These codes are accompanied to the following paper:
- Zongkang Zhang, Anbang Wang, Xiaosi Xu, Ying Li, Measurement-efficient quantum Krylov subspace diagonalisation, arXiv:2301.13353.
These codes are written in Mathematica and have been tested in Mathematica 13.
- In the folder measurement_overhead_benchmarking: chain&ladder.nb and random_graph.nb calculate the measurement overhead approaching the accuracy of classical Lanczos algorithm for different quantum Krylov subspace diagonalisation (KSD) algorithms. The corresponding results are collected in the subfolder data, which is used in empirical_distribution.nb to plot the empirical distribution of the measurement overhead. Taking the instance (Heisenberg, chain, d=5) as an example, example.nb gives a comparison between different quantum KSD algorithms. In the above scripts, packages Qubits_package.m and ExactKrylov_package.m are imported.
- In the folder necessary_measurement_number_etc: regularisation.nb shows that the sufficient measurement costs computed by the theorem are close to the necessary measurement costs when using the regularisation method. thresholding.nb compares the necessary measurement costs between different quantum KSD algorithms when using thresholding procedure. Energy_of_each_basis.nb illustrates the energy of each GP and P basis at different subspace dimension. M-epsilon.nb estimates the measurement number and the corresponding energy error at different subspace dimensions d for different bases. Gaussian-power.nb illustrates the Gaussian-power bases construct a filter, which effects the choice of tau. The above scripts import the package QLanczos_package.m and take the instance (Heisenberg, chain, d=5) as an example.
- ratio.nb computes the ratio between cost upper bound and norm upper bound of the Gaussian-power basis.
- The folder PDFs_of_Mathematica_notebooks contains the PDFs of the source code written in Mathematica notebooks.
This code is under the MIT license.