MQT QMAP - A tool for Quantum Circuit Mapping written in C++

A tool for quantum circuit mapping developed by the Chair for Design Automation at the Technical University of Munich based on methods proposed in [1] , [2] , [3] , [4].

[1] A. Zulehner, A. Paler, and R. Wille. An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures. IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems (TCAD), 2018.

[2] R. Wille, L. Burgholzer, and A. Zulehner. Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations. In Design Automation Conference (DAC), 2019.

[3] S. Hillmich, A. Zulehner, and R. Wille. Exploiting Quantum Teleportation in Quantum Circuit Mapping. In Asia and South Pacific Design Automation Conference (ASP-DAC), 2021.

[4] L. Burgholzer, S. Schneider, and R. Wille. Limiting the Search Space in Optimal Quantum Circuit Mapping. In Asia and South Pacific Design Automation Conference (ASP-DAC), 2022.

QMAP is part of the Munich Quantum Toolkit (MQT; formerly known as JKQ and developed by the Institute for Integrated Circuits at the Johannes Kepler University Linz). It builds upon our quantum functionality representation (QFR) and can be used for mapping quantum circuits in any of the following formats:

• QuantumCircuit object from IBM's Qiskit (only through the MQT QMAP Python bindings)
• OpenQASM (e.g. used by IBM's Qiskit),
• Real (e.g. from RevLib),
• TFC (e.g. from Reversible Logic Synthesis Benchmarks Page)
• QC (e.g. from Feynman)

to any given architecture with the following available methods:

• Heuristic Mapper: Heuristic solution based on A* search. For details see [1] and [3].
• Exact Mapper: Exact solution utilizing the SMT Solver Z3. For details see [2] and [4].

Note that, at the moment, circuits to be mapped are assumed to be already decomposed into elementary gates supported by the targeted device. More specifically, circuits must not contain gates acting on more than two qubits.

For more information, please visit cda.cit.tum.de/research/ibm_qx_mapping/.

If you have any questions, feel free to contact us via quantum.cda@xcit.tum.de or by creating an issue on GitHub.

Usage

MQT QMAP is developed as a C++ library with an easy to use Python interface.

• In order to make the library as easy to use as possible (without compilation), we provide pre-built wheels for most common platforms (64-bit Linux, MacOS, Windows). These can be installed using

  pip install mqt.qmap
  

  However, in order to get the best performance out of QMAP, it is recommended to build it locally from the source distribution (see system requirements) via

  pip install  mqt.qmap --no-binary mqt.qmap
  

  This enables platform specific compiler optimizations that cannot be enabled on portable wheels.

• Once installed, start using it in Python:

  from mqt import qmap
  
  circ_mapped, results = qmap.compile(circ, arch)
  

where circ is either a Qiskit QuantumCircuit object or the path to an input file (in any of the formats listed above) and arch is either

• a Qiskit Backend instance such as those defined under qiskit.providers.fake_provider (recommended),
• one of the pre-defined architectures (see below), or
• the path to a file containing the number of qubits and a line-by-line enumeration of the qubit connections.

Architectures that are available per default (either as strings or under qmap.Arch.<...>) include:

• IBM_QX4 (5 qubit, directed bow tie layout)
• IBM_QX5 (16 qubit, directed ladder layout)
• IBMQ_Yorktown (5 qubit, undirected bow tie layout)
• IBMQ_London (5 qubit, undirected T-shape layout)
• IBMQ_Bogota (5 qubit, undirected linear chain layout)
• IBMQ_Casablanca (7 qubit, undirected H-shape layout)
• IBMQ_Tokyo (20 qubit, undirected brick-like layout)
• Rigetti_Agave (8 qubit, undirected ring layout)
• Rigetti_Aspen (16 qubit, undirected dumbbell layout)

Whether the heuristic (default) or the exact mapper is used can be controlled by passing method="heuristic" or method="exact" to the compile function.

There are several configuration options that can be passed to the compile function:

• The heuristic mapper offers the initial_layout option, which allows to choose one of the following strategies for choosing an initial layout:

  • identity: map logical qubit q_i to physical qubit Q_i,
  • static: determine fixed initial layout statically at the start of mapping,
  • dynamic (default): determine initial layout on demand during the mapping (this is the only one compatible with teleportation).

• Both, the exact and the heuristic mapper also offer the layering option, which allows to choose one of the following strategies for partitioning the circuit:

  • individual_gates (default): consider each gate separately,
  • disjoint_qubits: consider gates acting on disjoint qubits as a layer,
  • odd_gates: group pairs of gates. (Note that this strategy was only tested for IBM QX4 with the exact mapping tool and may not work on different architectures)
  • qubit_triangle: add gates to a layer, as long as no more than three qubits are involved. (Note that this strategy only works if the architecture's coupling map contains a triangle, e.g. IBM QX4, and was only tested using the exact mapping tool)

• The exact mapper offers the encoding option, which allows to choose a different encoding for at-most-one and exactly-one constraints:

  • naive (default): use naive encoding for constraints
  • commander: use commander encoding for at-most-one and exactly-one constraints
  • bimander: use bimander encoding for at-most-one and commander for exactly-one constraints

  As the commander encoding can use different strategies to group the variables, there are different commander_grouping options:

  • halves (default): each group contains half of the total variables
  • logarithm: each group contains at most log2 of the total variables
  • fixed2: each group contains exactly two variables
  • fixed3: each group contains exactly three variables

• Per default, the exact mapper searches for a suitable mapping by considering every possible (connected) subset of qubits instead of the whole architecture at once. This can be disabled by setting use_subsets=False.

• The exact mapper also offers the swap_reduction option to enable limiting the number of swaps considered per layer ( as proposed in [4] , which offers the following options:

  • none: consider whole search space
  • coupling_limit (default): calculate the max swaps per layer based on the longest path of current choice of qubits, or if use_subsets is disabled considers the whole architecture
  • increasing: start with 0 swaps and geometrically increase the number of swaps per layer
  • custom: set a custom limit, needs the swap_limit option to set the limit

  Using the use_bdd option, the mapping utilizes BDDs instead of simply removing the permutations from the core routine. This option is not generally advised, as it is more resource intensive in most cases, but is something to try in cases of timeout.

Command-line Executable

QMAP also provides two standalone executables with command-line interface called qmap_heuristic and qmap_exact. They provide the same options as the Python module as flags. Per default, this produces JSON formatted output. In general, we recommend to use the Python approach described above, as these commandline executables might not be maintained in the future.

System Requirements

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.

boost/program_options >= 1.50 is required for building the commandline applications of the mapping tool.

In order to build the exact mapping tool and for the Python bindings to work, the SMT Solver Z3 >= 4.8.3 has to be installed and the dynamic linker has to be able to find the library. This can be accomplished in a multitude of ways:

• Under Ubuntu 20.04 and newer: sudo apt-get install libz3-dev
• Under macOS: brew install z3
• Alternatively: pip install z3-solver and then append the corresponding path to the library path (LD_LIBRARY_PATH under Linux, DYLD_LIBRARY_PATH under macOS), e.g. via

  export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$(python -c "import z3; print(z3.__path__[0]+'/lib')")
  

• Download pre-built binaries from https://github.com/Z3Prover/z3/releases and copy the files to the respective system directories
• Build Z3 from source and install it to the system

Library Organisation

Internally the MQT QMAP library works in the following way

• Import input file into a qc::QuantumComputation object

  qc::QuantumComputation qc{};
  std::string circ = "<PATH_TO_CIRCUIT_FILE>";
  qc.import(circ);
  

• Import architecture file into a Architecture object

  Architecture arch{};
  std::string cm = "<PATH_TO_ARCH_FILE>";
  arch.loadCouplingMap(cm);
  

• (Optional) Import calibration file into arch object

  std::string cal = "<PATH_TO_CAL_FILE>";
  arch.loadProperties(cal);
  

• Depending on Method, instantiate a HeuristicMapper or ExactMapper object with the circuit and the architecture

  HeuristicMapper mapper(qc, arch);
  

  or

  ExactMapper mapper(qc, arch);
  

• Set configuration options, e.g.,

  Configuration config{};
  config.layeringStrategy = Layering::DisjointQubits;
  

• Perform the actual mapping

  mapper.map(config);
  

• Dump the mapped circuit

  mapper.dumpResult("<PATH_TO_OUTPUT_FILE>");
  

• Print the results

  mapper.printResult(std::cout);
  

Configure, Build, and Install

To start off, clone this repository using

git clone --recurse-submodules -j8 https://github.com/cda-tum/qmap

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 heuristic library libqmap_heuristic_lib.a (Unix) / qmap_heuristic_lib.lib (Windows) in the build/src directory
• the heuristic mapper commandline executable qmap_heuristic in the build/apps directory (only available if Boost is found)
• a test executable qmap_heuristic_test containing a small set of unit tests for the heuristic mapper in the build/test directory
• the exact library libqmap_exact_lib.a (Unix) / qmap_exact_lib.lib (Windows) in the build/src directory (only available if Z3 is found)
• the exact mapper commandline executable qmap_exact in the build/apps directory (only available if Boost and Z3 is found)
• a test executable qmap_exact_test containing a small set of unit tests for the exact mapper in the build/test directory (only available if Z3 is found)

Extending the Python Bindings

To extend the Python bindings you can locally install the package in edit mode, so that changes in the Python code are instantly available. The following example assumes you have a virtual environment set up and activated.

(venv) $ pip install cmake
(venv) $ pip install --editable .

If you change parts of the C++ code, you have to run the second line to make the changes visible in Python.

Reference

If you use our tool for your research, we will be thankful if you refer to it by citing the appropriate publications.

For the heuristic mapping, please cite

@article{DBLP:journals/tcad/ZulehnerPW19,
  author    = {Alwin Zulehner and Alexandru Paler and Robert Wille},
  title     = {An Efficient Methodology for Mapping Quantum Circuits to the {IBM QX} Architectures},
  journal   = {{IEEE} Transactions on Computer-Aided Design of Integrated Circuits and Systems},
  volume    = {38},
  number    = {7},
  pages     = {1226--1236},
  year      = {2019}
}

For the teleportation in the heuristic mapping, please cite

@inproceedings{DBLP:conf/aspdac/HillmichZW21,
  author    = {Stefan Hillmich and Alwin Zulehner and Robert Wille},
  title     = {Exploiting Quantum Teleportation in Quantum Circuit Mapping},
  booktitle = {Asia and South Pacific Design Automation Conference},
  pages     = {792--797},
  publisher = {{ACM}},
  year      = {2021}
}

For the exact mapping, please cite

@inproceedings{DBLP:conf/dac/WilleBZ19,
  author    = {Robert Wille and Lukas Burgholzer and Alwin Zulehner},
  title     = {Mapping Quantum Circuits to {IBM QX} Architectures Using the Minimal Number of {SWAP} and {H} Operations},
  booktitle = {Design Automation Conference},
  publisher = {{ACM}},
  year      = {2019}
}

For the search space limitation in the exact mapping, please cite

@inproceedings{burgholzer2022limitingSearchSpace,
  author    = {Lukas Burgholzer and Sarah Schneider and Robert Wille},
  title     = {Limiting the Search Space in Optimal Quantum Circuit Mapping},
  booktitle = {Asia and South Pacific Design Automation Conference},
  year      = {2022}
}