pith. machine review for the scientific record. sign in

arxiv: 2604.04414 · v1 · submitted 2026-04-06 · 💻 cs.ET · cs.LG· quant-ph

Recognition: no theorem link

Eliminating Vendor Lock-In in Quantum Machine Learning via Framework-Agnostic Neural Networks

Lakshmi Rajendran, Poornima Kumaresan, Santhosh Sivasubramani, Shwetha Singaravelu

Pith reviewed 2026-05-10 19:55 UTC · model grok-4.3

classification 💻 cs.ET cs.LGquant-ph
keywords quantum machine learningframework agnosticvendor lock-inneural networkshardware abstractionmodel portabilityquantum circuitsclassification tasks
0
0 comments X

The pith

A framework-agnostic quantum neural network architecture removes the need to rewrite models when switching between different software ecosystems and hardware providers.

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

This paper aims to solve the problem of vendor lock-in in quantum machine learning by introducing an architecture that does not depend on any specific software framework. It achieves this through a shared way to represent computations, a layer that hides differences in hardware, and tools to convert models for different systems. A sympathetic reader would care because being tied to one ecosystem limits which hardware can be used and makes it hard to reproduce or build on others' work. If the approach holds, scientists could create a model in one place and run it on many different quantum computers and classical libraries without rewriting anything.

Core claim

The central discovery is a quantum neural network that uses one computational graph for the model structure, a hardware abstraction layer to connect to various quantum systems via a common interface, and an export pipeline that translates the model losslessly into formats used by different quantum software tools. It includes flexible methods to encode classical data into quantum states that work on all supported systems. Tests on standard datasets for classifying items like flowers and digits show training speeds nearly match direct use of single frameworks and produce the same accuracy levels.

What carries the argument

The framework-agnostic quantum neural network built on a unified computational graph, hardware abstraction layer for backend access, and export pipeline for cross-representation compatibility.

If this is right

  • A model developed once can execute on multiple quantum hardware providers through the same code.
  • Accuracy on classification problems matches that of implementations built directly for one framework.
  • The overhead from the abstraction stays small, under eight percent in training time.
  • Different data encoding approaches can be swapped in without affecting compatibility with backends.

Where Pith is reading between the lines

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

  • The design may reduce duplication of effort as groups no longer need to reimplement models for each new hardware.
  • It could support runtime decisions on which backend to use based on current availability or cost.
  • Extending the abstraction to include error mitigation techniques would be a natural next test of its generality.

Load-bearing premise

The unified computational graph and hardware abstraction layer can be made to handle every classical framework and every quantum backend at the same time with no loss of function or hidden extra costs.

What would settle it

Implementing a model with the architecture, exporting it to two different quantum software representations, running both on their native hardware, and checking if the classification results differ beyond normal variation or if one fails to run.

Figures

Figures reproduced from arXiv: 2604.04414 by Lakshmi Rajendran, Poornima Kumaresan, Santhosh Sivasubramani, Shwetha Singaravelu.

Figure 1
Figure 1. Figure 1: Top-level architecture of the framework-agnostic QNN. The QNN Core maintains [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Hardware compatibility matrix showing supported backend-framework com [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Circuit diagrams for the three data encoding strategies. Left: amplitude encoding [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Multi-framework export pipeline. A trained QNN model is exported from [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Training loss convergence across frameworks for three classification tasks. The [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: QPU gradient computation time across frameworks on IBM Brisbane. Each [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
read the original abstract

Quantum machine learning (QML) stands at the intersection of quantum computing and artificial intelligence, offering the potential to solve problems that remain intractable for classical methods. However, the current landscape of QML software frameworks suffers from severe fragmentation: models developed in TensorFlow Quantum cannot execute on PennyLane backends, circuits authored in Qiskit Machine Learning cannot be deployed to Amazon Braket hardware, and researchers who invest in one ecosystem face prohibitive switching costs when migrating to another. This vendor lock-in impedes reproducibility, limits hardware access, and slows the pace of scientific discovery. In this paper, we present a framework-agnostic quantum neural network (QNN) architecture that abstracts away vendor-specific interfaces through a unified computational graph, a hardware abstraction layer (HAL), and a multi-framework export pipeline. The core architecture supports simultaneous integration with TensorFlow, PyTorch, and JAX as classical co-processors, while the HAL provides transparent access to IBM Quantum, Amazon Braket, Azure Quantum, IonQ, and Rigetti backends through a single application programming interface (API). We introduce three pluggable data encoding strategies (amplitude, angle, and instantaneous quantum polynomial encoding) that are compatible with all supported backends. An export module leveraging Open Neural Network Exchange (ONNX) metadata enables lossless circuit translation across Qiskit, Cirq, PennyLane, and Braket representations. We benchmark our framework on the Iris, Wine, and MNIST-4 classification tasks, demonstrating training time parity (within 8\% overhead) compared to native framework implementations, while achieving identical classification accuracy.

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

3 major / 1 minor

Summary. The paper claims to present a framework-agnostic quantum neural network (QNN) architecture that eliminates vendor lock-in in quantum machine learning through a unified computational graph, a hardware abstraction layer (HAL), and a multi-framework export pipeline based on ONNX metadata. The architecture supports TensorFlow, PyTorch, and JAX as classical co-processors and provides transparent access to IBM Quantum, Amazon Braket, Azure Quantum, IonQ, and Rigetti backends via a single API. It introduces three pluggable data encoding strategies (amplitude, angle, and instantaneous quantum polynomial) and benchmarks on the Iris, Wine, and MNIST-4 classification tasks, reporting training time parity within 8% overhead and identical classification accuracy relative to native framework implementations.

Significance. If the central claims of lossless translation, full functionality preservation, and performance parity hold, the work would be significant for improving reproducibility and reducing switching costs across fragmented QML ecosystems. The pluggable encoding strategies represent a constructive step toward generality. However, the absence of detailed verification for the HAL and ONNX pipeline limits the demonstrated impact, leaving the contribution more prospective than empirically established.

major comments (3)
  1. [Abstract] Abstract: The claims of 'identical classification accuracy' and 'training time parity (within 8% overhead)' on Iris, Wine, and MNIST-4 are presented as summary assertions without implementation details, error bars, statistical tests, data splits, circuit diagrams, or references to specific tables/figures. These performance results are load-bearing for the central claim of practical viability and cannot be assessed from the given information.
  2. [Multi-framework export pipeline] Multi-framework export pipeline: The assertion that ONNX metadata enables 'lossless circuit translation' across Qiskit, Cirq, PennyLane, and Braket does not address how differences in gradient computation (parameter-shift vs. backprop-through-simulator), measurement semantics, or native gate sets are reconciled. Any internal transpilation to map circuits (e.g., PennyLane to Rigetti) would necessarily alter depth or introduce approximations, directly contradicting the lossless and identical-accuracy conditions.
  3. [Hardware Abstraction Layer (HAL)] Hardware Abstraction Layer (HAL): The HAL is described as providing transparent access to five distinct quantum backends through a single API, yet no mechanism is specified for abstracting backend-specific constraints such as connectivity graphs, calibration data, or noise models without per-backend overrides or hidden overheads. This omission undermines the framework-agnostic guarantee.
minor comments (1)
  1. The manuscript would benefit from explicit pseudocode or diagrams for the three pluggable encoding strategies to support reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major point below, agreeing where additional clarification or documentation is warranted and outlining specific revisions to strengthen the manuscript.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The claims of 'identical classification accuracy' and 'training time parity (within 8% overhead)' on Iris, Wine, and MNIST-4 are presented as summary assertions without implementation details, error bars, statistical tests, data splits, circuit diagrams, or references to specific tables/figures. These performance results are load-bearing for the central claim of practical viability and cannot be assessed from the given information.

    Authors: We acknowledge that the abstract, as a concise summary, does not embed the full experimental details. The manuscript reports the benchmark results in the Experimental Evaluation section, but we agree that explicit documentation of data splits, error bars from repeated runs, statistical tests, circuit diagrams, and direct table/figure references would improve verifiability. We will revise the abstract to include a brief pointer to the experimental section and key quantitative results with error bars, and expand the experimental section to add the missing implementation specifics and cross-references. revision: yes

  2. Referee: [Multi-framework export pipeline] Multi-framework export pipeline: The assertion that ONNX metadata enables 'lossless circuit translation' across Qiskit, Cirq, PennyLane, and Braket does not address how differences in gradient computation (parameter-shift vs. backprop-through-simulator), measurement semantics, or native gate sets are reconciled. Any internal transpilation to map circuits (e.g., PennyLane to Rigetti) would necessarily alter depth or introduce approximations, directly contradicting the lossless and identical-accuracy conditions.

    Authors: The architecture relies on a unified computational graph that normalizes representations before ONNX export, with gradient handling standardized at the graph level using the parameter-shift rule and measurement semantics normalized via the HAL. Gate-set mappings are performed by a semantics-preserving transpiler that maintains circuit depth for the supported encodings. We recognize that the manuscript does not provide sufficient detail on these reconciliation steps. We will add a new subsection in the architecture description that explicitly documents the gradient unification, measurement normalization, and transpilation rules, including examples demonstrating no depth increase or approximation for the benchmarked models. revision: yes

  3. Referee: [Hardware Abstraction Layer (HAL)] Hardware Abstraction Layer (HAL): The HAL is described as providing transparent access to five distinct quantum backends through a single API, yet no mechanism is specified for abstracting backend-specific constraints such as connectivity graphs, calibration data, or noise models without per-backend overrides or hidden overheads. This omission undermines the framework-agnostic guarantee.

    Authors: The HAL uses a standardized backend descriptor that encodes connectivity graphs, calibration data, and noise models, enabling automatic transpilation inside the unified graph without requiring user-level per-backend overrides. We agree that the current manuscript description remains at a high level and lacks concrete specification of these mechanisms. We will revise the HAL section to include the descriptor schema, an outline of the transpilation process, and empirical measurements of any overhead on the supported backends to substantiate the framework-agnostic claim. revision: yes

Circularity Check

0 steps flagged

No circularity: architecture described as independent design

full rationale

The paper presents a design for a framework-agnostic QNN using a unified computational graph, hardware abstraction layer, and ONNX-based export pipeline. No equations, fitted parameters, or self-referential definitions appear in the provided text. Claims of lossless translation and performance parity are stated as outcomes of the architecture rather than inputs used to define it. Benchmarks on Iris, Wine, and MNIST-4 are presented as independent empirical validation. The derivation consists of engineering choices motivated by vendor fragmentation, with no reduction to self-citation chains or tautological inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central claim rests on the introduction of new software abstractions rather than new physical laws, mathematical derivations, or data-fitted parameters.

axioms (1)
  • domain assumption Quantum computing frameworks and hardware backends can be unified through a single computational graph and hardware abstraction layer without inherent loss of functionality.
    Invoked as the basis for the HAL and multi-framework support in the architecture description.
invented entities (2)
  • Hardware Abstraction Layer (HAL) no independent evidence
    purpose: Provide transparent single-API access to IBM Quantum, Amazon Braket, Azure Quantum, IonQ, and Rigetti backends.
    New software component introduced to eliminate vendor-specific interfaces.
  • Multi-framework export pipeline using ONNX metadata no independent evidence
    purpose: Enable lossless circuit translation across Qiskit, Cirq, PennyLane, and Braket representations.
    New translation mechanism introduced for cross-framework compatibility.

pith-pipeline@v0.9.0 · 5615 in / 1459 out tokens · 61365 ms · 2026-05-10T19:55:49.406088+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 48 canonical work pages · 3 internal anchors

  1. [1]

    Cerezoet al., Variational quantum al- gorithms, Nat

    Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. Variational quantum algorithms. Nature Reviews Physics, 3 0 (9): 0 625--644, 2021. doi:10.1038/s42254-021-00348-9

  2. [2]

    Nature Communications5(1), 4213 (2014) https://doi.org/ 10.1038/ncomms5213

    Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Al \'a n Aspuru-Guzik, and Jeremy L O'Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5 0 (1): 0 4213, 2014. doi:10.1038/ncomms5213

  3. [3]

    Quantum computing in the NISQ era and beyond.Quantum, 2:79, 2018

    John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2: 0 79, 2018. doi:10.22331/q-2018-08-06-79

  4. [4]

    Quantum Science and Technology4(4), 043001 (2019) https://doi.org/10.1088/2058-9565/ab4eb5

    Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini. Parameterized quantum circuits as machine learning models. Quantum Science and Technology, 4 0 (4): 0 043001, 2019. doi:10.1088/2058-9565/ab4eb5

  5. [5]

    Supervised Learning with Quantum-Enhanced Feature Spaces

    Vojt e ch Havl \' c ek, Antonio D C \'o rcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta. Supervised learning with quantum-enhanced feature spaces. Nature, 567 0 (7747): 0 209--212, 2019. doi:10.1038/s41586-019-0980-2

  6. [6]

    Schuld, A

    Maria Schuld, Alex Bocharov, Krysta M Svore, and Nathan Wiebe. Circuit-centric quantum classifiers. Physical Review A, 101 0 (3): 0 032308, 2020. doi:10.1103/PhysRevA.101.032308

  7. [7]

    Representation learning via quantum neural networks

    Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme. Representation learning via quantum neural networks. Physical Review Research, 6: 0 L032057, 2024. doi:10.1103/PhysRevResearch.6.L032057

  8. [8]

    Variational quantum circuits for deep reinforcement learning

    Samuel Yen-Chi Chen, Chao-Han Huck Yang, Jun Qi, Pin-Yu Chen, Xiaoli Ma, and Hsi-Sheng Goan. Variational quantum circuits for deep reinforcement learning. IEEE Access, 8: 0 141007--141024, 2020. doi:10.1109/ACCESS.2020.3010470

  9. [9]

    Reinforcement learning with quantum variational circuit

    Owen Lockwood and Mei Si. Reinforcement learning with quantum variational circuit. Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, 16: 0 245--251, 2020. doi:10.1609/aiide.v16i1.7437

  10. [10]

    Broughton, G

    Michael Broughton, Guillaume Verdon, Trevor McCourt, Antonio J Martinez, Jae Hyeon Yoo, Sergei V Isakov, Philip Masber, Ramin Haber, Masoud Mohseni, Dave Bacon, et al. TensorFlow Quantum : A software framework for quantum machine learning. arXiv preprint arXiv:2003.02989, 2020. doi:10.48550/arXiv.2003.02989

  11. [11]

    Cirq : A Python framework for creating, editing, and invoking NISQ circuits

    Cirq Developers . Cirq : A Python framework for creating, editing, and invoking NISQ circuits. https://quantumai.google/cirq, 2023. Accessed: 2024-01-15

  12. [12]

    PennyLane: Automatic differentiation of hybrid quantum-classical computations

    Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M Sohaib Alam, Guillermo Alonso-Linaje, B AkashNarayanan, Ali Asber, et al. PennyLane : Automatic differentiation of hybrid quantum-classical computations. arXiv preprint arXiv:1811.04968, 2022. doi:10.48550/arXiv.1811.04968

  13. [13]

    Qiskit Machine Learning : An open-source framework for quantum machine learning

    Qiskit ML Contributors . Qiskit Machine Learning : An open-source framework for quantum machine learning. https://qiskit.org/ecosystem/machine-learning/, 2023. Accessed: 2024-01-15

  14. [14]

    Qiskit : An open-source framework for quantum computing

    Qiskit Contributors . Qiskit : An open-source framework for quantum computing. https://qiskit.org/, 2023

  15. [15]

    Amazon Braket Developer Guide

    Amazon Web Services . Amazon Braket Developer Guide . https://docs.aws.amazon.com/braket/, 2023. Accessed: 2024-01-15

  16. [16]

    Azure Quantum Documentation

    Microsoft . Azure Quantum Documentation . https://learn.microsoft.com/en-us/azure/quantum/, 2023. Accessed: 2024-01-15

  17. [17]

    IonQ quantum cloud

    IonQ Inc. IonQ quantum cloud. https://ionq.com/, 2023. Accessed: 2024-01-15

  18. [18]

    Rigetti quantum cloud services

    Rigetti Computing . Rigetti quantum cloud services. https://www.rigetti.com/, 2023. Accessed: 2024-01-15

  19. [19]

    ONNX : Open neural network exchange

    ONNX Consortium . ONNX : Open neural network exchange. https://onnx.ai/, 2023. Accessed: 2024-01-15

  20. [20]

    Evaluating analytic gradients on quantum hardware,

    Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Physical Review A, 99 0 (3): 0 032331, 2019. doi:10.1103/PhysRevA.99.032331

  21. [21]

    Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik

    Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S Kottmann, Tim Menke, et al. Noisy intermediate-scale quantum algorithms. Reviews of Modern Physics, 94 0 (1): 0 015004, 2022. doi:10.1103/RevModPhys.94.015004

  22. [22]

    Nature549(7671), 242–246 (2017) https://doi.org/10.1038/nature23879

    Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549 0 (7671): 0 242--246, 2017. doi:10.1038/nature23879

  23. [23]

    Variational quantum eigensolver with fewer qubits

    Jin-Guo Liu, Yi-Hong Zhang, Yuan Wan, and Lei Wang. Variational quantum eigensolver with fewer qubits. Physical Review Research, 1 0 (2): 0 023025, 2019. doi:10.1103/PhysRevResearch.1.023025

  24. [24]

    A Quantum Approximate Optimization Algorithm

    Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014. doi:10.48550/arXiv.1411.4028

  25. [25]

    Mitarai, M

    Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii. Quantum circuit learning. Physical Review A, 98 0 (3): 0 032309, 2018. doi:10.1103/PhysRevA.98.032309

  26. [26]

    Quantum machine learning in feature Hilbert spaces

    Maria Schuld and Nathan Killoran. Quantum machine learning in feature Hilbert spaces. Physical Review Letters, 122 0 (4): 0 040504, 2019. doi:10.1103/PhysRevLett.122.040504

  27. [27]

    A rigorous and robust quantum speed-up in supervised machine learning

    Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme. A rigorous and robust quantum speed-up in supervised machine learning. Nature Physics, 17 0 (9): 0 1013--1017, 2021. doi:10.1038/s41567-021-01287-z

  28. [28]

    Na- ture Communications12(1), 2631 (2021) https: //doi.org/10.1038/s41467-021-22539-9

    Hsin-Yuan Huang, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R McClean. Power of data in quantum machine learning. Nature Communications, 12 0 (1): 0 2631, 2021. doi:10.1038/s41467-021-22539-9

  29. [29]

    u bler, Simon Buchholz, and Bernhard Sch \

    Jonas M K \"u bler, Simon Buchholz, and Bernhard Sch \"o lkopf. The inductive bias of quantum kernels. Advances in Neural Information Processing Systems, 34: 0 12661--12673, 2021

  30. [30]

    \ Huang , author M

    Hsin-Yuan Huang, Michael Broughton, Jordan Cotler, Sitan Chen, Jerry Li, Masoud Mohseni, Hartmut Neven, Ryan Babbush, Richard Kueng, John Preskill, and Jarrod R McClean. Quantum advantage in learning from experiments. Science, 376 0 (6598): 0 1182--1186, 2022. doi:10.1126/science.abn7293

  31. [31]

    Dequantizing the quantum singular value transformation: Hardness and applications to quantum chemistry and the quantum PCP conjecture

    Ewin Tang et al. Dequantizing the quantum singular value transformation: Hardness and applications to quantum chemistry and the quantum PCP conjecture. Proceedings of STOC, 2021. doi:10.1145/3564246.3585234

  32. [32]

    Expressibility and entangling capability of parameter- ized quantum circuits for hybrid quantum-classical al- gorithms,

    Sukin Sim, Peter D Johnson, and Al \'a n Aspuru-Guzik. Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Advanced Quantum Technologies, 2 0 (12): 0 1900070, 2019. doi:10.1002/qute.201900070

  33. [33]

    Expressive power of parametrized quantum circuits

    Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, and Dacheng Tao. Expressive power of parametrized quantum circuits. Physical Review Research, 2 0 (3): 0 033125, 2020. doi:10.1103/PhysRevResearch.2.033125

  34. [34]

    Nature Communications9(1) (2018) https:// doi.org/10.1038/s41467-018-07090-4

    Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nature Communications, 9 0 (1): 0 4812, 2018. doi:10.1038/s41467-018-07090-4

  35. [35]

    Effect of barren plateaus on gradient-free optimization

    Andrew Arrasmith, Marco Cerezo, Piotr Czarnik, Lukasz Cincio, and Patrick J Coles. Effect of barren plateaus on gradient-free optimization. Quantum, 5: 0 558, 2021. doi:10.22331/q-2021-10-05-558

  36. [36]

    Quantum convolutional neural networks

    Iris Cong, Soonwon Choi, and Mikhail D Lukin. Quantum convolutional neural networks. Nature Physics, 15 0 (12): 0 1273--1278, 2019. doi:10.1038/s41567-019-0648-8

  37. [37]

    Absence of barren plateaus in quantum convolutional neural networks

    Arthur Pesah, Marco Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles. Absence of barren plateaus in quantum convolutional neural networks. Physical Review X, 11 0 (4): 0 041011, 2021. doi:10.1103/PhysRevX.11.041011

  38. [38]

    Hierarchical quantum classifiers

    Edward Grant, Marcello Benedetti, Shruti Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G Green, and Simone Severini. Hierarchical quantum classifiers. npj Quantum Information, 4 0 (1): 0 65, 2018. doi:10.1038/s41534-018-0116-9

  39. [39]

    Exploring entanglement and optimization within the Hamiltonian variational ansatz

    Roeland Wiersema, Cunlu Zhou, Yvette de Sereville, Juan F Carrasquilla, Yong Baek Kim, and Henry Yuen. Exploring entanglement and optimization within the Hamiltonian variational ansatz. PRX Quantum, 1 0 (2): 0 020319, 2020. doi:10.1103/PRXQuantum.1.020319

  40. [40]

    Trainability of dissipative perceptron-based quantum neural networks

    Kunal Sharma, Marco Cerezo, Enrico Fontana, Akira Sone, and Patrick J Coles. Trainability of dissipative perceptron-based quantum neural networks. Physical Review Letters, 128 0 (7): 0 070501, 2022. doi:10.1103/PhysRevLett.128.070501

  41. [41]

    Training deep quantum neural networks

    Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J Osborne, Robert Salzmann, Daniel Scheiermann, and Ramona Wolf. Training deep quantum neural networks. Nature Communications, 11 0 (1): 0 808, 2020. doi:10.1038/s41467-020-14454-2

  42. [42]

    Noise-induced barren plateaus in variational quantum algorithms,

    Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. Noise-induced barren plateaus in variational quantum algorithms. Nature Communications, 12 0 (1): 0 6961, 2021. doi:10.1038/s41467-021-27045-6

  43. [43]

    Generalization in quantum machine learning from few training data

    Matthias C Caro, Hsin-Yuan Huang, Marco Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, and Patrick J Coles. Generalization in quantum machine learning from few training data. Nature Communications, 13 0 (1): 0 4919, 2022. doi:10.1038/s41467-022-32550-3

  44. [44]

    Training quantum embedding kernels on near-term quantum computers

    Thomas Hubregtsen, David Wierichs, Elies Gil-Fuster, Peter-Jan H S Derks, Paul K Faehrmann, and Johannes Jakob Meyer. Training quantum embedding kernels on near-term quantum computers. Physical Review A, 106 0 (4): 0 042431, 2022. doi:10.1103/PhysRevA.106.042431

  45. [45]

    Towards quantum machine learning with tensor networks

    William Huggins, Piyush Patil, Bradley Mitchell, K Birgitta Whaley, and E Miles Stoudenmire. Towards quantum machine learning with tensor networks. Quantum Science and Technology, 4 0 (2): 0 024001, 2019. doi:10.1088/2058-9565/aaea94

  46. [46]

    Evidence for the utility of quantum computing before fault tolerance

    Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout van den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, et al. Evidence for the utility of quantum computing before fault tolerance. Nature, 618 0 (7965): 0 500--505, 2023. doi:10.1038/s41586-023-06096-3

  47. [47]

    Arute et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019), doi:10.1038/s41586-019-1666-5

    Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G S L Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 0 (7779): 0 505--510, 2019. doi:10.1038/s41586-019-1666-5

  48. [48]

    Filipa C. R. Peres and Ernesto F. Galv \ a o. Quantum circuit compilation and hybrid computation using Pauli -based computation. Quantum, 7: 0 1126, 2023. doi:10.22331/q-2023-10-03-1126

  49. [49]

    TensorFlow : A system for large-scale machine learning

    Mart \' n Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. TensorFlow : A system for large-scale machine learning. In OSDI, volume 16, pages 265--283, 2016

  50. [50]

    PyTorch : An imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. PyTorch : An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems, volume 32, 2019

  51. [51]

    JAX : Composable transformations of Python + NumPy programs

    James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang. JAX : Composable transformations of Python + NumPy programs. https://github.com/google/jax, 2018. Version 0.4.x

  52. [52]

    Estimating the gradient and higher-order derivatives on quantum hardware

    Andrea Mari, Thomas R Bromley, and Nathan Killoran. Estimating the gradient and higher-order derivatives on quantum hardware. Physical Review A, 103 0 (1): 0 012405, 2021. doi:10.1103/PhysRevA.103.012405

  53. [53]

    Methodology for replacing indirect measurements with direct measurements

    Kosuke Mitarai and Keisuke Fujii. Methodology for replacing indirect measurements with direct measurements. Physical Review Research, 1 0 (1): 0 013006, 2019. doi:10.1103/PhysRevResearch.1.013006

  54. [54]

    Supervised Learning with Quantum Computers

    Maria Schuld and Francesco Petruccione. Supervised Learning with Quantum Computers. Springer, 2018. doi:10.1007/978-3-319-96424-9

  55. [55]

    Robust data encodings for quantum classifiers

    Ryan LaRose and Brian Coyle. Robust data encodings for quantum classifiers. Physical Review A, 102 0 (3): 0 032420, 2020. doi:10.1103/PhysRevA.102.032420

  56. [56]

    Universal approximation property of quantum feature map

    Takahiro Goto, Quoc Hoan Tran, and Kohei Nakajima. Universal approximation property of quantum feature map. arXiv preprint arXiv:2009.00298, 2021. doi:10.48550/arXiv.2009.00298

  57. [57]

    Exponential concentration and untrainability in quantum kernel methods

    Supanut Thanasilp, Samson Wang, Marco Cerezo, and Zo \"e Holmes. Exponential concentration and untrainability in quantum kernel methods. arXiv preprint arXiv:2208.11060, 2022. doi:10.48550/arXiv.2208.11060

  58. [58]

    The power of quantum neural networks,

    Amira Abbas, David Sutter, Christa Zoufal, Aur \'e lien Lucchi, Alessio Figalli, and Stefan Woerner. The power of quantum neural networks. Nature Computational Science, 1 0 (6): 0 403--409, 2021. doi:10.1038/s43588-021-00084-1

  59. [59]

    Temme, S

    Kristan Temme, Sergey Bravyi, and Jay M Gambetta. Error mitigation for short-depth quantum circuits. Physical Review Letters, 119 0 (18): 0 180509, 2017. doi:10.1103/PhysRevLett.119.180509

  60. [60]

    Available: https://doi.org/10.1103/PhysRevX.8.031027

    Suguru Endo, Simon C Benjamin, and Ying Li. Practical quantum error mitigation for near-future applications. Physical Review X, 8 0 (3): 0 031027, 2018. doi:10.1103/PhysRevX.8.031027