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Research

Explore cutting-edge research using PennyLane. The demonstrations below implement ideas from inspiring papers that investigate the training of quantum circuits. You can find research that targets quantum machine learning in the Quantum machine learning section, or discover other variational quantum optimization algorithms under Optimization.

Quantum machine learning

Delve into the plethora of exciting research made by the scientific community in quantum machine learning. Implement and run a vast array of different QML applications on your own computer—using simulators from Xanadu, IBM, Google, Rigetti, and many more—or on real hardware devices.

.. customgalleryitem::
    :tooltip: Create a simple QGAN with Cirq and TensorFlow.
    :figure: demonstrations/QGAN/qgan3.png
    :description: :doc:`demos/tutorial_QGAN`
    :tags: cirq tensorflow

.. customgalleryitem::
    :tooltip: Fit one-dimensional noisy data with a quantum neural network.
    :figure: demonstrations/quantum_neural_net/qnn_output_28_0.png
    :description: :doc:`demos/quantum_neural_net`
    :tags: autograd strawberryfields photonics

.. customgalleryitem::
    :tooltip: Universal Quantum Classifier with data-reuploading.
    :figure: demonstrations/data_reuploading/universal_dnn.png
    :description: :doc:`demos/tutorial_data_reuploading_classifier`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Quantum transfer learning.
    :figure: demonstrations/quantum_transfer_learning/transfer_images.png
    :description: :doc:`demos/tutorial_quantum_transfer_learning`
    :tags: autograd pytorch

.. customgalleryitem::
    :tooltip: Training an embedding to perform metric learning.
    :figure: demonstrations/embedding_metric_learning/training.png
    :description: :doc:`demos/tutorial_embeddings_metric_learning`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Pre-process images with a quantum convolution.
    :figure: demonstrations/quanvolution/zoom.png
    :description: :doc:`demos/tutorial_quanvolution`
    :tags: tensorflow

.. customgalleryitem::
    :tooltip: Variational Quantum Linear Solver.
    :figure: demonstrations/vqls/vqls_zoom.png
    :description: :doc:`demos/tutorial_vqls`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Coherent implementation of a variational quantum linear solver.
    :figure: demonstrations/coherent_vqls/cvqls_zoom.png
    :description: :doc:`demos/tutorial_coherent_vqls`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Implement a multiclass variational classifier using PyTorch, PennyLane, and the iris dataset.
    :figure: demonstrations/multiclass_classification/margin_2.png
    :description: :doc:`demos/tutorial_multiclass_classification`
    :tags: pytorch

.. customgalleryitem::
    :tooltip: Differentiate any qubit gate with the stochastic parameter-shift rule.
    :figure: demonstrations/stochastic_parameter_shift/stochastic_parameter_shift_thumbnail.png
    :description: :doc:`demos/tutorial_stochastic_parameter_shift`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Using a quantum graph recurrent neural network to learn quantum dynamics.
    :figure: demonstrations/qgrnn/qgrnn_thumbnail.png
    :description: :doc:`demos/qgrnn`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Optimize a Quantum Optical Neural Network using NLopt.
    :figure: demonstrations/qonn/qonn_thumbnail.png
    :description: :doc:`demos/qonn`
    :tags: autograd photonics

.. customgalleryitem::
    :tooltip: Understand the link between variational quantum models and Fourier series.
    :figure: demonstrations/expressivity_fourier_series/expressivity_thumbnail.png
    :description: :doc:`demos/tutorial_expressivity_fourier_series`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Making a quantum machine learning model using neutral atoms
    :figure: demonstrations/pasqal/pasqal_thumbnail.png
    :description: :doc:`demos/tutorial_pasqal`
    :tags: cirq tensorflow

.. customgalleryitem::
    :tooltip: Meta-learning technique for variational quantum algorithms.
    :figure: demonstrations/learning2learn/l2l_thumbnail.png
    :description: :doc:`demos/tutorial_learning2learn`
    :tags: tensorflow

Optimization

Here you will find demonstrations showcasing quantum optimization. Explore various topics and ideas, such as the shots-frugal Rosalin optimizer, the variational quantum thermalizer, or the issue of barren plateaus in quantum neural networks.

.. customgalleryitem::
    :tooltip: Faster optimization convergence using quantum natural gradient.
    :figure: demonstrations/quantum_natural_gradient/qng_optimization.png
    :description: :doc:`demos/tutorial_quantum_natural_gradient`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Barren plateaus in quantum neural networks.
    :figure: demonstrations/barren_plateaus/surface.png
    :description: :doc:`demos/tutorial_barren_plateaus`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Rotoselect algorithm.
    :figure: demonstrations/rotoselect/rotoselect_structure.png
    :description: :doc:`demos/tutorial_rotoselect`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Doubly stochastic gradient descent.
    :figure: demonstrations/doubly_stochastic/single_shot.png
    :description: :doc:`Doubly stochastic gradient descent <demos/tutorial_doubly_stochastic>`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Frugal shot optimization with the Rosalin optimizer.
    :figure: demonstrations/rosalin/rosalin_thumb.png
    :description: :doc:`demos/tutorial_rosalin`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Understand the difference between local and global cost functions.
    :figure: demonstrations/local_cost_functions/Local_Thumbnail.png
    :description: :doc:`demos/tutorial_local_cost_functions`
    :tags: autograd

.. customgalleryitem::
    :tooltip: Optimizing measurement protocols with variational methods.
    :figure: demonstrations/quantum_metrology/illustration.png
    :description: :doc:`demos/tutorial_quantum_metrology`
    :tags: cirq metrology autograd

.. customgalleryitem::
    :tooltip: Learn about the variational quantum thermalizer algorithm, an extension of VQE.
    :figure: demonstrations/vqt/thumbnail.png
    :description: :doc:`demos/tutorial_vqt`
    :tags: chemistry

.. customgalleryitem::
    :tooltip: VQE optimization using quantum natural gradient.
    :figure: demonstrations/vqe_qng/vqe_qng_thumbnail.png
    :description: :doc:`demos/tutorial_vqe_qng`
    :tags: chemistry

.. customgalleryitem::
    :tooltip: Optimize and reduce the number of measurements required to evaluate a variational algorithm cost function.
    :figure: demonstrations/measurement_optimize/meas_optimize_thumbnail.png
    :description: :doc:`demos/tutorial_measurement_optimize`
    :tags: chemistry

Quantum computing

Explore the applications of PennyLane to more general quantum computing tasks such as benchmarking and characterizing quantum processors.

.. customgalleryitem::
    :tooltip: Beyond classical computing with qsim.
    :figure: demonstrations/qsim_beyond_classical/sycamore.png
    :description: :doc:`demos/qsim_beyond_classical`
    :tags: cirq qsim

.. customgalleryitem::
   :tooltip: Construct and simulate a Gaussian Boson Sampler.
   :figure: demonstrations/tutorial_gbs_thumbnail.png
   :description: :doc:`demos/tutorial_gbs`
   :tags: photonics strawberryfields

.. customgalleryitem::
   :tooltip: Learn how to compute the quantum volume of a quantum processor.
   :figure: demonstrations/quantum_volume/quantum_volume_thumbnail.png
   :description: :doc:`demos/quantum_volume`
   :tags: characterization qiskit

.. toctree::
    :maxdepth: 2
    :hidden:

    demos/tutorial_quantum_natural_gradient
    demos/tutorial_barren_plateaus
    demos/tutorial_rotoselect
    demos/tutorial_doubly_stochastic
    demos/tutorial_rosalin
    demos/tutorial_local_cost_functions
    demos/tutorial_vqls
    demos/tutorial_coherent_vqls
    demos/tutorial_quantum_metrology
    demos/tutorial_vqt
    demos/tutorial_vqe_qng
    demos/tutorial_measurement_optimize
    demos/tutorial_QGAN
    demos/quantum_neural_net
    demos/tutorial_data_reuploading_classifier
    demos/tutorial_quantum_transfer_learning
    demos/tutorial_embeddings_metric_learning
    demos/tutorial_quanvolution
    demos/tutorial_multiclass_classification
    demos/tutorial_stochastic_parameter_shift
    demos/tutorial_pasqal
    demos/qgrnn
    demos/qonn
    demos/tutorial_expressivity_fourier_series
    demos/qsim_beyond_classical
    demos/quantum_volume
    demos/tutorial_gbs
    demos/tutorial_learning2learn