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

References

Citing our work

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

The 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:

Xiang Meng, mengxianglgal@gmail.com
Yulong Dong, dongyl@berkeley.edu

Installation

>> startup

>> cd Examples