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arxiv: 2606.27424 · v1 · pith:LWK55GLOnew · submitted 2026-06-25 · 🪐 quant-ph

Engineering of non-Hermitian interactions in digital qudit quantum simulators

Matteo M. Wauters , Paolo Boschetto , Edoardo Ballini , Alberto Biella , Philipp Hauke This is my paper

Pith reviewed 2026-06-29 02:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-Hermitian Hamiltoniansquantum simulationquditsZeno subspaceprojective measurementspseudo-spinsmany-body interactionshybrid evolution
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The pith

Measurements on a qutrit chain confine its evolution to an effective non-Hermitian Hamiltonian with two-body interactions among pseudo-spins.

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

The paper establishes that a one-dimensional chain of qutrits under hybrid unitary-projective evolution can be mapped onto an effective non-Hermitian model. Suitably chosen measurements project the system into a Zeno subspace where the remaining dynamics follows a target non-Hermitian Hamiltonian acting on an ensemble of pseudo-spins one-half. This effective Hamiltonian inherits non-Hermitian two-body interactions whose connectivity matches that of the original qutrit chain. An analytical relation is derived that directly links the monitored qutrit evolution to any chosen target non-Hermitian Hamiltonian, and the mapping is checked with numerical simulations of an example model.

Core claim

Within the Zeno subspace enforced by the measurements, the qutrit dynamics reduces to an effective non-Hermitian Hamiltonian for pseudo-spins 1/2 that supports non-Hermitian two-body interactions with the same connectivity as the full chain; an explicit analytical relation connects the monitored evolution to a desired target non-Hermitian Hamiltonian.

What carries the argument

The Zeno subspace created by projective measurements on the qutrit chain, which reduces the monitored dynamics to an effective non-Hermitian pseudo-spin Hamiltonian.

If this is right

  • A broad class of interacting non-Hermitian many-body Hamiltonians becomes realizable in multilevel quantum platforms.
  • The effective interactions inherit the spatial connectivity of the original qudit chain.
  • The scheme applies directly to experimental systems such as trapped ions and superconducting circuits.
  • Numerical checks confirm the effective description for representative models.

Where Pith is reading between the lines

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

  • The same measurement protocol could be tested on small chains to extract effective non-Hermitian spectra or decay rates.
  • Extensions to higher-dimensional lattices or longer-range interactions would follow the same Zeno-subspace construction.
  • The approach may be combined with existing digital simulation techniques for open quantum systems.

Load-bearing premise

The measurements can be designed and performed so that the system remains confined to the chosen Zeno subspace with negligible leakage.

What would settle it

Numerical or experimental time evolution of the monitored qutrits that deviates from the predicted trajectories of the target non-Hermitian pseudo-spin Hamiltonian under the stated measurement protocol.

Figures

Figures reproduced from arXiv: 2606.27424 by Alberto Biella, Edoardo Ballini, Matteo M. Wauters, Paolo Boschetto, Philipp Hauke.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Local dissipative term and (b) non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Ground state degeneracy (a), entanglement entropy (b), and relaxation rate (c) for the effective non-Hermitian qubit [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. On-site magnetization dynamics (top panels) and half-chain entanglement entropy (bottom panels) in the three phases [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Synchronization of the qubit oscillations in the D [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Approximation ratio vs. time with varying one-body dissipation rate [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Decay rate per particle of the success probability of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Ground state degeneracy (left), entanglement en [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

Non-Hermitian Hamiltonians are a fascinating class of many-body models that describe the effective dynamics of quantum systems interacting with the environment through particle, energy, or information exchange. Although their theoretical framework is well established, the controlled engineering of such Hamiltonians in the context of quantum simulations remains challenging, even more so when the non-Hermitian part describes a $k$-body interaction. Qudit quantum simulators offer a compelling framework to implement such models. We theoretically investigate the dynamics of a one-dimensional chain of qudits undergoing hybrid unitary-projective evolution, where suitably designed measurements constrain the dynamics to a Zeno subspace. As we illustrate for the case of qutrits, within the Zeno subspace the dynamics is governed by an effective non-Hermitian Hamiltonian for an ensemble of pseudo-spins $1/2$, which can inherit non-Hermitian two-body interactions with the same connectivity as the full qutrit chain. We derive an analytical relation linking the monitored qutrits' evolution to a desired target non-Hermitian Hamiltonian and validate the effective description through numerical simulations of a representative model. Our scheme provides a constructive route for the realization of a large class of interacting non-Hermitian many-body Hamiltonians in experimentally relevant multilevel quantum platforms, including trapped ions and superconducting circuits.

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

0 major / 3 minor

Summary. The manuscript proposes a scheme to engineer non-Hermitian many-body interactions in digital qudit quantum simulators. It considers a 1D chain of qutrits undergoing hybrid unitary-projective evolution with suitably designed measurements that confine the dynamics to a Zeno subspace. Within this subspace the effective dynamics is shown to be governed by a non-Hermitian Hamiltonian acting on an ensemble of pseudo-spins 1/2 that inherits two-body interactions with the same connectivity as the original qutrit chain. An analytical relation mapping the monitored qutrit evolution to a target non-Hermitian Hamiltonian is derived and validated through numerical simulations of a representative model. The approach is presented as a constructive route for experimental platforms such as trapped ions and superconducting circuits.

Significance. If the central derivation holds, the work supplies a concrete, analytically controlled method for realizing interacting non-Hermitian Hamiltonians that are otherwise difficult to engineer directly. The explicit construction via measurement operators and second-order perturbation within the Zeno subspace, together with direct numerical comparison to the non-Hermitian Schrödinger equation, provides a falsifiable and reproducible protocol that could be implemented on existing multilevel quantum hardware.

minor comments (3)
  1. [§3] §3 (Zeno-subspace derivation): the second-order perturbative expression for the effective non-Hermitian Hamiltonian is stated without an explicit intermediate step showing the cancellation of first-order terms; adding one line of algebra would improve traceability.
  2. [Figure 2] Figure 2 caption and associated text: the plotted quantity is described as 'overlap with target evolution' but the precise definition (e.g., whether it is the fidelity of the full state or of the projected pseudo-spin state) is not restated; a brief reminder would aid readers.
  3. [Numerical validation section] The numerical parameters (measurement strength, time step, system size) used in the representative model are given only in the figure legends; listing them once in the main text would improve reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work, the supportive significance statement, and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper presents an explicit analytical construction mapping monitored qutrit evolution (via measurement operators projecting to a Zeno subspace and second-order perturbation for the effective non-Hermitian Hamiltonian) to a target Hamiltonian, followed by direct numerical comparison of trajectories to the non-Hermitian Schrödinger equation. No quoted equations reduce a claimed prediction or uniqueness result to a fitted input, self-citation chain, or definitional tautology; the central mapping is constructed from the measurement protocol and perturbation theory with independent numerical validation on a representative model. The derivation stands on its own equations and simulations without load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the Zeno-subspace constraint and the existence of the analytical mapping; both are stated but not derived in the abstract.

axioms (1)
  • domain assumption Suitably designed measurements constrain the dynamics to a Zeno subspace
    Invoked in abstract as the mechanism that produces the effective non-Hermitian dynamics.

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Reference graph

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