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arxiv: 2605.19047 · v1 · pith:J7E6Z35Nnew · submitted 2026-05-18 · 🪐 quant-ph

Signatures of quantum noise in the operation of Deutsch's algorithm

Ma{\l}gorzata Strza{\l}ka , Katarzyna Roszak This is my paper

Pith reviewed 2026-05-20 10:27 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Deutsch's algorithmpure dephasingquantum noisedecoherence correlationsquantum computingIBM Quantum processorNV centers
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The pith

Running Deutsch's algorithm twice exposes differences between quantum and classical models of environmental dephasing that remain hidden in single runs.

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

The paper employs Deutsch's algorithm as a test case to examine how the quantum character of environmental noise appears in the outcomes of quantum computations. Pure dephasing is treated once by retaining the full density matrix of qubits and environment and once through classical Kraus operators. A single execution of the algorithm produces matching results under both treatments, yet two executions make the models diverge because correlations between decoherence channels slow the loss of coherence for balanced functions and produce a qualitative shift in outcome dependence for constant functions. Experiments performed on an IBM Quantum processor confirm the distinction without depending on particular modeling choices, while NV-center qubits display additional complexity arising from their limited environment size.

Core claim

We model pure dephasing in Deutsch's algorithm using both a full quantum density matrix approach and a classical Kraus operator method. For a single run, both yield identical effects on the algorithm's performance. However, when the algorithm is executed twice, the inclusion of correlations and interplay between decoherence channels results in a slowing of decoherence for balanced functions, with an even stronger and qualitatively altered dependence on decoherence for constant functions. These theoretical distinctions are fully reproduced in experiments on IBM Quantum processors.

What carries the argument

Comparison of full quantum density matrix evolution versus Kraus operator representation for pure dephasing applied to the oracle function in Deutsch's algorithm, with focus on correlations that appear only on repeated execution.

If this is right

  • A single execution of Deutsch's algorithm produces the same effect whether dephasing is modeled quantum mechanically or classically.
  • Two executions make the two models diverge because correlations between decoherence processes enter the dynamics.
  • Decoherence effects slow for balanced functions once those correlations are taken into account.
  • Constant functions show a stronger and qualitatively different dependence of final measurement probabilities on the strength of dephasing.
  • Results obtained on IBM Quantum hardware match the predicted distinction independently of the modeling assumptions used in the derivation.

Where Pith is reading between the lines

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

  • Repeating simple algorithms could serve as a practical diagnostic for the quantum character of noise on other hardware platforms.
  • The stronger sensitivity seen for constant functions indicates that certain output classes may act as sharper probes of environmental quantumness.
  • Systems with small environments, such as NV centers, may reveal further signatures that require extensions of the basic correlation treatment.

Load-bearing premise

Deutsch's algorithm serves as a valid stand-in for more complex quantum algorithms when studying how quantum properties of an environment manifest in computational results.

What would settle it

If a quantum processor yields identical statistics of measurement outcomes under the full density matrix model and the Kraus operator model after two runs of Deutsch's algorithm, the claimed distinction would be ruled out.

Figures

Figures reproduced from arXiv: 2605.19047 by Katarzyna Roszak, Ma{\l}gorzata Strza{\l}ka.

Figure 1
Figure 1. Figure 1: FIG. 1. Two cycles of Deutsch’s algorithm with decoherence. The end of the first run of the algorithm ends with the measurement [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Conditional probabilities of measurement outcome [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Probabilities of measurement outcome after two cy [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. As Fig [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Flowchart of 2 cycles of Deutsch’s algorithm for [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Probabilities of measurement outcome after two cy [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in two different ways; one keeps the full density matrix of the qubits and environments (quantum) while the other uses Kraus operators (classical). We find that a single run of the algorithm yields the same effect in both cases, but running the algorithm twice leads to stark differences. Taking correlations and interplay between different decoherence processes into account leads to a slowing of decoherence effects for balanced functions. For constant functions, the effect is much more pronounced, and there is a qualitative change in the dependence of measurement outcomes on decoherence. We present results obtained on one of the IBM Quantum processors, which fully reproduce the predicted effect regardless of the assumptions made in the derivation. We further illustrate the findings on NV center spin qubits, which show more complex behavior due to a small size of the environment.

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 uses Deutsch's algorithm as a proxy for more complex quantum algorithms to distinguish signatures of quantum noise (full density matrix modeling of pure dephasing, retaining environment correlations) from classical noise (Kraus operators). It reports that a single run produces identical effects in both models, but two runs yield stark differences: correlations slow decoherence for balanced functions, while constant functions show more pronounced effects and a qualitative change in measurement outcome dependence on decoherence. IBM Quantum processor experiments fully reproduce the predicted effects independent of modeling assumptions, with additional illustration on NV center spin qubits exhibiting more complex behavior due to small environment size.

Significance. If the central distinctions hold, the work offers a minimal circuit testbed for detecting quantum environmental correlations in computational outcomes, with direct experimental validation on superconducting and spin qubits. The parameter-free reproduction on hardware and the explicit contrast between correlated quantum and uncorrelated classical models are strengths that could inform noise characterization in larger algorithms.

major comments (2)
  1. [Abstract] Abstract and introduction: the claim that Deutsch's algorithm serves as a valid stand-in for more complex quantum algorithms is load-bearing for the broader significance but receives no further justification or limitation analysis; the single-oracle, two-qubit structure may confine the observed correlation-induced slowing and qualitative shifts to this minimal case rather than revealing universal signatures of quantum environments.
  2. The abstract states that IBM results 'fully reproduce the predicted effect regardless of the assumptions made in the derivation,' yet the provided text contains no equations, explicit Kraus vs. density-matrix operators, or tabulated measurement probabilities; without these, the support for the reported stark differences after two runs cannot be verified at the level required for the central claim.
minor comments (1)
  1. The abstract mentions 'one of the IBM Quantum processors' and 'NV center spin qubits' without citing specific device names, run counts, or figure references for the reproduced data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: the claim that Deutsch's algorithm serves as a valid stand-in for more complex quantum algorithms is load-bearing for the broader significance but receives no further justification or limitation analysis; the single-oracle, two-qubit structure may confine the observed correlation-induced slowing and qualitative shifts to this minimal case rather than revealing universal signatures of quantum environments.

    Authors: We agree that additional justification and a limitations analysis are needed to support the use of Deutsch's algorithm as a proxy. In the revised manuscript we have expanded the introduction with a dedicated paragraph explaining that Deutsch's algorithm provides the simplest setting in which a single oracle query exploits quantum interference to distinguish constant from balanced functions; the correlation effects we identify arise precisely from the way environmental memory modifies the relative phases accumulated during the two oracle calls. We have also added a short limitations subsection noting that the two-qubit, single-oracle structure is minimal and that the quantitative slowing or qualitative shifts may not appear identically in larger circuits, while arguing that the underlying mechanism of retained environment-qubit correlations affecting interference is expected to be relevant whenever oracles are implemented via unitary gates on a register coupled to a non-Markovian bath. revision: yes

  2. Referee: The abstract states that IBM results 'fully reproduce the predicted effect regardless of the assumptions made in the derivation,' yet the provided text contains no equations, explicit Kraus vs. density-matrix operators, or tabulated measurement probabilities; without these, the support for the reported stark differences after two runs cannot be verified at the level required for the central claim.

    Authors: The full manuscript contains explicit derivations of both the quantum density-matrix evolution (retaining system-environment correlations) and the classical Kraus-operator treatment in the Theory and Results sections, together with the resulting measurement probabilities after one and two runs. To address the concern directly, we have added a compact summary table listing the key operators and the analytic probabilities for both models as functions of the dephasing strength, plus a supplementary figure comparing the two-run outcomes. The IBM hardware data are presented with the exact circuit transpilation and post-processing steps, showing quantitative agreement with the quantum-model predictions independent of the modeling assumptions. These additions make the stark differences after two runs and the reproduction on hardware verifiable from the text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows standard methods with independent validation

full rationale

The paper models pure dephasing via full density matrix (quantum) versus Kraus operators (classical) applied to Deutsch's algorithm, deriving that single runs match but double runs differ due to correlations slowing decoherence for balanced functions and causing qualitative shifts for constant ones. These differences are obtained from the open-system equations without reduction to fitted parameters or self-citations. IBM Quantum processor data are presented as an external reproduction of the predicted effect, not a fit or input to the derivation. The stand-in assumption for Deutsch's algorithm is explicit but does not make any reported result equivalent to its inputs by construction. No self-definitional steps, fitted predictions, or load-bearing self-citations are present.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that Deutsch's algorithm is representative of noise effects in larger algorithms and on standard quantum-mechanical modeling of pure dephasing; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Deutsch's algorithm can serve as a stand-in for more complex quantum algorithms to study environmental noise effects.
    Explicitly stated in the opening sentence of the abstract.

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