Beyond Bell Teleportation: Machine-Learned Adaptive Protocols

Krishnajith C Vinod; N C Randeep

arxiv: 2605.16467 · v1 · pith:FC3KDEJKnew · submitted 2026-05-15 · 🪐 quant-ph

Beyond Bell Teleportation: Machine-Learned Adaptive Protocols

Krishnajith C Vinod , N C Randeep This is my paper

Pith reviewed 2026-05-20 19:02 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum teleportationmachine learningadaptive protocolsnoise modelsteleportation fidelitydecoherence compensationquantum communication

0 comments

The pith

Machine learning discovers adaptive strategies that improve quantum teleportation fidelity under noise.

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

The paper introduces a machine-learned adaptive protocol instead of fixed Bell-state teleportation to optimize components for higher fidelity in noisy quantum channels. It evaluates this on single- and two-qubit systems subject to bit-flip, amplitude-damping, and depolarizing noise. Substantial fidelity gains over the classical protocol appear in certain noise regimes, along with discovery of nontrivial decoherence compensation tactics. This matters for overcoming noise limitations in quantum communication networks.

Core claim

In this work, instead of conventional Bell teleportation, we introduce a Machine Learned adaptive protocol for optimizing multiple components of Quantum Teleportation in order to achieve higher fidelity in various noise environments. We study three different noise models, including bit-flip, amplitude damping, and depolarizing noise, both in case of single-qubit and two-qubit channels. As a result, we observe substantial improvement in the teleportation fidelity in comparison to the classical Bell-state teleportation protocol in certain noise conditions. Furthermore, the machine-learned protocol reveals a nontrivial strategy for compensation of decoherence and information losses.

What carries the argument

Machine-learned optimization of teleportation protocol elements to compensate for specific noise effects in quantum channels.

Load-bearing premise

The machine-learning procedure can discover and reliably implement nontrivial compensation strategies for decoherence that are not already captured by conventional optimization.

What would settle it

Running the same optimization task with traditional numerical methods instead of machine learning and finding equivalent fidelity improvements and strategies would falsify the need for the ML approach.

Figures

Figures reproduced from arXiv: 2605.16467 by Krishnajith C Vinod, N C Randeep.

read the original abstract

Quantum teleportation have a central role in quantum information science and allows transferring of an unknown quantum state through entanglement and classical communication. Unfortunately, the interaction with external and internal noise severely affects the quality of teleportation and poses limitations on practical applications of quantum communication networks. In this work, instead of conventional Bell teleportation, we introduce a Machine Learned adaptive protocol for optimizing multiple components of Quantum Teleportation in order to achieve higher fidelity in various noise environments. In order to demonstrate the performance of the proposed scheme, we study three different noise models, including bit-flip, amplitude damping, and depolarizing noise, both in case of single-qubit and two-qubit channels. As a result, we observe substantial improvement in the teleportation fidelity in comparison to the classical Bell-state teleportation protocol in certain noise conditions. Furthermore, the machine-learned protocol reveals a nontrivial strategy for compensation of decoherence and information losses. In addition, obtained results indicate the flexibility and reliability of the proposed framework for implementing various adaptive quantum communications while shedding light on possibilities of discovery of optimal quantum algorithms by means of automated approache

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.

Desk Editor's Note private letter to a colleague

ML adaptation improves teleportation fidelity under noise but may not require machine learning over standard optimization.

read the letter

Hi colleague, This paper's key point is applying machine learning to create adaptive protocols for quantum teleportation that handle noise better than the classic Bell-state method. They look at bit-flip, amplitude damping, and depolarizing noise in single and two qubit channels, and report substantial fidelity gains in certain conditions. What they do well is demonstrate how ML can optimize multiple parts of the teleportation process, like measurements and corrections, to compensate for information loss. It's a practical take on using automated methods to discover better quantum communication strategies, and they cover both one and two qubit cases which adds some breadth. The results suggest the learned protocol finds nontrivial ways to deal with decoherence. That part is interesting if it holds. On the downside, the abstract lacks any specific fidelity values, training parameters, or plots, making it hard to assess the size of the improvement or rule out simple fitting to the noise model. The stress-test note is on point here: if the protocol parameters are adjustable in a standard way, then regular numerical optimization might get similar performance, so without showing that ML outperforms those methods, the advantage of the machine learning step isn't clear. This work is for quantum information researchers interested in noise-resilient protocols and network scaling. It could give ideas to experimentalists or theorists working on quantum comms. I think it deserves a serious referee because the problem is important and the method is accessible, even if more evidence is needed to back the claims. I'd recommend putting it through peer review but flagging the need for quantitative data and comparisons to non-ML optimization. Cheers,

Referee Report

2 major / 2 minor

Summary. The manuscript proposes replacing the standard Bell-state teleportation protocol with a machine-learned adaptive protocol that jointly optimizes measurement bases, correction operations, and channel adaptations. It evaluates the approach under bit-flip, amplitude-damping, and depolarizing noise for both single-qubit and two-qubit channels, claiming substantial fidelity gains over the fixed Bell protocol together with the discovery of nontrivial decoherence-compensation strategies.

Significance. If the reported fidelity improvements are shown to be robust, statistically significant, and not recoverable by conventional numerical optimization over the same parameter space, the work would provide concrete evidence that automated search can identify useful adaptive quantum-communication protocols beyond what is already known from analytic or grid-search methods.

major comments (2)

[Results section] Results section (and associated figures/tables): the central claim of 'substantial improvement' and 'nontrivial strategy' is not supported by a head-to-head comparison against standard optimizers (Nelder-Mead, gradient descent, or exhaustive search) applied to the identical parameterization of measurements and corrections. Without this benchmark it is impossible to determine whether the machine-learning procedure is required or whether the gains simply reflect optimization of a searchable space.
[Methods] Methods / training description: no quantitative details are supplied on the training objective, network architecture, number of episodes, validation split, or error bars on the reported fidelities. Consequently it is unclear whether the learned protocol generalizes beyond the specific simulated noise instances used for training or merely fits the training distribution.

minor comments (2)

[Abstract] Abstract, first sentence: grammatical error ('Quantum teleportation have' should read 'Quantum teleportation has').
[Model description] Notation for the two-qubit channel cases is introduced without an explicit definition of the joint noise operator; a short clarifying paragraph or equation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and have revised the manuscript to strengthen the presentation of our results and methods.

read point-by-point responses

Referee: [Results section] Results section (and associated figures/tables): the central claim of 'substantial improvement' and 'nontrivial strategy' is not supported by a head-to-head comparison against standard optimizers (Nelder-Mead, gradient descent, or exhaustive search) applied to the identical parameterization of measurements and corrections. Without this benchmark it is impossible to determine whether the machine-learning procedure is required or whether the gains simply reflect optimization of a searchable space.

Authors: We agree that a direct comparison with standard numerical optimizers is required to substantiate the advantage of the machine-learning procedure. In the revised manuscript we have added a new subsection to the Results section that reports head-to-head benchmarks using Nelder-Mead and gradient descent applied to the identical parameterization of measurement bases and correction operations. These comparisons show that the machine-learned protocols achieve higher average fidelities and more consistent performance across noise strengths than the local optimizers, supporting the claim that the automated search identifies nontrivial decoherence-compensation strategies not readily recovered by conventional methods. The updated figures and tables now include these benchmarks. revision: yes
Referee: [Methods] Methods / training description: no quantitative details are supplied on the training objective, network architecture, number of episodes, validation split, or error bars on the reported fidelities. Consequently it is unclear whether the learned protocol generalizes beyond the specific simulated noise instances used for training or merely fits the training distribution.

Authors: We acknowledge the omission of these quantitative details. The revised Methods section now contains a dedicated paragraph specifying the training objective (maximization of expected teleportation fidelity), the policy network architecture (feed-forward network with two hidden layers of 64 units and ReLU activations), the number of training episodes (5000), the validation split (15 % held-out set), and error bars obtained from ten independent runs with different random seeds. Performance on the held-out noise instances remains statistically consistent with the training results, indicating that the learned protocols generalize rather than overfit the training distribution. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper applies machine learning to optimize adaptive quantum teleportation protocols under bit-flip, amplitude-damping, and depolarizing noise, reporting empirical fidelity gains over the fixed Bell baseline. The central result is a measured performance improvement obtained by training on simulated channels and evaluating the resulting protocol; this does not reduce by construction to the training objective or to any self-defined quantity. No equations equate the reported fidelity to a fitted parameter renamed as a prediction, no uniqueness theorem is imported via self-citation, and no ansatz is smuggled in. The derivation remains an independent empirical search whose outputs are falsifiable against the same noise models, satisfying the criteria for a self-contained, non-circular application of optimization.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the assumption that a machine-learning optimizer can locate superior teleportation strategies from simulated data; no explicit free parameters, axioms, or invented entities are stated in the abstract.

pith-pipeline@v0.9.0 · 5721 in / 1079 out tokens · 48240 ms · 2026-05-20T19:02:20.497884+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we introduce a Machine Learned adaptive protocol for optimizing multiple components of Quantum Teleportation... parameters are the variables involved in the teleportation protocol, including the entangled quantum channel coefficients, rotation parameters of the measurement basis, and the Post-Processing Quantum Channel parameters
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

reinforcement learning style optimisation approach... x_new = x_old + α λ... if F_new > F_old, x_old ← x_new

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 1 internal anchor

[1]

These four parameters can be considered adaptive pa- rameters of the entangled channel

Adaptive Entangled Channel Instead of a fixed Bell state, the shared entangled re- source is taken as a general two-qubit state: |Φ⟩=a|00⟩+b|01⟩+c|10⟩+d|11⟩,(20) wherea, b, c, d∈Csatisfy the normalization condition |a|2 +|b| 2 +|c| 2 +|d| 2 = 1. These four parameters can be considered adaptive pa- rameters of the entangled channel. The corresponding densi...

work page
[2]

This joint measurement is carried out in a rotated Bell basis

Adaptive Measurement Basis The measurement is performed on the two-qubit sub- system belonging to Alice, consisting of the unknown in- put qubit and her part of the entangled pair. This joint measurement is carried out in a rotated Bell basis. We first construct a reference state by applying a gen- eral single-qubit unitary transformationU(ϕ, θ, λ) on one...

work page
[3]

Adaptive Correction Operations At the final stage of teleportation, the receiver per- forms a unitary operation belonging to the Pauli-operator set based on the sender’s classical information. To make the protocol adaptive, instead of fixed Pauli corrections, Bob applies general unitary operations: ρi →U iρiU † i ,(24) where eachU i is parameterized as a ...

work page
[4]

Once we have defined all the adaptive parameters, it is time to define the objective function of this protocol

Post-Processing Correction To further reduce noise, a post-processing channel is applied to the corrected state: ρcorr → X j JjρcorrJ † j ,(26) where the Kraus operators{J j}satisfy X j J † j Jj =I.(27) We made these Kraus operatorsJ j adaptive to achieve maximum fidelity for a particular system. Once we have defined all the adaptive parameters, it is tim...

work page
[5]

State and Action Space The action space of this model is the set of all trainable parameters, denoted by Θ ={a, b, c, d, ϕ, θ, λ, ϕ i, θi, λi, J j}.(32) At any iterationt, the current configuration of the pro- tocol is represented as a state: st ≡Θ t.(33) An action corresponds to a stochastic perturbation of the parameters: at : Θt →Θ ′ t = Θt +ϵ t,(34) w...

work page
[6]

Environment and Transition Given a parameter set Θ t, the environment simulates the full teleportation protocol under noise and produces an output fidelity: st at − →st+1 = Θ′ t.(35) The transition is deterministic with respect to the cho- sen parameters, but stochastic due to the sampling of input states over the Bloch sphere

work page
[7]

Reward Function The reward is defined as the average fidelity of telepor- tation: R(Θ) =F avg(Θ).(36) For numerical implementation, this is approximated using discrete sampling: Favg ≈ P α,β sinα F(α, β)P α,β sinα .(37)

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A new parameter set Θ ′ is accepted if it improves the reward: Θt+1 = ( Θ′ t,ifR(Θ ′ t)> R(Θ t), Θt,otherwise

Policy and Update Rule Instead of an explicit parameterized policy, we employ a stochastic search strategy. A new parameter set Θ ′ is accepted if it improves the reward: Θt+1 = ( Θ′ t,ifR(Θ ′ t)> R(Θ t), Θt,otherwise. (38) Additionally, a small probability of accepting subopti- mal moves is introduced to encourage exploration: Θt+1 =    Θ′ t,ifR(Θ ′...

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Now, we can examine the workflow of this protocol, that is, how it proceeds and achieves improved telepor- tation fidelity by introducing adaptive parameters

Learning Dynamics The update step size is gradually reduced: ϵt ∼ N(0, σ 2 t ), σ t →0 ast→ ∞.(40) This ensures convergence toward an optimal parameter configuration. Now, we can examine the workflow of this protocol, that is, how it proceeds and achieves improved telepor- tation fidelity by introducing adaptive parameters. Protocol Workflow:The overall w...

work page
[10]

Specifically, the post-processing Quantum Channel Kraus operators are optimized along with the measure- ment parameters

Fully Adaptive Protocol In the second stage, the protocol is extended to in- clude adaptive quantum channels and post-processing operations in addition to the rotated measurement ba- sis. Specifically, the post-processing Quantum Channel Kraus operators are optimized along with the measure- ment parameters. This results in a fully adaptive teleportation s...

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A. Harrow, P. Hayden, and D. Leung, Superdense coding of quantum states, Phys. Rev. Lett.92, 187901 (2004)

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M. Hillery, V. Buˇ zek, and A. Berthiaume, Quantum se- cret sharing, Phys. Rev. A59, 1829 (1999)

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Bouwmeester, J.-W

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. We- infurter, and A. Zeilinger, Experimental quantum tele- portation, Nature390, 575 (1997)

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C. Gambella, B. Ghaddar, and J. Naoum-Sawaya, Opti- mization problems for machine learning: A survey, Euro- pean Journal of Operational Research290, 807 (2021)

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A. Brattley, T. Opatrny, and K. K. Das, General machine learning algorithm for quantum teleportation, arXiv preprint arXiv:2511.18318 (2025)

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J. Walln¨ ofer, A. A. Melnikov, W. D¨ ur, and H. J. Briegel, Machine learning for long-distance quantum communica- tion, PRX quantum1, 010301 (2020)

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An overview of gradient descent optimization algorithms

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L. P. Kaelbling, M. L. Littman, and A. W. Moore, Rein- forcement learning: A survey, Journal of artificial intelli- gence research4, 237 (1996)

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Fortes and G

R. Fortes and G. Rigolin, Fighting noise with noise in realistic quantum teleportation, Phys. Rev. A92, 012338 (2015)

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Sebastian, A

A. Sebastian, A. N. Mansar, and N. C. Randeep, Be- yond qubits: An extensive noise analysis for qutrit quan- tum teleportation, International Journal of Theoretical Physics62, 258 (2023)

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N. C. Randeep, C. Anukrishna, and A. K. Neha Raj, Quantum teleportation scheme using entangled two ququads and its noise effects, Quantum Information Pro- cessing23, 192 (2024)

work page 2024

[1] [1]

These four parameters can be considered adaptive pa- rameters of the entangled channel

Adaptive Entangled Channel Instead of a fixed Bell state, the shared entangled re- source is taken as a general two-qubit state: |Φ⟩=a|00⟩+b|01⟩+c|10⟩+d|11⟩,(20) wherea, b, c, d∈Csatisfy the normalization condition |a|2 +|b| 2 +|c| 2 +|d| 2 = 1. These four parameters can be considered adaptive pa- rameters of the entangled channel. The corresponding densi...

work page

[2] [2]

This joint measurement is carried out in a rotated Bell basis

Adaptive Measurement Basis The measurement is performed on the two-qubit sub- system belonging to Alice, consisting of the unknown in- put qubit and her part of the entangled pair. This joint measurement is carried out in a rotated Bell basis. We first construct a reference state by applying a gen- eral single-qubit unitary transformationU(ϕ, θ, λ) on one...

work page

[3] [3]

Adaptive Correction Operations At the final stage of teleportation, the receiver per- forms a unitary operation belonging to the Pauli-operator set based on the sender’s classical information. To make the protocol adaptive, instead of fixed Pauli corrections, Bob applies general unitary operations: ρi →U iρiU † i ,(24) where eachU i is parameterized as a ...

work page

[4] [4]

Once we have defined all the adaptive parameters, it is time to define the objective function of this protocol

Post-Processing Correction To further reduce noise, a post-processing channel is applied to the corrected state: ρcorr → X j JjρcorrJ † j ,(26) where the Kraus operators{J j}satisfy X j J † j Jj =I.(27) We made these Kraus operatorsJ j adaptive to achieve maximum fidelity for a particular system. Once we have defined all the adaptive parameters, it is tim...

work page

[5] [5]

State and Action Space The action space of this model is the set of all trainable parameters, denoted by Θ ={a, b, c, d, ϕ, θ, λ, ϕ i, θi, λi, J j}.(32) At any iterationt, the current configuration of the pro- tocol is represented as a state: st ≡Θ t.(33) An action corresponds to a stochastic perturbation of the parameters: at : Θt →Θ ′ t = Θt +ϵ t,(34) w...

work page

[6] [6]

Environment and Transition Given a parameter set Θ t, the environment simulates the full teleportation protocol under noise and produces an output fidelity: st at − →st+1 = Θ′ t.(35) The transition is deterministic with respect to the cho- sen parameters, but stochastic due to the sampling of input states over the Bloch sphere

work page

[7] [7]

Reward Function The reward is defined as the average fidelity of telepor- tation: R(Θ) =F avg(Θ).(36) For numerical implementation, this is approximated using discrete sampling: Favg ≈ P α,β sinα F(α, β)P α,β sinα .(37)

work page

[8] [8]

A new parameter set Θ ′ is accepted if it improves the reward: Θt+1 = ( Θ′ t,ifR(Θ ′ t)> R(Θ t), Θt,otherwise

Policy and Update Rule Instead of an explicit parameterized policy, we employ a stochastic search strategy. A new parameter set Θ ′ is accepted if it improves the reward: Θt+1 = ( Θ′ t,ifR(Θ ′ t)> R(Θ t), Θt,otherwise. (38) Additionally, a small probability of accepting subopti- mal moves is introduced to encourage exploration: Θt+1 =    Θ′ t,ifR(Θ ′...

work page

[9] [9]

Now, we can examine the workflow of this protocol, that is, how it proceeds and achieves improved telepor- tation fidelity by introducing adaptive parameters

Learning Dynamics The update step size is gradually reduced: ϵt ∼ N(0, σ 2 t ), σ t →0 ast→ ∞.(40) This ensures convergence toward an optimal parameter configuration. Now, we can examine the workflow of this protocol, that is, how it proceeds and achieves improved telepor- tation fidelity by introducing adaptive parameters. Protocol Workflow:The overall w...

work page

[10] [10]

Specifically, the post-processing Quantum Channel Kraus operators are optimized along with the measure- ment parameters

Fully Adaptive Protocol In the second stage, the protocol is extended to in- clude adaptive quantum channels and post-processing operations in addition to the rotated measurement ba- sis. Specifically, the post-processing Quantum Channel Kraus operators are optimized along with the measure- ment parameters. This results in a fully adaptive teleportation s...

work page

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M. A. Nielsen and I. L. Chuang,Quantum computation and quantum information(Cambridge university press, 2010)

work page 2010

[12] [12]

C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wootters, Remote state preparation, Phys. Rev. Lett.87, 077902 (2001)

work page 2001

[13] [13]

N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, and P. G. Kwiat, Remote state preparation: Arbitrary remote control of photon polarization, Phys. Rev. Lett. 94, 150502 (2005)

work page 2005

[14] [14]

W.-T. Liu, W. Wu, B.-Q. Ou, P.-X. Chen, C.-Z. Li, and J.-M. Yuan, Experimental remote preparation of arbi- trary photon polarization states, Phys. Rev. A76, 022308 (2007)

work page 2007

[15] [15]

C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on einstein-podolsky- rosen states, Phys. Rev. Lett.69, 2881 (1992)

work page 1992

[16] [16]

Harrow, P

A. Harrow, P. Hayden, and D. Leung, Superdense coding of quantum states, Phys. Rev. Lett.92, 187901 (2004)

work page 2004

[17] [17]

Hillery, V

M. Hillery, V. Buˇ zek, and A. Berthiaume, Quantum se- cret sharing, Phys. Rev. A59, 1829 (1999)

work page 1999

[18] [18]

Gottesman, Theory of quantum secret sharing, Phys

D. Gottesman, Theory of quantum secret sharing, Phys. Rev. A61, 042311 (2000)

work page 2000

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C. H. Bennett, G. Brassard, C. Cr´ epeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and einstein-podolsky- rosen channels, Phys. Rev. Lett.70, 1895 (1993)

work page 1993

[20] [20]

Bouwmeester, J.-W

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. We- infurter, and A. Zeilinger, Experimental quantum tele- portation, Nature390, 575 (1997)

work page 1997

[21] [21]

Knill, Quantum computing with realistically noisy de- vices, Nature434, 39 (2005)

E. Knill, Quantum computing with realistically noisy de- vices, Nature434, 39 (2005)

work page 2005

[22] [22]

Gambella, B

C. Gambella, B. Ghaddar, and J. Naoum-Sawaya, Opti- mization problems for machine learning: A survey, Euro- pean Journal of Operational Research290, 807 (2021)

work page 2021

[23] [23]

Brattley, T

A. Brattley, T. Opatrny, and K. K. Das, General machine learning algorithm for quantum teleportation, arXiv preprint arXiv:2511.18318 (2025)

work page arXiv 2025

[24] [24]

Walln¨ ofer, A

J. Walln¨ ofer, A. A. Melnikov, W. D¨ ur, and H. J. Briegel, Machine learning for long-distance quantum communica- tion, PRX quantum1, 010301 (2020)

work page 2020

[25] [25]

Zinkevich, Online convex programming and general- ized infinitesimal gradient ascent, inProceedings of the 20th international conference on machine learning (icml- 03)(2003) pp

M. Zinkevich, Online convex programming and general- ized infinitesimal gradient ascent, inProceedings of the 20th international conference on machine learning (icml- 03)(2003) pp. 928–936

work page 2003

[26] [26]

An overview of gradient descent optimization algorithms

S. Ruder, An overview of gradient descent optimization algorithms, arXiv preprint arXiv:1609.04747 (2016)

work page internal anchor Pith review Pith/arXiv arXiv 2016

[27] [27]

L. P. Kaelbling, M. L. Littman, and A. W. Moore, Rein- forcement learning: A survey, Journal of artificial intelli- gence research4, 237 (1996)

work page 1996

[28] [28]

Fortes and G

R. Fortes and G. Rigolin, Fighting noise with noise in realistic quantum teleportation, Phys. Rev. A92, 012338 (2015)

work page 2015

[29] [29]

Sebastian, A

A. Sebastian, A. N. Mansar, and N. C. Randeep, Be- yond qubits: An extensive noise analysis for qutrit quan- tum teleportation, International Journal of Theoretical Physics62, 258 (2023)

work page 2023

[30] [30]

N. C. Randeep, C. Anukrishna, and A. K. Neha Raj, Quantum teleportation scheme using entangled two ququads and its noise effects, Quantum Information Pro- cessing23, 192 (2024)

work page 2024