Sequential Quantum Gate Decomposer  v1.5 Powerful decomposition of general unitarias into one- and two-qubit gates gates
Introduction to SQUANDER v1.5

Sequential Quantum Gate Decomposer (SQUANDER) v1.5 is an open source software distributed under the GNU General Public License. The project was supported by OTKA PD123927 grant and by the Ministry of Innovation and Technology and the National Research, Development and Innovation Office within the Quantum Information National Laboratory of Hungary.

The SQUANDER package provides a novel solution to decompose any n-qubit unitary into a sequence of one-qubit rotations and two-qubit controlled gates (such as controlled NOT or controlled phase gate). SQUANDER utilizes a new gate synthesis technique that applies periodic layers of two-qubit and parametric one-qubit gates to an n-qubit unitary such that the resulting unitary is 1-qubit decoupled, i.e., is a tensor product of an (n-1)-qubit and a 1-qubit unitary. Continuing the decoupling procedure sequentially one arrives at the end to a full decomposition of the original unitary into 1- and 2-qubit gates. SQUANDER provides lower CNOT counts for generic n-qubit unitaries (up to n=6) than the previously provided lower bounds.

The SQUANDER library is written in C/C++ providing a Python interface via C++ extensions. The present package is supplied with Python building script and CMake tools to ease its deployment. The SQUANDER package can be built with both Intel and GNU compilers, and can be link against various CBLAS libraries installed on the system. (So far the CLBAS libraries of the GNU Scientific Library, OpenBLAS and the Intel MKL packages were tested.) In the following we briefly summarize the steps to build, install and use the SQUANDER package.

# Dependencies

The optimization algorithm of SQUANDER relies on the multimin component of the GNU Scientific Library. We developed and tested the SQUANDER package with GNU Scientific Library of version 2.5 and 2.6. The dependencies necessary to compile and build the SQUANDER package are the followings:

The Python interface of SQUANDER was developed and tested with Python 3.6 and 3.7. The SQUANDER Python interface needs the following packages to be installed on the system:

# How to build GNU Scientific Library

If the GNU Scientific Library is not installed on the system, it can be easily easily downloaded and deployed from source by the end user even without administrative privileges. The GNU Scientific Library can be downloaded from the site https://www.gnu.org/software/gsl/. After the downloaded package is extracted somewhere in the home directory of the user (path/to/gsl/source), one should configure the compiling environment using the configure tool. Depending on the individual settings the default compiler to be invoked might be different from HPC to HPC. To ensure the usage of the GNU compiler, the following shell command should be executed inside the directory path/to/gsl/source:

$./configure –prefix=path/to/gsl FC=gfortran CC=gcc CXX=g++ (Similarly, Intel compiler can be forced by setting FC=ifort CC=icc and CXX=icpc.) The installation directory of the compiled GNU Scientific Library is given by –prefix=path/to/gsl (which is different from the directory path of the source files given by path/to/gslsource). To install GNU Scientific Library the user should have read and write permissions on the path path/to/gsl (which might be for example /home/username/gsl). After the successful configuration the GNU Scientific Library can be compiled by the shell command$ make

The compilation of the GNU Scientific Library takes some time. When the compilation is done, the package (including the C header files and the static and shared libraries) is installed into the directory path/to/gsl by the shell command:

$make install # Download the SQUANDER package The developer version of the SQUANDER package can be downloaded from github repository https://github.com/rakytap/quantum-gate-decomposer/tree/master. After the package is downloaded into the directory path/to/QGD/package (which would be the path to the source code of the SQUANDER package), one can proceed to the compilation steps described in the next section. # How to build the SQUANDER package The SQUANDER package is equipped with a Python build script and CMake tools to ease the compilation and the deployment of the package. To ensure that SQUANDER package would find the necessary libraries and header files during compilation time it is advised to define the following environment variables:$ export GSL_LIB_DIR=path/to/gsl/lib(64) && export GSL_INC_DIR=path/to/gsl/include

The SQUANDER package is parallelized via Threading Building Block (TBB) libraries. If TBB is not present in the system, it can be easily installed via python package tbb-devel. Alternatively the TBB libraries can be installed via apt or yum utility (sudo apt install libtbb-dev) or it can be downloaded from https://github.com/oneapi-src/oneTBB and built from source. In this case one should supply the necessary environment variables pointing to the header and library files of the TBB package. For newer Intel compilers the TBB package is part of the Intel compiler package, similarly to the MKL package. If the TBB library is located at non-standrad path or the SQUANDER package is compiled with GNU compiler, then setting the following environment variables:

The command above starts the compilation of the C++ library and builds the necessary C++ Python extensions for the Python interface of the $QGD package in place. ### Binary distribution After the environment variables are set it is possible to build wheel binaries of the$QGD package. In order to launch the compilation process from python, scikit-build package is necessary. (It is optional to install the ninja package which speeds up the building process by parallel compilation.) The binary wheel can be constructed by command

$python3 setup.py bdist_wheel in the root directory of the$QGD package. The created $QGD wheel can be installed on the local machine by issuing the command from the directory path/to/SQUANDER/package/dist$ pip3 install qgd-*.whl

We notice, that the created wheel is not portable, since it contains hard coded link to external libraries (TBB and CBLAS).

### Source distribution

A portable source distribution of the SQUANDER package can be created by a command launched from the root directory of the SQUANDER package:

$python3 setup.py sdist In order to create a source distribution it is not necessary to set the environment variables, since this script only collects the necessary files and pack them into a tar ball located in the directory path/to/SQUANDER/package/dist. In order to install the$QGD package from source tar ball, see the previous section discussing the initialization of the environment variables. The package can be compiled and installed by the command