Merge pull request #99 from CQCL/compilation_and_notebooks

Add barren plateaus notebook, `repeat_circuit` function

README.md

@@ -5,8 +5,8 @@
 
 * [Installation](#installation)
 * [Quick start](#quick-start)
-  + [Pure state simulation](#pure-state-simulations)
-  + [Mixed state simulation](#mixed-state-simulations)
+  + [Pure state simulation](#pure-state-simulation)
+  + [Mixed state simulation](#mixed-state-simulation)
 * [Converting from TKET](#converting-from-tket)
 * [Examples](#examples)
 * [Contributing](#contributing)
@@ -131,13 +131,15 @@ An example of this can be found in the [`pytket-qujax_heisenberg_vqe.ipynb`](htt
 
 Below are some use-case notebooks. These both illustrate the flexibility of qujax and the power of directly interfacing with JAX and its package ecosystem.
 
-- [`heisenberg_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/heisenberg_vqe.ipynb) - an implementation of the variational quantum eigensolver to find the ground state of a quantum Hamiltonian.
-- [`maxcut_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/maxcut_vqe.ipynb) - an implementation of the variational quantum eigensolver to solve a MaxCut problem. Trains with Adam via [`optax`](https://github.com/deepmind/optax) and uses more realistic stochastic parameter shift gradients.
-- [`noise_channel.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/noise_channel.ipynb) - uses the densitytensor simulator to fit the parameters of a depolarising noise channel.
-- [`qaoa.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/qaoa.ipynb) - uses a problem-inspired QAOA ansatz to find the ground state of a quantum Hamiltonian. Demonstrates how to encode more sophisticated parameters that control multiple gates.
-- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions.
-- [`classification.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/classification.ipynb) - train a quantum circuit for binary classification using data re-uploading.
-- [`generative_modelling.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/generative_modelling.ipynb) - uses a parameterised quantum circuit as a generative model for a real life dataset. Trains via stochastic gradient Langevin dynamics on the maximum mean discrepancy between statetensor and dataset.
+- [`heisenberg_vqe.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/heisenberg_vqe.ipynb) - an implementation of the variational quantum eigensolver to find the ground state of a quantum Hamiltonian.
+- [`maxcut_vqe.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/maxcut_vqe.ipynb) - an implementation of the variational quantum eigensolver to solve a MaxCut problem. Trains with Adam via [`optax`](https://github.com/deepmind/optax) and uses more realistic stochastic parameter shift gradients.
+- [`noise_channel.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/noise_channel.ipynb) - uses the densitytensor simulator to fit the parameters of a depolarising noise channel.
+- [`qaoa.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/qaoa.ipynb) - uses a problem-inspired QAOA ansatz to find the ground state of a quantum Hamiltonian. Demonstrates how to encode more sophisticated parameters that control multiple gates.
+- [`barren_plateaus.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/barren_plateaus.ipynb) - illustrates how to sample gradients of a cost function to identify the presence of barren plateaus. Uses batched/vectorized evaluation to speed up computation.
+- [`reducing_jit_compilation_time.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/reducing_jit_compilation_time.ipynb) - explains how JAX compilation works and how that can lead to excessive compilation times when executing quantum circuits. Presents a solution for the case of circuits with a repeating structure.
+- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions.
+- [`classification.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/classification.ipynb) - train a quantum circuit for binary classification using data re-uploading.
+- [`generative_modelling.ipynb`](https://github.com/CQCL/qujax/blob/develop/examples/generative_modelling.ipynb) - uses a parameterised quantum circuit as a generative model for a real life dataset. Trains via stochastic gradient Langevin dynamics on the maximum mean discrepancy between statetensor and dataset.
 
 The [`pytket`](https://github.com/CQCL/pytket) repository also contains `tk_to_qujax` implementations for some of the above at [`pytket-qujax_classification.ipynb`](https://github.com/CQCL/pytket/blob/main/examples/pytket-qujax-classification.ipynb), 
 [`pytket-qujax_heisenberg_vqe.ipynb`](https://github.com/CQCL/pytket/blob/main/examples/pytket-qujax_heisenberg_vqe.ipynb)