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arxiv: 2605.29838 · v1 · pith:AIRR6IKKnew · submitted 2026-05-28 · 🪐 quant-ph · cond-mat.stat-mech· hep-th

Gate Parameter Lee-Yang Zeros and Dynamical Phases in Quantum Circuits

Chang Liu , Yu Wu , Yunfeng Jiang , Yang Zhang This is my paper

Pith reviewed 2026-06-29 07:12 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechhep-th
keywords Lee-Yang zerosLoschmidt amplitudedynamical phase transitionsquantum circuitsFloquet operatorbrickwork model
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The pith

Gate-parameter Lee-Yang zeros of Loschmidt amplitudes reorganize abruptly to mark dynamical phase transitions in finite quantum circuits.

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

The paper proposes gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. In a brickwork Floquet model the Loschmidt amplitude is expressed as a rational function of the gate parameters. At fixed system size and large depth its zeros condense onto limiting curves that include a universal component from equimodular Floquet eigenvalues. As one parameter is varied the zeros reorganize abruptly, supplying a finite-qubit diagnostic of the transition. The mechanism relies only on spectral competition and local unitarity and does not require integrability.

Core claim

The Loschmidt amplitude is a rational function of the gate parameters; at fixed system size and large circuit depth its zeros in one complexified gate parameter condense onto limiting curves comprising a universal component governed by equimodular Floquet eigenvalues together with state-dependent contributions from eigenstate overlaps, and these curves reorganize abruptly when a parameter crosses a dynamical phase boundary.

What carries the argument

Gate-parameter Lee-Yang zeros of the Loschmidt amplitude, which condense onto curves set by the Beraha-Kahane-Weiss theorem applied to equimodular Floquet eigenvalues.

If this is right

  • Dynamical phase transitions become detectable with modest qubit numbers without taking the thermodynamic limit.
  • The diagnostic applies to non-integrable circuits because condensation follows from local unitarity and spectral competition alone.
  • State-dependent overlaps control part of the zero curves, so initial-state choice can tune the visibility of the transition.

Where Pith is reading between the lines

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

  • The same zero-reorganization signature could be checked in other Floquet models or in circuits with different gate sets to test generality beyond the brickwork example.
  • If the rational-function property holds for open systems or noisy circuits, the zeros might still condense and provide a practical diagnostic on near-term hardware.

Load-bearing premise

The Loschmidt amplitude can be written as a rational function of the gate parameters whose zeros at fixed size and large depth condense onto limiting curves whose reorganization tracks the dynamical transition.

What would settle it

Compute the zeros of the Loschmidt amplitude for a non-integrable brickwork circuit at increasing depths; if the reorganization point fails to approach the known dynamical transition location the claim is false.

Figures

Figures reproduced from arXiv: 2605.29838 by Chang Liu, Yang Zhang, Yunfeng Jiang, Yu Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. Construction of the brickwork Floquet circuit. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. GPLY zeros in the massive regime. The four plots [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. GPLY zeros in the massless regime. The four plots [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of the GPLY zeros around ∆ = 1. Here the initial state is the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Zero-density diagnostic near the universal curves. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

We propose gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. We illustrate this approach using a brickwork model, where the time evolution is generated by repeated application of a Floquet operator. The Loschmidt amplitude can be expressed as a rational function of the gate parameters. At fixed system size and large circuit depth, its zeros in one complexified gate parameter, with the other parameter held fixed, condense onto limiting curves. We show that these curves comprise a universal component governed by equimodular Floquet eigenvalues, as described by the Beraha-Kahane-Weiss theorem, together with state-dependent contributions controlled by the overlap of eigenstate of the Floquet operator with the initial state. As one of the parameters is varied, the set of zeros reorganizes abruptly, providing a finite-qubit diagnostic of a dynamical phase transition. This mechanism does not rely on integrability: while integrability enables an exact calculation of the Loschmidt amplitude, the condensation of zeros follows from spectral competition and local unitarity alone.

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 / 1 minor

Summary. The paper proposes gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. Using a brickwork Floquet model, it argues that the Loschmidt amplitude, expressed as a rational function of gate parameters, has zeros that condense onto limiting curves at fixed system size and large depth. These curves have a universal component from equimodular Floquet eigenvalues per the Beraha-Kahane-Weiss theorem and state-dependent contributions from eigenstate overlaps. Abrupt reorganization of zeros as a parameter varies provides a finite-qubit diagnostic of dynamical phase transitions, relying on spectral competition and local unitarity rather than integrability.

Significance. If the central mechanism is substantiated with explicit derivations, this offers a valuable finite-system diagnostic for dynamical phase transitions in quantum circuits that does not require integrability, potentially applicable to experimental and numerical studies of non-equilibrium phases. The connection to the Beraha-Kahane-Weiss theorem provides a rigorous foundation for the universal aspects of the zero condensation. The manuscript correctly notes that the mechanism follows from general spectral properties and local unitarity.

major comments (2)
  1. [Abstract] Abstract: The central claim that the Loschmidt amplitude is a rational function whose zeros condense onto curves governed by the Beraha-Kahane-Weiss theorem is stated without any explicit expression for the amplitude, the overlaps c_j, or the Floquet eigenvalues in the brickwork model, preventing direct verification of the rational-function property or the condensation mechanism.
  2. [Abstract] Abstract and implied main text: The assertion that reorganization of zeros provides a finite-qubit diagnostic of the dynamical transition rests on the spectral decomposition L = sum c_j λ_j^n and modulus competition, but no derivation or numerical check of how the state-dependent overlaps control the limiting curves is supplied, leaving the load-bearing step from spectral properties to observable reorganization unsupported in the given text.
minor comments (1)
  1. [Abstract] Abstract: The sentence 'We show that these curves comprise a universal component...' would benefit from an explicit forward reference to the section containing the application of the Beraha-Kahane-Weiss theorem.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We respond point by point to the major comments below, clarifying the content of the main text while agreeing to revisions that improve explicitness and verifiability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the Loschmidt amplitude is a rational function whose zeros condense onto curves governed by the Beraha-Kahane-Weiss theorem is stated without any explicit expression for the amplitude, the overlaps c_j, or the Floquet eigenvalues in the brickwork model, preventing direct verification of the rational-function property or the condensation mechanism.

    Authors: The abstract is a concise summary. The main text defines the brickwork Floquet circuit explicitly in terms of the two gate parameters, constructs the Floquet operator as a product of local two-qubit gates, and derives the Loschmidt amplitude via the spectral decomposition L = sum_j c_j λ_j^n, where the λ_j are the eigenvalues of the Floquet operator and the c_j are the overlaps with the initial state. The rational-function character follows directly from the finite-dimensional matrix representation of the circuit (a polynomial in each gate parameter). The Beraha-Kahane-Weiss theorem is then applied to the equimodular eigenvalues to obtain the universal component of the limiting curves. To address the verification concern, we will insert a short explicit formula for L and the relevant eigenvalues in the revised introduction. revision: yes

  2. Referee: [Abstract] Abstract and implied main text: The assertion that reorganization of zeros provides a finite-qubit diagnostic of the dynamical transition rests on the spectral decomposition L = sum c_j λ_j^n and modulus competition, but no derivation or numerical check of how the state-dependent overlaps control the limiting curves is supplied, leaving the load-bearing step from spectral properties to observable reorganization unsupported in the given text.

    Authors: The main text derives the limiting curves from the BKW theorem applied to equimodular Floquet eigenvalues and explains that the state-dependent overlaps c_j determine which eigenvalues dominate the sum at large depth, thereby selecting the particular curves that appear. Reorganization occurs when a parameter variation causes a change in the dominant pair of eigenvalues, which is diagnosed by the abrupt rearrangement of zeros. While this mechanism is grounded in the spectral decomposition and local unitarity, we agree that an expanded derivation of the overlap-controlled selection together with a numerical illustration of the reorganization would strengthen the presentation. We will add both in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external theorem and general spectral properties

full rationale

The paper's central claim—that zeros of the Loschmidt amplitude condense onto curves whose reorganization tracks dynamical transitions—rests on the spectral decomposition of the Floquet operator and the Beraha-Kahane-Weiss theorem on equimodular eigenvalues. This theorem is external (not derived or cited from the authors' prior work in the provided text). The argument explicitly states that condensation follows from spectral competition and local unitarity alone, independent of integrability (which is used only for exact Loschmidt amplitude calculation). No self-citations are load-bearing, no parameters are fitted and renamed as predictions, and no ansatz or uniqueness result is smuggled via self-reference. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into parameters or assumptions; the approach invokes the Beraha-Kahane-Weiss theorem and assumes the Loschmidt amplitude is rational in the gate parameters.

axioms (2)
  • standard math Beraha-Kahane-Weiss theorem governs the universal component of the zero curves via equimodular Floquet eigenvalues
    Explicitly referenced in the abstract as describing the limiting curves
  • domain assumption Loschmidt amplitude is a rational function of the gate parameters
    Stated directly in the abstract as the basis for locating zeros

pith-pipeline@v0.9.1-grok · 5725 in / 1348 out tokens · 25103 ms · 2026-06-29T07:12:35.475327+00:00 · methodology

discussion (0)

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