QSP phase factors solvers

A toolbox for solving phase factors in quantum signal processing.

Problems and solvers

Given a real polynomial of degree with definite parity such that , the package contains codes for solving phase factors such that

$U_\Phi(x) = e^{\mathrm{i} \phi_0 \sigma_z} \prod_{j=1}^{d} \left[ e^{\mathrm{i} \arccos(x) \sigma_x} e^{\mathrm{i} \phi_j \sigma_z} \right] = \left( \begin{array}{cc} P(x) & \mathrm{i} Q(x) \sqrt{1 - x^2}\\ \mathrm{i} Q^*(x) \sqrt{1 - x^2} & P^*(x) \end{array} \right),$

where .

The package contains two kinds of solvers:

Optimization-based solver
Direct solver (namely the GSLW method and the Haah method)

The package also contains an implementation of the Remez algorithm for finding polynomial approximation.

Applications have been solved by these solvers:

Hamiltonian simulation
Eigenstate filter
Matrix inversion

Citing our work

If you find our work useful or you use our work in your own project, please consider to cite our work.

Y. Dong, X. Meng, K. B. Whaley, and L. Lin. Efficient Phase Factor Evaluation in Quantum Signal Processing, Phys. Rev. A 103, 042419, 2021

Other references:

Authors

We hope that the package is useful for your application. If you have any bug reports or comments, please feel free to email one of the software authors:

Installation

You can download qsppack and run

>> startup

This adds the folder of the solver to MATLAB's path variable.

Alternatively you can install qsppack to your current directory by pasting the code below to your MATLAB command window:

unzip('https://github.com/qsppack/qsppack/archive/master.zip')
movefile('QSPPACK-master', 'qsppack')
addpath(fullfile(cd,'qsppack','Solvers','Optimization')), savepath

Then you can test qsppack by running

>> cd Examples

>> test_HS

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A toolbox for solving phase factors in Quantum signal processing.

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