stabiliser-tools: Fast checks and conversions for stabiliser states, Cliffords and Paulis

Paper

PyPI project page

This is a Python wrapper for our C++ library of fast algorithms for converting between classical specifications of stabiliser states and Clifford gates.

stabiliser-tools supports the following specifications:

• Stabiliser states:
  • [S_V]: a complex vector of amplitudes;
  • [S_P]: a quadratic form, a linear map, and an affine subspace of $\mathbb{Z}_2^n$;
  • [S_Q]: a check matrix, i.e. a compact list of Pauli gate generators for the stabiliser group.
• Cliffords:
  • [C_U]: a unitary matrix;
  • [C_T]: a list of $2n$ Pauli gates representing the images of basic Pauli gates under conjugation, i.e. a tableau.

Installing stabiliser-tools

The PyPI page for this project is here.

pip install stabiliser-tools

After installing the package, its classes and functions can be accessed via

import stab_tools

Note that on Linux and other Unix-like operating systems, you may receive the following output upon importing:

WARNING: You may be about to receive an ImportError. (If you don't, you can safely ignore this message.) To resolve this, try running the following command in your terminal:

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:<path-to-python-environment>/lib/python3.10/site-packages/stab_tools

This is due to the way shared libraries are linked in Linux. In order to stop this error from occurring in every new terminal session, consider updating LD_LIBRARY_PATH in your .bashrc or .bashprofile file.

Functions and classes

After successfully importing stab_tools, run help(stab_tools) to view the list of functions and classes.

Available classes:

Clifford
Pauli
Check_Matrix
Stabiliser_State

Example code:

>>> import stab_tools
>>> import numpy as np
>>> v = np.array([0, 1, 0, 0, 0, 0, 1, 0]) / np.sqrt(2)
>>> stab_tools.is_stabiliser_state(v)
True
>>> s = stab_tools.stabiliser_state_from_statevector(v)
>>> paulis = stab_tools.Check_Matrix(s).get_paulis()
>>> paulis[0].get_matrix()
[[0j, 0j, 0j, 0j, 0j, 0j, 0j, (1-0j)], [0j, 0j, 0j, 0j, 0j, 0j, (1-0j), 0j], [0j, 0j, 0j, 0j, 0j, (1-0j), 0j, 0j], [0j, 0j, 0j, 0j, (1-0j), 0j, 0j, 0j], [0j, 0j, 0j, (1-0j), 0j, 0j, 0j, 0j], [0j, 0j, (1-0j), 0j, 0j, 0j, 0j, 0j], [0j, (1-0j), 0j, 0j, 0j, 0j, 0j, 0j], [(1-0j), 0j, 0j, 0j, 0j, 0j, 0j, 0j]]
>>> pauli_xs = [stab_tools.Pauli(3, 2**n, 0, 0, 0) for n in range(3)]
>>> pauli_xs[0].get_matrix()
[[0j, (1-0j), 0j, 0j, 0j, 0j, 0j, 0j], [(1-0j), 0j, 0j, 0j, 0j, 0j, 0j, 0j], [0j, 0j, 0j, (1-0j), 0j, 0j, 0j, 0j], [0j, 0j, (1-0j), 0j, 0j, 0j, 0j, 0j], [0j, 0j, 0j, 0j, 0j, (1-0j), 0j, 0j], [0j, 0j, 0j, 0j, (1-0j), 0j, 0j, 0j], [0j, 0j, 0j, 0j, 0j, 0j, 0j, (1-0j)], [0j, 0j, 0j, 0j, 0j, 0j, (1-0j), 0j]]
>>> H = np.array([[1, 1], [1, -1]]) / np.sqrt(2)
>>> H2 = np.kron(H, H)
>>> H2
array([[ 0.5,  0.5,  0.5,  0.5],
       [ 0.5, -0.5,  0.5, -0.5],
       [ 0.5,  0.5, -0.5, -0.5],
       [ 0.5, -0.5, -0.5,  0.5]])
>>> stab_tools.is_clifford_matrix(H2)
True

Compatibility

We have compiled and built the underlying C++ source code for a variety of different platforms and CPU architectures. Our testing has mostly been done on Windows, Ubuntu and Arch Linux. If your machine is incompatible with any of the Python wheels, the full source code can be found in the source distribution, as well as in this GitHub repo. You will need the libraries Catch2 and pybind11.

If you are unable to build the code yourself, or if you have any other questions, contact the developers at ming_yin_2[at]sfu.ca.