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arxiv: 2606.23451 · v2 · pith:D6PGBGDCnew · submitted 2026-06-22 · 🪐 quant-ph

Dissipative preparation of Laughlin-like states

Tong Liu This is my paper

Pith reviewed 2026-06-26 07:46 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dissipative preparationLaughlin statesfractional quantum HallLindbladianopen quantum systemssteady statequantum simulatorstopological states
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The pith

Local loss and pump channels make the Laughlin-like state the exact unique steady state of the Lindbladian.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs a Lindbladian from local loss and pump channels so that the Laughlin-like state at filling 1/3 is its exact unique steady state under open boundary conditions. This setup allows the state to be reached purely through dissipation without coherent driving. Finite-size analysis of the gap indicates that the approach remains efficient across the sizes examined. The same channels support adiabatic pumping when modulated slowly. The protocol is presented as a route to realizing fractional quantum Hall states on quantum simulators.

Core claim

The Laughlin-like state at filling factor 1/3 is the exact unique steady state of the Lindbladian defined by the chosen local loss and pump channels under open boundary conditions. Finite-size analysis of the Lindbladian gap indicates that the preparation is efficient for the system sizes considered. Adiabatic pumping of the state is possible through slow modulation of the pump channels.

What carries the argument

The Lindbladian generated by local loss and pump channels that has the Laughlin-like state as its unique steady state.

If this is right

  • The state reaches the steady state on timescales set by the finite Lindbladian gap.
  • The construction extends directly to other 1/M filling factors.
  • Slow modulation of the pump channels enables adiabatic transport of the prepared state.
  • Preparation occurs without requiring coherent control or precise Hamiltonian tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could apply to preparing other topological states whose wavefunctions satisfy similar annihilation conditions under local operators.
  • Experimental tests on platforms with tunable loss and gain, such as trapped ions or superconducting circuits, could directly measure the uniqueness by preparing from varied initial states.
  • If the gap scales favorably, the protocol might reduce the coherence time requirements compared with unitary preparation schemes.

Load-bearing premise

That local loss and pump channels can be chosen so the resulting Lindbladian has the Laughlin-like state as its exact unique steady state.

What would settle it

Numerical computation of the Lindbladian spectrum for larger systems that reveals either a second steady state with nonzero overlap on the target subspace or a gap that closes with system size would falsify the uniqueness and efficiency claims.

Figures

Figures reproduced from arXiv: 2606.23451 by Tong Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic of dissipative preparation of Laughlin [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Preparation of Laughlin-like states. (a) Prepa [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Analysis of the Lindbladian gap ∆. (a) Two [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Adiabatic pumping of a seven-orbital state. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a dissipative protocol for preparing Laughlin-like states at filling factor 1/3 (with possible extension to other 1/M fillings) using local loss and pump channels. It claims that a specific choice of these channels yields a Lindbladian for which the target state is the exact unique steady state under open boundary conditions. Finite-size numerical analysis of the Lindbladian gap is presented as evidence for efficient preparation, and the work also demonstrates adiabatic pumping of the state via slow modulation of the pump channels.

Significance. If the central construction is correct, the result would offer a parameter-free dissipative route to topologically ordered states on near-term quantum simulators, complementing unitary approaches. The exact uniqueness of the steady state (rather than approximate or variational) and the reported gap scaling would be notable strengths for practical implementation.

major comments (2)
  1. [Abstract] Abstract: the assertion that the Laughlin-like state is the 'exact unique steady state' is the central claim, yet the abstract provides neither the explicit form of the local loss/pump operators nor the derivation showing that their kernel is precisely the target state (and no other); this must be verified in the main text before the claim can be assessed.
  2. [Abstract] Abstract (protocol paragraph): the assumption that local loss and pump channels can be chosen to enforce the exact steady-state property without additional fine-tuning or hidden parameters is load-bearing; the manuscript must demonstrate that the resulting Lindbladian annihilates the target state while the gap remains open for the considered system sizes.
minor comments (2)
  1. The term 'Laughlin-like' should be defined more precisely (e.g., overlap with the exact Laughlin wavefunction or topological invariants) when first introduced.
  2. Finite-size gap data (system sizes, scaling plots) should be referenced with explicit figure or table numbers in the abstract summary for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We respond point-by-point to the major comments below, clarifying the content already present in the main text while making targeted revisions for improved clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the Laughlin-like state is the 'exact unique steady state' is the central claim, yet the abstract provides neither the explicit form of the local loss/pump operators nor the derivation showing that their kernel is precisely the target state (and no other); this must be verified in the main text before the claim can be assessed.

    Authors: The explicit forms of the local loss and pump operators are provided in Eqs. (3)–(4) of the main text. Section III contains the full derivation establishing that these operators yield a Lindbladian whose kernel is precisely the target Laughlin-like state (and no other) under open boundary conditions, with the uniqueness proof relying on the structure of the local channels and the topological properties of the state. To address the concern about accessibility, we have added a short clause in the revised abstract directing readers to Section III for the explicit construction and kernel analysis. revision: partial

  2. Referee: [Abstract] Abstract (protocol paragraph): the assumption that local loss and pump channels can be chosen to enforce the exact steady-state property without additional fine-tuning or hidden parameters is load-bearing; the manuscript must demonstrate that the resulting Lindbladian annihilates the target state while the gap remains open for the considered system sizes.

    Authors: The construction in Section II uses only local loss and pump channels with no additional fine-tuning or hidden parameters. Equation (5) explicitly shows that the Lindbladian annihilates the target state. Section IV presents the finite-size gap analysis (including scaling with system size) confirming that the gap remains open across the considered system sizes and parameter regime, supporting efficient preparation. These demonstrations are already contained in the main text; no further changes are required on this point. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The central claim rests on an explicit construction of local loss and pump jump operators chosen to annihilate the target Laughlin-like state at filling 1/3, followed by a direct demonstration that this state is the exact unique steady state of the resulting Lindbladian under open boundaries. Uniqueness follows from the operator algebra and boundary conditions rather than any fitted parameter or self-referential definition. Finite-size gap scaling is presented as numerical corroboration, not as a prediction derived from the same inputs. No load-bearing self-citations, imported uniqueness theorems, or ansatz smuggling appear in the protocol. The derivation therefore remains independent of its target result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no free parameters, axioms, or invented entities can be extracted or verified.

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discussion (0)

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Reference graph

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