Preparation of a Laughlin-like fractional Chern insulator on a superconducting quantum processor

Kamil Dutkiewicz; Bárbara Andrade; Geza Giedke; Tobias Grass

AI summary · arXiv: 2610.41017v1 · quant-ph

Preparation of a Laughlin-like fractional Chern insulator on a superconducting quantum processor

Kamil Dutkiewicz, Bárbara Andrade, Geza Giedke, Tobias Grass

Original paper Submitted to arXiv on 29 Oct. 2026 13 pages, 7 figures License: NONEXCLUSIVE-DISTRIB 1.0 Also in: fr

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The essentials

A superconducting quantum processor prepared small bosonic Laughlin-like fractional Chern insulator states and reproduced their density, correlation, and quasihole-current signatures.

Question

Can shallow, particle-number-conserving variational circuits prepare and probe Laughlin-like fractional Chern insulator states on a superconducting quantum processor? The work tests this for a four-boson ground state and a three-boson state with two quasiholes on a 4×4 torus.

Method

The authors used exact diagonalization of the Kapit–Mueller parent Hamiltonian to obtain target manifolds, then classically optimized nearest-neighbor variational circuits that conserve particle number. On a 4×4 qubit patch of an IBM Nighthawk processor, the N=3 and N=4 circuits used 168 and 264 CZ gates, respectively, and each reached a noiseless manifold fidelity of 0.95; measurements used particle-number post-selection, with 80,000 and 60,000 shots, and two-qubit correlations to reconstruct currents.

Findings

Result The optimized three- and four-particle circuits achieved a noiseless target-manifold fidelity of 0.95.
See the passage in the paper
The optimized $p=3$ and $p=4$ circuits both reach $F=0.95$ in noiseless simulations.
Result Measured local densities and conditional spatial correlations closely matched the target states, with a small approximately uniform noise background.
See the passage in the paper
Overall, the measured conditional distributions closely match those calculated for the target states, apart from a small, approximately uniform noise background.
Result The experimental configuration distributions retained the target states’ characteristic structure but were attenuated toward the fixed-particle-number mixed-state distribution.
See the passage in the paper
The configuration distributions therefore show that the characteristic structure of the target states survives on hardware, with predominantly noise-induced attenuation toward the mixed-state background.
Result The reconstructed quasihole currents showed finite chiral circulation with the predicted direction and spatial structure, though attenuated relative to noiseless values.
See the passage in the paper
The experimental profile reproduces the spatial structure and direction of the simulated current, although with an overall attenuation toward zero.
Authors’ interpretation The authors argue that particle-number-conserving variational circuits provide a digital route to preparing and probing strongly correlated lattice states with fractional quantum Hall character.
See the passage in the paper
These results demonstrate that gate-based quantum processors can prepare and probe strongly correlated lattice states with fractional quantum Hall character using circuits of experimentally accessible depth.

Limitations

The optimization depends on classically accessible target states, which limits scalability.
See the passage in the paper
The present optimization relies on classically accessible target states, limiting its scalability.
Hardware noise remains the principal experimental limitation; post-selection does not remove all errors affecting measured probabilities and coherences.
See the passage in the paper
The principal limitation of the present experiment is hardware noise.
The noise-based estimates depend on an assumed model that omits some hardware effects and cannot independently fit gate and readout noise.
See the passage in the paper
These estimates depend on the assumed noise model.

Why it matters

The authors establish a digital approach for preparing Laughlin-like fractional Chern insulator states and probing quasihole currents on a superconducting processor. They present this as a basis for future measurements of topological invariants and anyonic braiding, while noting that scaling will require improved hardware and preparation strategies beyond classically accessible target states.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: fractional Chern insulator Kapit–Mueller model digital quantum simulation quasiholes superconducting quantum processor

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Comprehensive Summary
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Original abstract

The paper investigates whether a digital superconducting quantum processor can prepare and probe a bosonic fractional Chern insulator (FCI) with Laughlin-like properties. The authors study the Kapit–Mueller model, a lattice Hamiltonian with long-range complex hopping. Its flat Chern band reproduces key features of the lowest Landau level. The experiment uses a $4 \times 4$ lattice with periodic, magneto-periodic boundary conditions and a flux density of one-half per plaquette. This torus geometry eliminates physical edges. At half filling, four hard-core bosons form a twofold-degenerate, Laughlin-like ground-state manifold. Removing one boson and adding strong repulsive potentials at two sites creates a three-boson state with two pinned quasiholes. Instead of implementing the target Hamiltonian’s long-range dynamics, the team classically optimized particle-number-conserving circuits built from nearest-neighbor hopping, selected nearest-neighbor interactions, and on-site rotations. They optimized the circuit parameters against target states obtained by exact diagonalization, maximizing overlap with the two-dimensional target manifold. The three-boson and four-boson circuits used three and four variational steps, respectively. In noiseless simulation, both achieved a manifold fidelity of 0.95. The circuits required 168 and 264 controlled-Z gates, with two-qubit gate depths of 28 and 44. The team ran the circuits on a $4 \times 4$ patch of IBM’s 120-qubit Nighthawk R1 processor. Particle-number post-selection retained 34.6% of 80,000 shots for the three-boson state and 33.3% of 60,000 shots for the four-boson state. Measurements supported the intended spatial structures. The four-boson density was approximately uniform, at around 0.25 particles per site, while the three-boson density was suppressed at the quasihole pins. Conditional particle densities showed the expected avoidance between nearby particles. In the quasihole state, they also showed additional suppression near the pins across the periodic boundary. Measured configuration probabilities followed the target-state patterns but were shifted toward the maximally mixed distribution within the fixed-particle-number sector. Linear fits gave attenuation factors of 0.813 for three bosons and 0.742 for four. A noise-model analysis estimated post-selected error-free fractions of 60(2)% and 46(5)%, respectively. The authors caution that these estimates depend on the assumed noise model. For the quasihole state, the authors also reconstructed Kapit–Mueller bond-current expectation values from two-qubit Pauli measurements of hopping coherences. The measured current pattern had the predicted spatial structure and chirality, but its magnitude was reduced, consistent with decoherence. The fitted attenuation was 0.624. Net measured circulation was $-0.19 \pm 0.06$, compared with $-0.300$ in noiseless circuit simulation and $-0.319$ for the projected target state. Although the target manifold’s detailed currents vary among its states, the net circulation has the same sign throughout the manifold. The work demonstrates a route to preparing and measuring small, strongly correlated lattice states with fractional quantum Hall character using relatively shallow, optimized digital circuits. It does not establish scalability: the optimization relies on classically computed target states, and larger topologically ordered states may require deeper circuits and more entangling operations. Hardware noise remains the central experimental limitation. Number post-selection cannot remove errors that preserve particle number or restore lost coherences. The authors identify measurements of topological invariants and quasihole braiding as future goals, not results of this experiment.

Preparing a Laughlin-Like Quantum State on a Superconducting Processor

Can a digital quantum processor create and probe a state that resembles a fractional quantum Hall liquid? In “Preparation of a Laughlin-like fractional Chern insulator on a superconducting quantum processor,” Kamil Dutkiewicz, Bárbara Andrade, Geza Giedke, and Tobias Grass explore this question with a small lattice of superconducting qubits. Their experiment takes an important step toward studying strongly correlated quantum matter on programmable hardware—while also making clear how much noise and scaling challenges remain.

A lattice model with quantum Hall character

The researchers focus on the Kapit–Mueller model, a lattice Hamiltonian featuring long-range hopping with complex phases. Its unusually flat Chern band shares key properties with the lowest Landau level, the setting in which fractional quantum Hall states arise. This makes the model a useful route to exploring related physics in a lattice system.

The experiment uses a 4 × 4 lattice with periodic, magneto-periodic boundary conditions and a flux density of one-half per plaquette. Because the lattice wraps around, it has the geometry of a torus rather than a system with physical edges. That helps the researchers focus on bulk behavior without edge effects.

At half filling, four hard-core bosons occupy a twofold-degenerate ground-state manifold with Laughlin-like properties. The team also studies a state with three bosons: removing one particle and introducing strong repulsive potentials at two lattice sites pins two quasiholes. These localized defects offer a way to examine how particles and currents behave around fractionalized excitations.

Building the states with optimized circuits

Rather than directly implementing the Kapit–Mueller model’s long-range dynamics, the team designed circuits from more hardware-friendly ingredients: nearest-neighbor hopping, selected nearest-neighbor interactions, and on-site rotations. The circuits conserve particle number. Their parameters were optimized classically by comparing the circuit output with target states calculated through exact diagonalization.

The optimization aimed to maximize overlap with the target’s two-dimensional ground-state manifold, rather than with one particular state in that manifold. The three-boson and four-boson preparations required three and four variational steps, respectively. In noiseless simulation, each reached a manifold fidelity of 0.95. The circuits used 168 and 264 controlled-Z gates, with two-qubit gate depths of 28 and 44.

The researchers ran the circuits on a 4 × 4 patch of IBM’s 120-qubit Nighthawk R1 processor. They collected 80,000 shots for the quasihole state and 60,000 for the four-boson state. Keeping only measurements with the desired particle number retained 34.6% and 33.3% of the shots, respectively.

What the measurements revealed

The measured particle densities showed the broad spatial patterns expected from the target states. For four bosons, the density was approximately uniform, at around 0.25 particles per site. In the three-boson state, the density was suppressed at the two quasihole pins. Conditional-density measurements also showed that nearby particles tend to avoid one another. For the quasihole state, there was additional suppression near the pins across the periodic boundary.

Measured configuration probabilities followed the target-state patterns, but appeared more like a uniform, maximally mixed distribution within the fixed-particle-number sector. Linear fits captured this contrast with attenuation factors of 0.813 for three bosons and 0.742 for four. In other words, the expected structure remained visible, but its measured strength was reduced.

The team also reconstructed bond-current expectations for the quasihole state using two-qubit Pauli measurements of hopping coherences. The current pattern had the predicted spatial structure and chirality, though again with a reduced magnitude. The fitted attenuation was 0.624. Net circulation was measured as −0.19 ± 0.06, compared with −0.300 in noiseless circuit simulation and −0.319 for the projected target state. Although detailed currents vary among states in the target manifold, the net circulation has the same sign across the manifold.

Noise, limits, and what comes next

A noise-model analysis estimated that the post-selected data contained error-free fractions of 60(2)% for the three-boson state and 46(5)% for the four-boson state. These figures depend on the assumed noise model, so they should be treated as estimates rather than direct measurements of error-free runs. Particle-number post-selection helps discard some faulty outcomes, but it cannot remove errors that preserve particle number or restore quantum coherences lost through decoherence.

The result demonstrates a practical route to preparing and measuring small, strongly correlated lattice states with fractional quantum Hall character using relatively shallow, optimized digital circuits. It does not yet establish that the approach will scale. The optimization depends on classically computed target states, while larger topologically ordered systems may demand deeper circuits and more entangling operations. Hardware noise remains a central obstacle.

Still, the experiment offers a foundation for more ambitious studies. Measuring topological invariants and observing quasihole braiding are important future goals, not achievements of this work. For now, the paper shows that a superconducting quantum processor can reproduce several characteristic signatures of a small Laughlin-like state—and gives researchers a concrete platform on which to pursue the deeper questions.

Created on 03 Nov. 2026

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Weekly letter Presented in "Quantum physics this week" of 2 November 2026. Quantum physics this week: Making noise, measurement and matter work for quantum devices

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Preparation of a Laughlin-like fractional Chern insulator on a superconducting quantum processor

The essentials

Question

Method

Findings

Limitations

Why it matters

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Definitions

Preparing a Laughlin-Like Quantum State on a Superconducting Processor

A lattice model with quantum Hall character

Building the states with optimized circuits

What the measurements revealed

Noise, limits, and what comes next

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