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arxiv: 2402.16944 · v3 · submitted 2024-02-26 · 🪐 quant-ph · cond-mat.str-el

Probing anyonic statistics via Mach-Zehnder interferometry in quantum computers

Shiyu Zhou , Yi Teng , Claudio Chamon , Claudio Castelnovo , Armin Rahmani This is my paper

Pith reviewed 2026-05-24 04:10 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords anyonic statisticsMach-Zehnder interferometryquantum computerstoric ladderquantum spin liquidsbraiding phaseinterference patternsLindbladian noise
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The pith

A synthetic Mach-Zehnder interferometer on a quantum computer detects anyonic braiding phases via interference from electric excitations in a toric ladder.

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

The paper introduces a digitized Mach-Zehnder interferometer that runs on quantum hardware to measure the fractional exchange statistics of anyons in quantum spin liquid models. It tests the scheme on the toric ladder, a one-dimensional slice of the toric code, by moving electric excitations with and without magnetic ones present. On an IonQ device the measured interference patterns match the expected anyonic phase shift. The authors also simulate device noise with a depolarizing Lindbladian model and obtain quantitative agreement with the experimental data. The same interferometer can therefore serve as a probe of multi-qubit coherence times and lengths.

Core claim

Digitizing a Mach-Zehnder interferometer on a quantum computer produces interference that encodes the braiding phase acquired when electric anyons move past magnetic anyons in the toric ladder; the observed patterns agree with the anyonic prediction once noise is included via Lindbladian dynamics.

What carries the argument

The synthetic Mach-Zehnder interferometer, realized by a sequence of controlled gates that move electric excitations along two paths and accumulate the statistical phase from braiding with magnetic excitations.

If this is right

  • The visibility or phase of the interference depends on whether magnetic excitations are present.
  • Depolarizing Lindbladian dynamics quantitatively reproduce the observed noise on the IonQ device.
  • The interferometer also extracts coherence length and time scales of the multi-qubit processor.
  • Anyonic statistics become accessible on digital hardware without needing a physical two-dimensional topological phase.

Where Pith is reading between the lines

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

  • The same circuit template could be adapted to other lattice models that host anyons, provided the gate sequence can be compiled.
  • The method offers an independent benchmark for quantum devices that goes beyond single-qubit or two-qubit gate fidelity.
  • Because the toric ladder is closely related to quantum error-correcting codes, the interferometer may also serve as a diagnostic for topological protection under noise.

Load-bearing premise

The quantum circuit faithfully implements the anyonic braiding phase of the toric ladder rather than hardware errors producing a signal that only coincidentally matches the expected pattern.

What would settle it

Absence of any change in the interference fringe when magnetic excitations are added to the circuit, or a large mismatch between the measured data and the Lindbladian noise model while still deviating from the pure anyonic prediction.

Figures

Figures reproduced from arXiv: 2402.16944 by Armin Rahmani, Claudio Castelnovo, Claudio Chamon, Shiyu Zhou, Yi Teng.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematics of the original 2D toric code where the star operators [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Spinon propagation in the background of four initial vison configurations as indicated in the schematics on the top [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spinon propagation in a 2D surface code of 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. The Trotter approximation error versus the number of Trotter steps [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Circuit diagram: the blue solid box marks the initial state preparation (for the case of no visons), the orange solid [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Square error from Lindblad simulation and IonQ hardware data summed over all stars and vison configurations. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

We introduce a synthetic Mach-Zehnder interferometer for digitized quantum computing devices to probe fractional exchange statistics of anyonic excitations that appear in quantum spin liquids. Employing an IonQ quantum computer, we apply this scheme to the toric ladder, a quasi-one-dimensional reduction of the toric code. We observe interference patterns resulting from the movement of `electric' excitations in the presence and absence of `magnetic' ones. We model the noise in IonQ via depolarizing Lindbladian dynamics, and find quantitative agreement with the measurements obtained from the quantum device. The synthetic Mach-Zehnder interferometer can thus also serve as an effective means to probe the coherence length and time scales of multi-qubit noisy quantum devices.

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 paper introduces a synthetic Mach-Zehnder interferometer implemented on digitized quantum hardware to probe fractional exchange statistics of anyons in the toric ladder model (a quasi-1D reduction of the toric code). Using an IonQ trapped-ion device, the authors create and move 'electric' excitations in the presence and absence of 'magnetic' ones, report interference patterns, and show that the measured visibilities agree quantitatively with simulations of the ideal circuit under a depolarizing Lindbladian noise model. The interferometer is also positioned as a diagnostic for device coherence length and time scales.

Significance. If the observed difference in interference is unambiguously due to the anyonic braiding phase rather than device-specific errors, the work demonstrates a concrete route to realizing and detecting fractional statistics on NISQ hardware and supplies a practical coherence probe. The quantitative match to the Lindbladian model is a positive feature, but its evidentiary weight hinges on independent confirmation that the digital circuit faithfully encodes the toric-ladder anyon operators.

major comments (2)
  1. [Methods / Circuit Implementation] The manuscript does not supply the explicit gate sequence, circuit diagram, or qubit mapping that implements the anyon creation, transport, and braiding operators of the toric ladder inside the Mach-Zehnder interferometer (Methods / Circuit Implementation section). Without this, it is impossible to verify that the reported difference between the two interference traces originates from the fractional exchange phase rather than from the specific error channels of the IonQ device.
  2. [Results / Noise Modeling] It is not stated whether the depolarizing rates in the Lindbladian noise model were fixed by independent calibration experiments performed on the same device or were adjusted to reproduce the interferometer visibilities. If the latter, the quantitative agreement does not discriminate between a correct anyonic implementation and a noise-dominated circuit that happens to produce similar fringes (Results / Noise Modeling section).
minor comments (2)
  1. [Figures] Figure captions should explicitly label which trace corresponds to the presence versus absence of magnetic excitations and state the number of shots per data point.
  2. [Abstract / Results] The abstract claims 'quantitative agreement' but the main text should report the precise metric (e.g., reduced chi-squared or visibility difference) used to quantify that agreement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which highlight important points for improving the clarity and verifiability of our work. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods / Circuit Implementation] The manuscript does not supply the explicit gate sequence, circuit diagram, or qubit mapping that implements the anyon creation, transport, and braiding operators of the toric ladder inside the Mach-Zehnder interferometer (Methods / Circuit Implementation section). Without this, it is impossible to verify that the reported difference between the two interference traces originates from the fractional exchange phase rather than from the specific error channels of the IonQ device.

    Authors: We agree that the explicit implementation details are necessary for independent verification. In the revised manuscript we will add the full gate sequences, circuit diagram, and qubit mapping for anyon creation, transport, and braiding in the toric ladder Mach-Zehnder interferometer. These additions will be placed in an expanded Methods section and will enable readers to confirm that the operators correctly encode the toric-ladder anyonic statistics. revision: yes

  2. Referee: [Results / Noise Modeling] It is not stated whether the depolarizing rates in the Lindbladian noise model were fixed by independent calibration experiments performed on the same device or were adjusted to reproduce the interferometer visibilities. If the latter, the quantitative agreement does not discriminate between a correct anyonic implementation and a noise-dominated circuit that happens to produce similar fringes (Results / Noise Modeling section).

    Authors: The manuscript indeed does not specify the provenance of the depolarizing rates. In the revision we will explicitly state that the rates were obtained from independent calibration experiments performed on the same IonQ device prior to the interferometer runs, and we will include the relevant calibration data or references. This clarification will strengthen the evidentiary value of the quantitative match to the Lindbladian model. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurement on hardware with external noise model

full rationale

The paper implements a known toric-ladder circuit on IonQ hardware, measures interference fringes for electric excitations with and without magnetic ones, and compares to a depolarizing Lindbladian simulation. No equation or claim reduces to a fitted parameter by construction, no self-citation is load-bearing for the central observation, and the noise model is presented as an independent characterization tool rather than a post-hoc fit that forces agreement. The result is an empirical measurement whose validity rests on hardware fidelity, not on any definitional or self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard anyonic properties of the toric code and the assumption that the digital circuit implements the correct braiding operator.

axioms (1)
  • domain assumption The toric ladder model supports electric and magnetic anyonic excitations with fractional exchange statistics.
    Invoked when interpreting the interference patterns as signatures of anyonic statistics.

pith-pipeline@v0.9.0 · 5658 in / 1121 out tokens · 25451 ms · 2026-05-24T04:10:35.271634+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Tunable anyonic permeability across ${\mathbb{Z}_2}$ spin liquid junctions

    cond-mat.str-el 2025-06 unverdicted novelty 6.0

    Junctions in toric code spin liquids enable tunable anyon transmission, with one class showing complete electric transparency but critical-field magnetic transmission and the other tuned by pseudospin fluctuations.

Reference graph

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