General parameter-shift rules for quantum gradients

This repository contains the code used to produce the data and figures in our paper on general parameter-shift rules for quantum gradients.

• QAOA_circuit_evaluations.ipynb computes bounds for the number of required circuit evaluations in MaxCut-QAOA applications as discussed in Section 5.1, and correspondingly produces Figure 3.
• plot_QAD_landscapes.ipynb computes the variants of the model cost landscape used in Quantum Analytic Descent as discussed in Section 5.3. It outputs Figure 4.

Please note that the circuit evaluation estimation in its current implementation is rather slow, because multiple semi-definite programs (SDPs) are solved for the various bounds we discuss. It is very well possible that this code can be optimized to run faster, but in the meantime, we store the precomputed data in data/QAOA_circuit_evaluations_20.json and let the plotting notebook simply access that data. Recomputing it takes about 5 hours on a proper desktop computer. Reducing the largest considered system size (max_num_vertices) significantly reduces the runtime.

All functionalities and helper functions are stored in lib.py.

Citing this work

If you use this code, please consider citing the paper if applicable:

@misc{wierichs2021general,
      title={General parameter-shift rules for quantum gradients}, 
      author={David Wierichs and Josh Izaac and Cody Wang and Cedric Yen-Yu Lin},
      year={2021},
      eprint={2107.12390},
      archivePrefix={arXiv},
      primaryClass={quant-ph}
}