to fractional quantum Hall physics beyond the constraints of conventional electronic materials. However, previous theoretical studies have mostly focused on their ground state properties. It remains unclear to what extent such platforms could reveal key excitation properties of fractional quantum Hall states. Here, we study charge-neutral collective excitations in a non-abelian lattice fractional quantum Hall state realized in the bosonic Harper-Hofstadter model at unity filling factior, realizing a Moore-Read ground state. Combining full exact diagonalization, band-projected exact diagonalization, and matrix-product-state simulations, we demonstrate the existence of a long-lived chiral graviton mode, probed by chiral 3-body correlators, for the first time on lattice non-Abelian states. The graviton signal is topological sector-independent and could be observed via geometric quenches in small open droplets directly relevant to current cold-atom experiments, while other neutral modes, such as the magnetoroton and neutral fermion, are less resolved at presently achievable volumes.
The realization of fractional quantum Hall (FQH) states, characterized by fractional charge and intrinsic topological order, on quantum computers represents a central challenge at the interface of condensed matter physics and quantum information science. Current methods are grouped into two types: methods based on (quasi-)adiabatic evolution of complex parent Hamiltonians to yield target states, and circuit-based approaches for direct state preparation, which are confined to effectively one-dimensional systems near the thin cylinder or torus limit. We introduce a complementary scheme relying on direct quantum circuit construction, which works for arbitrary geometries. Specifically, we present a method to precisely prepare the ν=1/3 Laughlin state on the sphere geometry and demonstrate that it significantly reduces the required number of two-qubit gates and circuit depth, compared to variational quantum circuit approaches. In addition, we employ optimal control techniques to design control pulses for both superconducting and Rydberg atom platforms, identifying experimentally feasible protocols for state preparation. Our results provide an efficient and hardware-relevant pathway for realizing generic FQH states on both noisy intermediate-scale and fault-tolerant quantum devices.
Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read--Rezayi Z3 state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi Z4 state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian e/4 quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.
We introduce a quench of the geometry of Landau level orbitals as a probe of nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that such geometric quenches induce coherent many-body dynamics of neutral degrees of freedom of FQH fluids. The simplest case of mass anisotropy quench can be experimentally implemented as a sudden tilt of the magnetic field, and the resulting dynamics reduces to the harmonic motion of the spin-2 ``graviton'' mode, i.e., the long-wavelength limit of the Girvin-MacDonald-Platzman magnetoroton. We derive an analytical description of the graviton dynamics using the bimetric theory of FQH states and find agreement with exact numerical simulations at short times. We show that certain types of geometric quenches excite higher-spin collective modes, thus establishing their existence in a microscopic model and motivating an extension of geometric theories of FQH states.
Chiral graviton modes are hallmark collective excitations of Fractional Quantum Hall (FQH) liquids. However, their existence on the lattice, where continuum symmetries that protect them from decay are lost, is still an open and urgent question, especially considering the recent advances in the realization of Fractional Chern Insulators (FCI) in transition metal dichalcogenides and rhombohedral pentalayer graphene. Here we present a comprehensive theoretical and numerical study of graviton-modes in fermionic FCI, and thoroughly demonstrate their existence. We first derive a lattice stress tensor operator in the context of the fermionic Harper-Hofstadter(HH) model which captures the graviton in the flat band limit. Importantly, we discover that such lattice stress-tensor operators are deeply connected to lattice quadrupolar density correlators, readily generalizable to generic Chern bands. We then explicitly show the adiabatic connection between FQH and FCI chiral graviton modes by interpolating from a low flux HH model to a Checkerboard lattice model that hosts a topological flat band. In particular, using state-of-the-art matrix product state and exact diagonalization simulations, we provide strong evidence that chiral graviton modes are long-lived excitations in FCIs despite the lack of continuous symmetries and the scattering with a two-magnetoroton continuum. By means of a careful finite-size analysis, we show that the lattice generates a finite but small intrinsic decay rate for the graviton mode. We discuss the relevance of our results for the exploration of graviton modes in FCI phases realized in solid state settings, as well as cold atom experiments.