Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1811.04968

PennyLane: Automatic differentiation of hybrid quantum-classical computations

Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Ajith, Vishnu, M. Sohaib Alam, Alonso-Linaje, Guillermo, AkashNarayanan, B., Asadi, Ali, Juan Miguel Arrazola, Azad, Utkarsh, Banning, Sam, Carsten Blank, Bromley, Thomas R, Benjamin A. Cordier, Ceroni, Jack, Alain Delgado, Di Matteo, Olivia, Dusko, Amintor, Garg, Tanya, Guala, Diego, Hayes, Anthony, Hill, Ryan, Ijaz, Aroosa, Isacsson, Theodor, Ittah, David, Soran Jahangiri, Jain, Prateek, Jiang, Edward, Khandelwal, Ankit, Korbinian Kottmann, Lang, Robert A., Lee, Christina, Loke, Thomas, Lowe, Angus, Keri A. McKiernan, Johannes Jakob Meyer, Montañez-Barrera, J. A., Moyard, Romain, Zeyue Niu, O'Riordan, Lee James, Oud, Steven, Panigrahi, Ashish, Park, Chae-Yeun, Polatajko, Daniel, Quesada, Nicolás, Roberts, Chase, Sá, Nahum, Schoch, Isidor, Shi, Borun, Shu, Shuli, Sim, Sukin, Singh, Arshpreet, Strandberg, Ingrid, Soni, Jay, Antal Száva, Thabet, Slimane, Rodrigo A. Vargas–Hernández, Vincent, Trevor, Vitucci, Nicola, Maurice Weber, Wierichs, David, Wiersema, Roeland, Moritz Willmann, Wong, Vincent, Zhang, Shaoming, Nathan Killoran

Published Nov 12, 2018• 732 citations
arXivHTMLPDF

Abstract

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

DOI
10.48550/arxiv.1811.04968

Related papers

Hybrid Quantum-Classical Machine Learning with PennyLane: A Comprehensive Guide for Computational Research

Sidney Shapiro

Hybrid quantum-classical machine learning represents a frontier in computational research, combining the potential advantages of quantum computing with established classical optimization techniques. PennyLane provides a Python framework that seamlessly bridges quantum circuits and classical machine learning, enabling researchers to build, optimize, and deploy variational quantum algorithms. This paper introduces PennyLane as a versatile tool for quantum machine learning, optimization, and quantum chemistry applications. We demonstrate use cases including quantum kernel methods, variational quantum eigensolvers, portfolio optimization, and integration with classical ML frameworks such as PyTorch, TensorFlow, and JAX. Through concrete Python examples with widely used libraries such as scikit-learn, pandas, and matplotlib, we show how PennyLane facilitates efficient quantum circuit construction, automatic differentiation, and hybrid optimization workflows. By situating PennyLane within the broader context of quantum computing and machine learning, we highlight its role as a methodological building block for quantum-enhanced data science. Our goal is to provide researchers and practitioners with a concise reference that bridges foundational quantum computing concepts and applied machine learning practice, making PennyLane a default citation for hybrid quantum-classical workflows in Python-based research.

arXiv:2511.14786•Nov 13, 2025•0 citations

Exploring quantum machine learning frameworks

Balajee Maram

Among notable applications, quantum machine learning (QML) is a promising task that combines quantum computing with machine learning, cited for various types of complex computational problems. This chapter briefly summarizes the frameworks, software platforms, and toolchains currently available for implementing, simulating, and executing hybrid quantum–classical learning algorithms. Major frameworks (e.g., Qiskit Machine Learning, PennyLane, TensorFlow Quantum, and the PyTorch-based toolsets) are analyzed in detail based on their architectural design, functionality, and integration capabilities. They have several key features, such as variational quantum circuits, parameterized quantum gates, automatic differentiation capabilities, and easy integration into a classical deep learning ecosystem. The chapter groups together ongoing research in different architectural paradigms, practical usability aspects, and empirical performance tests. Additionally, it explores aspects of scalability, adaptability to hardware, noise resistance, and reproducibility. The results bring to light elements of the design of trade-offs for creating robust and efficient toolchains for QML, a QML best practice, and guidance for future QML design.

CRC Press eBooks•Oct 21, 2026•0 citations

Hybridlane: A Software Development Kit for Hybrid Continuous-Discrete Variable Quantum Computing

Jim Furches, Timothy J. Stavenger, Carlos Ortiz Marrero

Hybrid quantum computing systems that combine discrete-variable qubits with continuous-variable qumodes offer promising advantages for quantum simulation, error correction, and sensing applications. However, existing quantum software frameworks lack native support for expressing and manipulating hybrid circuits, forcing developers to work with fragmented toolchains or rely on simulation-coupled representations that limit scalability. We present Hybridlane, an open-source software development kit providing a unified frontend for hybrid continuous-discrete variable quantum computing. Hybridlane introduces automatic wire type inference to distinguish qubits from qumodes without manual annotations, enabling compile-time validation of circuit correctness. By decoupling gate semantics from matrix representations, Hybridlane can describe wide and deep circuits with minimal memory consumption and without requiring simulation. The framework implements a comprehensive library of hybrid gates and decompositions following established instruction set architectures, while remaining compatible with PennyLane's extensive qubit algorithm library. Furthermore, it supports multiple backends including classical simulation with Bosonic Qiskit and hardware compilation to Sandia National Laboratories' QSCOUT ion trap. We demonstrate Hybridlane's capabilities through bosonic quantum phase estimation and ion trap calibration workflows.

quant-pharXiv:2603.10919•Mar 12, 2026•0 citations

Differentiable quantum computational chemistry with PennyLane

Juan Miguel Arrazola, Soran Jahangiri, Alain Delgado +15 more

This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.

arXiv:2111.09967•Nov 18, 2021•9 citations

Investigating Quantum Machine Learning Frameworks and Simulating Quantum Approaches

Muhammad Jawad Khan, Sumeera Bibi, Muzammil Ahmad Khan +4 more

Quantum machine learning (QML) has emerged as a promising field, combining the power of quantum computing with classical machine learning techniques to solve complex computational tasks. As the demand for efficient quantum simulations grows, multiple QML frameworks, including PennyLane, Qiskit, and TensorFlow Quantum (TFQ), have been developed to facilitate hybrid quantum-classical computations. This study aims to evaluate and compare the performance of three leading QML frameworks PennyLane, Qiskit, and TensorFlow Quantum in simulating quantum machine learning models, focusing on accuracy, execution time, and noise tolerance. The study examined three leading quantum machine learning (QML) frameworks PennyLane (v0.24), Qiskit (v0.43.2), and TensorFlow Quantum (TFQ, v0.7) each tested on a 64-bit Ubuntu Linux system with an Intel Core i7 processor, 32 GB RAM, and NVIDIA GeForce RTX 3080 GPU. Quantum algorithms like variational quantum circuits (VQCs) and quantum support vector machines (QSVMs) were simulated using these frameworks. Various quantum gates, including Pauli-X, Y, Z, Hadamard, CNOT, and Rotation gates (Rx, Ry, Rz), were used for parameter optimization and quantum superposition. The Iris and MNIST datasets were adapted for quantum encoding using Amplitude and Angle Encoding for binary classification tasks. Simulations were run on classical computers, while select circuits were executed on IBM Quantum’s Falcon r5.11 processor to compare hardware performance. PennyLane achieved the highest accuracy (92%) in quantum simulations, excelling in hybrid quantum-classical model integration. TensorFlow Quantum provided the fastest execution time, especially in classical simulations, making it suitable for rapid prototyping. Qiskit produced deeper quantum circuits but had higher error rates (6%) on real quantum hardware, highlighting noise and decoherence effects. The VQC models optimized by stochastic gradient descent (SGD) showed significant improvements in model performance, and QSVMs effectively classified both linearly separable and non-separable datasets, demonstrating the potential of quantum algorithms over classical approaches. Statistical analysis confirmed the significance of the results (p < 0.05). PennyLane is the most robust framework for hybrid quantum-classical models, while TensorFlow Quantum is suited for rapid prototyping. Qiskit, despite longer execution times, excels in hardware implementation. The choice of framework should align with the specific needs of quantum machine learning tasks.

The Asian Bulletin of Big Data Management•Oct 21, 2024•2 citations

PennyLane–Qiskit Plugin: A Protocol for Integrating Noisy, Fake, and Real Quantum Backends

Matthieu Hubert, Quang Le, Emmanuel E. Haven

Quantum computing frameworks like PennyLane, Qiskit, and others offer powerful tools for developing quantum algorithms. However, integrating their devices can be challenging for newcomers, especially given the frequent updates in frameworks like Qiskit, which can create significant barriers to learning and thus slow down the growth of quantum computing and quantum machine learning. The PennyLane–Qiskit plugin is a particularly interesting framework that allows researchers and practitioners interested in quantum computing and quantum machine learning to implement and simulate realistic models in a simple and efficient way. This work provides a practical method to use the PennyLane–Qiskit plugin, focusing on three main device types: the Aer simulator with noise models, IBM fake backends (with FakeManilaV2 as a representative example), and real IBM Quantum hardware accessed remotely (with ibm_torino used in this study). We demonstrate how to set up and use each of these devices within PennyLane using a simple example of a quantum machine learning regression task on simulated stock price data. Our goal is to simplify the process for all interested users, especially (but not only) beginners by clearly explaining and demonstrating how to use each of these device options while highlighting best practices for effectively leveraging PennyLane and Qiskit together via Pennylane–Qiskit plugin. This work aims to provide a turnkey solution enabling users with only minimal foundational knowledge to quickly start running meaningful simulations. The three devices implementation will be explained with the code here. The accompanying full code will be provided to ensure that all results can be easily reproduced, including with users’ own datasets.

EAI Endorsed Transactions on Tourism Technology and Intelligence•Jun 11, 2026•0 citations
PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.
Hybrid quantum-classical machine learning represents a frontier in computational research, combining the potential advantages of quantum computing with established classical optimization techniques. PennyLane provides a Python framework that seamlessly bridges quantum circuits and classical machine learning, enabling researchers to build, optimize, and deploy variational quantum algorithms. This paper introduces PennyLane as a versatile tool for quantum machine learning, optimization, and quantum chemistry applications. We demonstrate use cases including quantum kernel methods, variational quantum eigensolvers, portfolio optimization, and integration with classical ML frameworks such as PyTorch, TensorFlow, and JAX. Through concrete Python examples with widely used libraries such as scikit-learn, pandas, and matplotlib, we show how PennyLane facilitates efficient quantum circuit construction, automatic differentiation, and hybrid optimization workflows. By situating PennyLane within the broader context of quantum computing and machine learning, we highlight its role as a methodological building block for quantum-enhanced data science. Our goal is to provide researchers and practitioners with a concise reference that bridges foundational quantum computing concepts and applied machine learning practice, making PennyLane a default citation for hybrid quantum-classical workflows in Python-based research.
Among notable applications, quantum machine learning (QML) is a promising task that combines quantum computing with machine learning, cited for various types of complex computational problems. This chapter briefly summarizes the frameworks, software platforms, and toolchains currently available for implementing, simulating, and executing hybrid quantum–classical learning algorithms. Major frameworks (e.g., Qiskit Machine Learning, PennyLane, TensorFlow Quantum, and the PyTorch-based toolsets) are analyzed in detail based on their architectural design, functionality, and integration capabilities. They have several key features, such as variational quantum circuits, parameterized quantum gates, automatic differentiation capabilities, and easy integration into a classical deep learning ecosystem. The chapter groups together ongoing research in different architectural paradigms, practical usability aspects, and empirical performance tests. Additionally, it explores aspects of scalability, adaptability to hardware, noise resistance, and reproducibility. The results bring to light elements of the design of trade-offs for creating robust and efficient toolchains for QML, a QML best practice, and guidance for future QML design.
Hybrid quantum computing systems that combine discrete-variable qubits with continuous-variable qumodes offer promising advantages for quantum simulation, error correction, and sensing applications. However, existing quantum software frameworks lack native support for expressing and manipulating hybrid circuits, forcing developers to work with fragmented toolchains or rely on simulation-coupled representations that limit scalability. We present Hybridlane, an open-source software development kit providing a unified frontend for hybrid continuous-discrete variable quantum computing. Hybridlane introduces automatic wire type inference to distinguish qubits from qumodes without manual annotations, enabling compile-time validation of circuit correctness. By decoupling gate semantics from matrix representations, Hybridlane can describe wide and deep circuits with minimal memory consumption and without requiring simulation. The framework implements a comprehensive library of hybrid gates and decompositions following established instruction set architectures, while remaining compatible with PennyLane's extensive qubit algorithm library. Furthermore, it supports multiple backends including classical simulation with Bosonic Qiskit and hardware compilation to Sandia National Laboratories' QSCOUT ion trap. We demonstrate Hybridlane's capabilities through bosonic quantum phase estimation and ion trap calibration workflows.
This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.
Quantum machine learning (QML) has emerged as a promising field, combining the power of quantum computing with classical machine learning techniques to solve complex computational tasks. As the demand for efficient quantum simulations grows, multiple QML frameworks, including PennyLane, Qiskit, and TensorFlow Quantum (TFQ), have been developed to facilitate hybrid quantum-classical computations. This study aims to evaluate and compare the performance of three leading QML frameworks PennyLane, Qiskit, and TensorFlow Quantum in simulating quantum machine learning models, focusing on accuracy, execution time, and noise tolerance. The study examined three leading quantum machine learning (QML) frameworks PennyLane (v0.24), Qiskit (v0.43.2), and TensorFlow Quantum (TFQ, v0.7) each tested on a 64-bit Ubuntu Linux system with an Intel Core i7 processor, 32 GB RAM, and NVIDIA GeForce RTX 3080 GPU. Quantum algorithms like variational quantum circuits (VQCs) and quantum support vector machines (QSVMs) were simulated using these frameworks. Various quantum gates, including Pauli-X, Y, Z, Hadamard, CNOT, and Rotation gates (Rx, Ry, Rz), were used for parameter optimization and quantum superposition. The Iris and MNIST datasets were adapted for quantum encoding using Amplitude and Angle Encoding for binary classification tasks. Simulations were run on classical computers, while select circuits were executed on IBM Quantum’s Falcon r5.11 processor to compare hardware performance. PennyLane achieved the highest accuracy (92%) in quantum simulations, excelling in hybrid quantum-classical model integration. TensorFlow Quantum provided the fastest execution time, especially in classical simulations, making it suitable for rapid prototyping. Qiskit produced deeper quantum circuits but had higher error rates (6%) on real quantum hardware, highlighting noise and decoherence effects. The VQC models optimized by stochastic gradient descent (SGD) showed significant improvements in model performance, and QSVMs effectively classified both linearly separable and non-separable datasets, demonstrating the potential of quantum algorithms over classical approaches. Statistical analysis confirmed the significance of the results (p < 0.05). PennyLane is the most robust framework for hybrid quantum-classical models, while TensorFlow Quantum is suited for rapid prototyping. Qiskit, despite longer execution times, excels in hardware implementation. The choice of framework should align with the specific needs of quantum machine learning tasks.
Quantum computing frameworks like PennyLane, Qiskit, and others offer powerful tools for developing quantum algorithms. However, integrating their devices can be challenging for newcomers, especially given the frequent updates in frameworks like Qiskit, which can create significant barriers to learning and thus slow down the growth of quantum computing and quantum machine learning. The PennyLane–Qiskit plugin is a particularly interesting framework that allows researchers and practitioners interested in quantum computing and quantum machine learning to implement and simulate realistic models in a simple and efficient way. This work provides a practical method to use the PennyLane–Qiskit plugin, focusing on three main device types: the Aer simulator with noise models, IBM fake backends (with FakeManilaV2 as a representative example), and real IBM Quantum hardware accessed remotely (with ibm_torino used in this study). We demonstrate how to set up and use each of these devices within PennyLane using a simple example of a quantum machine learning regression task on simulated stock price data. Our goal is to simplify the process for all interested users, especially (but not only) beginners by clearly explaining and demonstrating how to use each of these device options while highlighting best practices for effectively leveraging PennyLane and Qiskit together via Pennylane–Qiskit plugin. This work aims to provide a turnkey solution enabling users with only minimal foundational knowledge to quickly start running meaningful simulations. The three devices implementation will be explained with the code here. The accompanying full code will be provided to ensure that all results can be easily reproduced, including with users’ own datasets.