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arXiv:2512.09982 · Physical review. B./Physical review. B

Measuring the Hall Viscosity of the Laughlin State on Noisy Quantum Computers

Ammar Kirmani, Andrew A. Allocca, Jian-Xin Zhu, Armin Rahmani, Sriram Ganeshan, Pouyan Ghaemi

cond-mat.str-elquant-phSubmitted Dec 10, 2025• Announced Dec 12, 2025• 0 citations
v1 · Dec 10, 2025v2 · Oct 1, 2026
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Abstract

Hall viscosity is a quantized nondissipative stress response of a fractional quantum Hall (FQH) fluid to adiabatic geometric deformations. Despite strong theoretical interest, its experimental observation in the FQH state has remained elusive, making it a promising target for realization on current NISQ devices. In this work, we employ a quasi-one-dimensional model of an FQH state coupled to a background metric to probe the geometric response under a metric quench. We design and implement a quantum-circuit protocol that realizes a Hilbert-space-truncated version of the model and extracts the Hall viscosity from the geometric response encoded in the wavefunction dynamics of the device. While the truncation prevents us from accessing the fully quantized value of Hall viscosity, the hardware data nevertheless show excellent agreement with analytical and numerical predictions within this restricted regime.

Journal reference
Phys. Rev. B 114, 185121 (2026)
DOI
10.1103/2g6v-fqbr
Comments
6+7 pages, 3+2 figures

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Hall viscosity is a quantized nondissipative stress response of a fractional quantum Hall (FQH) fluid to adiabatic geometric deformations. Despite strong theoretical interest, its experimental observation in the FQH state has remained elusive, making it a promising target for realization on current NISQ devices. In this work, we employ a quasi-one-dimensional model of an FQH state coupled to a background metric to probe the geometric response under a metric quench. We design and implement a quantum-circuit protocol that realizes a Hilbert-space-truncated version of the model and extracts the Hall viscosity from the geometric response encoded in the wavefunction dynamics of the device. While the truncation prevents us from accessing the fully quantized value of Hall viscosity, the hardware data nevertheless show excellent agreement with analytical and numerical predictions within this restricted regime.
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=1/3ν=1/3ν=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.
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It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantum Hall states—the filling ν=1/3\nu =1/3ν=1/3 Laughlin state. We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulk off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a 'pair amplitude' operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. These various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantum Hall states—the filling Laughlin state. We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulk off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a 'pair amplitude' operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. These various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.
We develop a field theory description of fractional quantum Hall (FQH) states. We show that in the leading approximation in a gradient expansion, Laughlin states are described by a Gaussian free field theory with a background charge which is identified with the anomalous viscosity of the states. The background charge increases the central charge of the corresponding conformal field theory above 1, similar to that of the theory of 2D quantum gravity. Gradient corrections to the Gaussian field theory arising from ultraviolet regularization reflect the gravitational anomaly. They are also related to the Liouville theory of quantum gravity. We show how the gradient expansion of the field action encodes the universal features of the FQH effect beyond that of Hall conductance. This method provides a more transparent and useful alternative for computing the gravitational anomaly and correlation functions of the FQHE in a curved space than the method of iterating the Ward identity employed by the authors in previous papers.
We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts, and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known fractional quantum Hall (FQH) states, which allows us to predict families of new FQH states that can be realized in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level.