A JKQ library for the representation of quantum functionality by the Institute for Integrated Circuits at the Johannes Kepler University Linz. This package is part of the JKQ toolset.

Developers: Lukas Burgholzer, Hartwig Bauer, Stefan Hillmich and Robert Wille.

If you have any questions feel free to contact us using [email protected] or by creating an issue on GitHub.

The package can be used for a multitude of tasks, as illustrated in the following:

• Obtaining intermediate representations from circuit descriptions.

  Currently available file formats are:

  • OpenQASM (e.g. used by Qiskit)
  • Real (e.g. from RevLib)
  • GRCS Google Random Circuit Sampling Benchmarks (see GRCS)
  • TFC (e.g. from Reversible Logic Synthesis Benchmarks Page)
  • QC (e.g. from Feynman)

  Importing a circuit from a file in either of those formats is done via:

  std::string filename = "PATH_TO_FILE";
  qc::QuantumComputation qc(filename);

  or by calling

  qc.import(filename);

  which first resets the qc object before importing the new file.

• Generating circuit representations for important quantum algorithms.

  Currently available algorithms are:

  • Entanglement

    unsigned short n = 2;
    qc::Entanglement entanglement(n); // generates bell circuit

    Generates the circuit for preparing an n qubit GHZ state. Primarily used as a simple test case.

  • Bernstein-Vazirani

    unsigned long long hiddenInteger = 16777215ull;
    qc::BernsteinVazirani bv(hiddenInteger); // generates Bernstein-Vazirani circuit for given hiddenInteger

    Generates the circuit for the Berstein-Vazirani algorithm using the provided hiddenInteger

  • Quantum Fourier Transform (QFT)

    unsigned short n = 3;
    qc::QFT qft(n); // generates the QFT circuit for n qubits

    Generates the circuit for the n qubit Quantum Fourier Transform.

  • Grover's search algorithm

    unsigned short n = 2;
    qc::Grover grover(n); // generates Grover's algorithm for a random n-bit oracle

    The algorithm performs ~ π/4 √2ⁿ Grover iterations. An optional unsigned int parameter controls the seed of the random number generation for the oracle generation.

• Constructing a functional representation of a given quantum computation.

  Thereby we use our decision diagram (DD) package, which is included as a git-submodule in this project, in order to construct a DD representation from the individual gate descriptions.

  For more information on decision diagrams for quantum computing, please visit iic.jku.at/eda/research/quantum_dd.

  The following example shows how to construct the functionality of the three-qubit QFT from above.

  auto dd = make_unique<dd::Package>(); // create an instance of the DD package
  auto functionality = qft.buildFunctionality(dd);  // obtain DD representation

  The matrix representation of the constructed functionality can be printed by calling

  qft.printMatrix(dd, functionality, std::cout);

  which results in the following output

  Common Factor: √½ ½
         1	       1	       1	       1	       1	       1	       1	       1	
         1	       1	       1	       1	      -1	      -1	      -1	      -1	
         1	       1	      -1	      -1	      +i	      +i	      -i	      -i	
         1	       1	      -1	      -1	      -i	      -i	      +i	      +i	
         1	      -1	      +i	      -i	       √½(1+i)	      -√½(1+i)	      -√½(1-i)	       √½(1-i)	
         1	      -1	      +i	      -i	      -√½(1+i)	       √½(1+i)	       √½(1-i)	      -√½(1-i)	
         1	      -1	      -i	      +i	      -√½(1-i)	       √½(1-i)	       √½(1+i)	      -√½(1+i)	
         1	      -1	      -i	      +i	       √½(1-i)	      -√½(1-i)	      -√½(1+i)	       √½(1+i)	
  

  Note that matrix output factors in initial assignments as well as output permutations of the system (i.e. initialLayout and outputPermutation).

  The (much more compact) DD representation that was actually constructed can be visualized as a *.dot file (which is automatically converted to SVG if GraphViz is installed) by calling

  dd::export2Dot(functionality, "functionality.dot");

  which produces

  

  See below for a description of the visualization options and their interpretation.

• Basic support for DD-based simulation of quantum algorithms.

  Only the calculation of a DD state vector representation is supported (without intermediate measurements). For a more powerful approach, see our dedicated simulator JKQ DDSIM.

  The following example shows the simulation of Grover's algorithm from above (searching for the 2-bit string 00). Note that 00 is just an example here, as the oracle that is generated by Grover(n) depends on a random seed.

  auto dd = make_unique<dd::Package>(); // create an instance of the DD package
  auto initial_state = dd->makeZeroState(n); // create initial state |0...0>
  auto state_vector = grover.simulate(initial_state, dd);

  The vector representation of the resulting state vector can be printed by calling

  grover.printVector(dd, state_vector, std::cout);

  which results in the following output

  Common Factor: -1
    0: 1
    1: 0
   10: 0
   11: 0
  100: 0
  101: 0
  110: 0
  111: 0
  

  As expected, the probabilities for obtaining the state |x00> (the ancillary qubit x is ignored) sum up to 1.

  The (much more compact) DD representation, that was actually produced by the simulation, can again be visualized as SVG file by calling

  dd::export2Dot(state_vector, "state_vector.dot", true);

  which produces

  

• Visualization and output of functional representations.

  Quantum computations can be visualized by printing them to any given output stream, e.g.

  std::cout << grover << std::endl;

  yields

     i: 		0	1	2	
     1: 	X   	|	|	X 	
     2: 	H   	H 	|	|	
     3: 	H   	|	H 	|	
     4: 	Z   	c	c	Z 	
     5: 	H   	H 	|	|	
     6: 	H   	|	H 	|	
     7: 	X   	X 	|	|	
     8: 	X   	|	X 	|	
     9: 	H   	|	H 	|	
    10: 	X   	c	X 	|	
    11: 	H   	|	H 	|	
    12: 	X   	|	X 	|	
    13: 	X   	X 	|	|	
    14: 	H   	|	H 	|	
    15: 	H   	H 	|	|
    16: 	X   	|	|	X 	
     o: 		0	1	2	
  

  As already demonstrated above, the function dd::exportDD(...) can be used to create visualizations of DDs representing vectors as well as matrices. To this end, the thickness of each edge indicates the edge weight's magnitude, while a color code indicates its phase. We use the HSV color wheel (at 50% lightness and 50% saturation) given below

  

  Furthermore, the export function has several options to tune the look and feel of the resulting DDs, e.g., enabling/disabling color, enabling/disabling edge weights, enabling/disabling classic mode.

If you ever want to visually explore how decision diagrams are employed in quantum computing for tasks such as simulation and verification, check out our installation-free web-tool JKQ DDVis.

The library also supports the output of circuits in various formats by calling

std::string filename = "PATH_TO_DESTINATION_FILE.{qasm | py}";
qc.dump(filename);

Currently available file formats are:

* `OpenQASM` (.qasm)
* `Qiskit` (.py) Qiskit export generates a python file, which can be used to transpile a respective circuit to a suitable architecture using the Qiskit toolset (specifically Qiskit Terra 0.12.0).

• Circuit transcription

  The project also includes a small command line application qfr_app which can be used to transcribe circuits from one format into another format, e.g.

  qfr_app circuit.real circuit.py
  

  can be used to transcribe a circuit from real format to a Qiskit realization

Building (and running) is continuously tested under Linux, MacOS, and Windows using the latest available system versions for GitHub Actions. However, the implementation should be compatible with any current C++ compiler supporting C++17 and a minimum CMake version of 3.14.

It is recommended (although not required) to have GraphViz installed for visualization purposes.

To start off, clone this repository using

git clone --recurse-submodules -j8 https://github.com/iic-jku/qfr 

Note the --recurse-submodules flag. It is required to also clone all the required submodules. If you happen to forget passing the flag on your initial clone, you can initialize all the submodules by executing git submodule update --init --recursive in the main project directory.

Our projects use CMake as the main build configuration tool. Building a project using CMake is a two-stage process. First, CMake needs to be configured by calling

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release

This tells CMake to search the current directory . (passed via -S) for a CMakeLists.txt file and process it into a directory build (passed via -B). The flag -DCMAKE_BUILD_TYPE=Release tells CMake to configure a Release build (as opposed to, e.g., a Debug build).

After configuring with CMake, the project can be built by calling

 cmake --build build --config Release

This tries to build the project in the build directory (passed via --build). Some operating systems and developer environments explicitly require a configuration to be set, which is why the --config flag is also passed to the build command. The flag --parallel <NUMBER_OF_THREADS> may be added to trigger a parallel build.

Building the project this way generates

• the library libqfr.a (Unix) / qfr.lib (Windows) in the build/src folder
• a test executable qfr_test containing a small set of unit tests in the build/test folder
• a small demo example executable qfr_example in the build/test directory.
• the commandline transcription executable qfr_app in the build/apps directory.

You can link against the library built by this project in other CMake project using the JKQ::qfr target.