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arxiv: 2604.26146 · v1 · submitted 2026-04-28 · 🪐 quant-ph · cond-mat.str-el

Minimal action shortcut to adiabaticity in a driven Kitaev chain: competing gaps in a topological transition at finite-time

Rafael Bentes de Sales , Krissia Zawadzki This is my paper

Pith reviewed 2026-05-07 16:03 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords Kitaev chainshortcut to adiabaticitytopological phase transitionmany-body dynamicsfinite-time protocolswork fluctuations
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The pith

Adapting the minimal action shortcut to adiabaticity with a multi-step strategy enables high-fidelity driving of the Kitaev chain across its topological transition in short times.

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

The paper applies the minimal action shortcut to adiabaticity to the Kitaev chain and develops a multi-step strategy to cross the topological transition where gaps close in different symmetry sectors. This produces control protocols that reach the target ground state with high fidelity on time scales much shorter than linear ramps. The work also checks how these protocols compare to linear driving in reducing work fluctuations during the process. A sympathetic reader would care because preparing many-body ground states in critical systems is hard, and competing symmetries make standard shortcuts ineffective.

Core claim

The central claim is that the minimal action shortcut to adiabaticity can be adapted to the Kitaev chain via a multi-step strategy to handle competing gaps across different symmetry sectors, allowing high-fidelity preparation of the target state at time scales much shorter than linear ramp protocols while also suppressing work fluctuations.

What carries the argument

The adapted minimal-action shortcut to adiabaticity (MA-STA) using a multi-step strategy that optimizes control across competing gaps in the driven Kitaev chain.

If this is right

  • High fidelities are reached at time scales much shorter than linear ramp protocols.
  • Work fluctuations are suppressed more effectively than in linear driving.
  • The multi-step approach guides design of shortcuts in many-body systems with competing energy scales and symmetries.

Where Pith is reading between the lines

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

  • The same multi-step adaptation could extend to other models with multiple symmetry sectors and gap closings.
  • Numerical tests on longer chains would show how the time advantage scales with system size.
  • Adding decoherence or noise would test whether the fidelity gain survives realistic conditions.

Load-bearing premise

The minimal-action principle can be directly adapted via a multi-step strategy to handle competing gaps across different symmetry sectors without introducing uncontrolled errors in the many-body dynamics.

What would settle it

Measuring that the final fidelity achieved by the adapted MA-STA at a given short time is no higher than that of a linear ramp protocol at the same time would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2604.26146 by Krissia Zawadzki, Rafael Bentes de Sales.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Evolution of the energy eigenvalues view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Kitaev Chain’s phases. The main feature of the topological view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison between the two-plateaus protocol (2pMA, solid view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fidelities (a) and time-dependent control protocol view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Fidelities for view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Work probability distribution view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Fidelity for various values of view at source ↗
read the original abstract

One of the main difficulties in preparing many-body ground states is achieving the target state through simple counterdiabatic controls. For critical systems crossing a transition to a topological phase, this task becomes even more challenging due to the closing of the gaps in multiple symmetry sectors. This is the case of the Kitaev chain, whose transition between the trivial and topological phases involves states belonging to different symmetry sectors. In this work, we apply the recently introduced minimal action shortcut to adiabaticity (MA-STA) to a Kitaev chain and propose a multi-step strategy to obtain the optimal control protocol to drive the system across its different phases. Our results show that high fidelities can be achieved through the adapted MA-STA at time scales much shorter than those of linear ramp protocols. We also compare the performance of both controls in suppressing work fluctuations. These findings may guide the design of STA protocols in many-body systems where competing energy scales and symmetries shape the global dynamics.

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 adapts the minimal-action shortcut to adiabaticity (MA-STA) to the driven Kitaev chain, proposing a multi-step protocol that separately optimizes controls for the competing gaps in different parity sectors during the topological transition. It reports that the resulting finite-time drives achieve high ground-state fidelities at times substantially shorter than linear ramps and also reduce work fluctuations relative to the ramp protocol.

Significance. If the central numerical claims hold, the work supplies a concrete, symmetry-aware route to finite-time state preparation in a many-body topological system whose gap closings occur in distinct sectors. This is a non-trivial extension of single-gap STA methods and could inform control design for other critical chains or lattices where multiple symmetry sectors compete.

major comments (2)
  1. [§4.2 and Fig. 3] §4.2 and Fig. 3: the global many-body fidelity is computed only for chains up to N=20; no explicit bound or numerical check on parity-sector leakage (e.g., via the off-diagonal blocks of the time-ordered exponential or a Magnus expansion of the inter-sector coupling) is provided, leaving open whether the reported high fidelities survive in the thermodynamic limit or for times much shorter than the linear ramp.
  2. [§3.1, Eq. (12)] §3.1, Eq. (12): the multi-step MA-STA construction assumes that the instantaneous eigenstates of different parity sectors remain decoupled under the time-dependent control; the manuscript does not demonstrate that the chosen control term preserves this block-diagonal structure to the required accuracy when the gaps close at different rates.
minor comments (2)
  1. [§4.3] The definition of the work-fluctuation measure in §4.3 should be stated explicitly (including the precise operator whose variance is plotted) rather than referenced only to prior MA-STA literature.
  2. [Fig. 2 caption] Fig. 2 caption: the linear-ramp protocol parameters (total time T and ramp shape) used for the comparison should be given numerically so that the claimed speed-up factor is reproducible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address each major point below and indicate the changes we will make in the revised version.

read point-by-point responses

  1. Referee: [§4.2 and Fig. 3] §4.2 and Fig. 3: the global many-body fidelity is computed only for chains up to N=20; no explicit bound or numerical check on parity-sector leakage (e.g., via the off-diagonal blocks of the time-ordered exponential or a Magnus expansion of the inter-sector coupling) is provided, leaving open whether the reported high fidelities survive in the thermodynamic limit or for times much shorter than the linear ramp.

    Authors: We agree that the system-size limitation and the absence of an explicit leakage analysis constitute a gap in the current presentation. Exact diagonalization restricts us to N ≤ 20, but in the revised manuscript we will (i) extend the fidelity plots to include all accessible sizes and show the N-dependence explicitly, (ii) compute and display the norm of the off-diagonal parity blocks of the time-evolution operator for the MA-STA protocol, and (iii) add a short discussion of the expected thermodynamic-limit behavior based on the locality of the control and the fact that inter-sector matrix elements remain identically zero by parity symmetry. While a rigorous analytic bound for arbitrarily short times is beyond the scope of the present numerical study, the added checks will quantify the leakage for the reported protocol durations. revision: yes

  2. Referee: [§3.1, Eq. (12)] §3.1, Eq. (12): the multi-step MA-STA construction assumes that the instantaneous eigenstates of different parity sectors remain decoupled under the time-dependent control; the manuscript does not demonstrate that the chosen control term preserves this block-diagonal structure to the required accuracy when the gaps close at different rates.

    Authors: The driving term we employ is constructed to be parity-even, so that the full time-dependent Hamiltonian remains block-diagonal in the even/odd parity subspaces for all t. In the revised manuscript we will insert an explicit verification: we recompute the time-dependent Hamiltonian in the parity basis and confirm that the off-diagonal blocks are numerically zero (to machine precision) throughout the protocol, including at the points where the gaps close at different rates. This symmetry argument, together with the numerical check, demonstrates that the sectors remain decoupled to the accuracy required by the multi-step MA-STA construction. revision: yes

Circularity Check

0 steps flagged

No circularity: MA-STA protocol applied to Kitaev chain via external framework and numerical evolution

full rationale

The derivation applies the minimal-action STA (cited as recently introduced) to the Kitaev Hamiltonian with a multi-step control strategy across parity sectors. Fidelities and fluctuation suppression are obtained from direct integration of the time-dependent Schrödinger equation on finite chains; these outputs are not algebraically forced by the inputs or by any fitted parameter renamed as prediction. The block-diagonal structure of the Kitaev Hamiltonian is used only to justify sector-wise optimization, not to define the target fidelity. No self-citation chain, ansatz smuggling, or uniqueness theorem imported from the authors' prior work is required for the central claim. The protocol remains falsifiable by independent many-body numerics outside the fitted controls.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the work relies on the standard Kitaev Hamiltonian and the recently introduced MA-STA framework without detailing new postulates.

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