References

MQT Core has a strong foundation in peer‑reviewed research. Many of its built‑in algorithms are based on methods published in scientific journals and conferences. For an overview of MQT Core and its features, see [38]. If you want to cite this article, please use the following BibTeX entry:

@article{burgholzer2025MQTCore,
  title        = {{{MQT Core}}: {{The}} Backbone of the {{Munich Quantum Toolkit (MQT)}}},
  author       = {Burgholzer, Lukas and Stade, Yannick and Peham, Tom and Wille, Robert},
  year         = 2025,
  journal      = {Journal of Open Source Software},
  publisher    = {The Open Journal},
  volume       = 10,
  number       = 108,
  pages        = 7478,
  doi          = {10.21105/joss.07478},
  url          = {https://doi.org/10.21105/joss.07478}
}

MQT Core is part of the Munich Quantum Toolkit, which is described in [39]. If you want to cite the Munich Quantum Toolkit, please use the following BibTeX entry:

@inproceedings{mqt,
  title        = {The {{MQT}} Handbook: {{A}} Summary of Design Automation Tools and Software for Quantum Computing},
  shorttitle   = {{The MQT Handbook}},
  author       = {Wille, Robert and Berent, Lucas and Forster, Tobias and Kunasaikaran, Jagatheesan and Mato, Kevin and Peham, Tom and Quetschlich, Nils and Rovara, Damian and Sander, Aaron and Schmid, Ludwig and Schoenberger, Daniel and Stade, Yannick and Burgholzer, Lukas},
  year         = 2024,
  booktitle    = {IEEE International Conference on Quantum Software (QSW)},
  doi          = {10.1109/QSW62656.2024.00013},
  eprint       = {2405.17543},
  eprinttype   = {arxiv},
  addendum     = {A live version of this document is available at \url{https://mqt.readthedocs.io}}
}

A full list of references is given below.

[1]

Randal E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, C-35(8):677–691, 1986. doi:10.1109/TC.1986.1676819.

[2]

Randal E. Bryant. Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Compute. Surv., 24(3):293–318, 1992. doi:10.1145/136035.136043.

[3]

Ingo Wegener. Branching programs and binary decision diagrams: theory and applications. Society for Industrial and Applied Mathematics, 2000. doi:10.1137/1.9780898719789.

[4]

J. Gergov and C. Meinel. Efficient boolean manipulation with OBDD's can be extended to FBDD's. IEEE Transactions on Computers, 43(10):1197–1209, 1994. doi:10.1109/12.324545.

[5]

R. Drechsler, A. Sarabi, M. Theobald, B. Becker, and M. A. Perkowski. Efficient representation and manipulation of switching functions based on ordered kronecker functional decision diagrams. In Design Automation Conf., 415–419. 1994. doi:10.1145/196244.196444.

[6]

R. I. Bahar, E. A. Frohm, C. M. Gaona, G. D. Hachtel, E. Macii, A. Pardo, and F. Somenzi. Algebraic decision diagrams and their applications. In Int'l Conf. on CAD. 1993. doi:10.1109/ICCAD.1993.580054.

[7]

S. Minato. Zero-suppressed BDDs for set manipulation in combinatorial problems. In Design Automation Conf., 272–277. 1993. doi:10.1145/157485.164890.

[8]

Robert Wille, Stefan Hillmich, and Lukas Burgholzer. Decision Diagrams for Quantum Computing. In Design Automation of Quantum Computers. 2023. doi:10.1007/978-3-031-15699-1_1.

[9]

Robert Wille, Stefan Hillmich, and Burgholzer Lukas. Tools for quantum computing based on decision diagrams. ACM Transactions on Quantum Computing, 2022. doi:10.1145/3491246.

[10]

D.M. Miller and M.A. Thornton. QMDD: A decision diagram structure for reversible and quantum circuits. In Int'l Symp. on Multi-Valued Logic. 2006. doi:10.1109/ISMVL.2006.35.

[11]

Philipp Niemann, Robert Wille, David Michael Miller, Mitchell A. Thornton, and Rolf Drechsler. QMDDs: Efficient quantum function representation and manipulation. IEEE Trans. on CAD of Integrated Circuits and Systems, 2016. doi:10.1109/TCAD.2015.2459034.

[12]

Alwin Zulehner, Stefan Hillmich, and Robert Wille. How to efficiently handle complex values? Implementing decision diagrams for quantum computing. In Int'l Conf. on CAD. 2019. doi:10.1109/ICCAD45719.2019.8942057.

[13]

Xin Hong, Xiangzhen Zhou, Sanjiang Li, Yuan Feng, and Mingsheng Ying. A tensor network based decision diagram for representation of quantum circuits. ACM Trans. Des. Autom. Electron. Syst., 2022. [PDF], doi:10.1145/3514355.

[14]

Lieuwe Vinkhuijzen, Tim Coopmans, David Elkouss, Vedran Dunjko, and Alfons Laarman. LIMDD: A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States. Quantum, 7:1108, 2023. doi:10.22331/q-2023-09-11-1108.

[15]

George F. Viamontes, Igor L. Markov, and John P. Hayes. Improving gate-level simulation of quantum circuits. Quantum Information Processing, 2(5):347–380, 2003. doi:10.1023/B:QINP.0000022725.70000.4a.

[16]

Alwin Zulehner and Robert Wille. Advanced simulation of quantum computations. IEEE Trans. on CAD of Integrated Circuits and Systems, 2019. doi:10.1109/TCAD.2018.2834427.

[17]

Stefan Hillmich, Igor L. Markov, and Robert Wille. Just like the real thing: Fast weak simulation of quantum computation. In Design Automation Conf. 2020. doi:10.1109/DAC18072.2020.9218555.

[18]

Lukas Burgholzer, Hartwig Bauer, and Robert Wille. Hybrid Schrödinger-Feynman simulation of quantum circuits with decision diagrams. In Int'l Conf. on Quantum Computing and Engineering. 2021. doi:10.1109/QCE52317.2021.00037.

[19]

Stefan Hillmich, Alwin Zulehner, Richard Kueng, Igor L. Markov, and Robert Wille. Approximating decision diagrams for quantum circuit simulation. ACM Transactions on Quantum Computing, 3(4):1–21, 2022. doi:10.1145/3530776.

[20]

Lukas Burgholzer, Alexander Ploier, and Robert Wille. Simulation paths for quantum circuit simulation with decision diagrams: What to learn from tensor networks, and what not. IEEE Trans. on CAD of Integrated Circuits and Systems, 2022. arXiv:2203.00703, doi:10.1109/TCAD.2022.3197969.

[21]

Thomas Grurl, Jurgen Fuß, and Robert Wille. Noise-aware quantum circuit simulation with decision diagrams. IEEE Trans. on CAD of Integrated Circuits and Systems, 42(3):860–873, 2023. doi:10.1109/TCAD.2022.3182628.

[22]

Kevin Mato, Stefan Hillmich, and Robert Wille. Mixed-dimensional quantum circuit simulation with decision diagrams. In Int'l Conf. on Quantum Computing and Engineering. 2023. arXiv:2308.12332, doi:10.1109/QCE57702.2023.00112.

[23]

Aaron Sander, Lukas Burgholzer, and Robert Wille. Towards hamiltonian simulation with decision diagrams. In Int'l Conf. on Quantum Computing and Engineering. 2023. arXiv:2305.02337, doi:10.1109/QCE57702.2023.00039.

[24]

Philipp Niemann, Robert Wille, and Rolf Drechsler. Efficient synthesis of quantum circuits implementing Clifford group operations. In Asia and South Pacific Design Automation Conf., 483–488. 2014. doi:10.1109/ASPDAC.2014.6742938.

[25]

A. Abdollahi and M. Pedram. Analysis and synthesis of quantum circuits by using quantum decision diagrams. In Design, Automation and Test in Europe. 2006. doi:10.1109/DATE.2006.244176.

[26]

M. Soeken, R. Wille, C. Hilken, N. Przigoda, and R. Drechsler. Synthesis of reversible circuits with minimal lines for large functions. In Asia and South Pacific Design Automation Conf., 85–92. 2012. doi:10.1109/ASPDAC.2012.6165069.

[27]

A. Zulehner and R. Wille. One-pass design of reversible circuits: Combining embedding and synthesis for reversible logic. IEEE Trans. on CAD of Integrated Circuits and Systems, 37(5):996–1008, 2018. doi:10.1109/TCAD.2017.2729468.

[28]

Smaran Adarsh, Lukas Burgholzer, Tanmay Manjunath, and Robert Wille. SyReC Synthesizer: An MQT tool for synthesis of reversible circuits. Software Impacts, 2022. doi:10.1016/j.simpa.2022.10045.

[29]

Kevin Mato, Stefan Hillmich, and Robert Wille. Mixed-dimensional qudit state preparation using edge-weighted decision diagrams. In Design Automation Conf. 2024. doi:10.1145/3649329.3656260.

[30]

Lukas Burgholzer and Robert Wille. Advanced equivalence checking for quantum circuits. IEEE Trans. on CAD of Integrated Circuits and Systems, 2021. doi:10.1109/TCAD.2020.3032630.

[31]

Lukas Burgholzer, Richard Kueng, and Robert Wille. Random stimuli generation for the verification of quantum circuits. In Asia and South Pacific Design Automation Conf. 2021. doi:10.1145/3394885.3431590.

[32]

Lukas Burgholzer, Rudy Raymond, and Robert Wille. Verifying results of the IBM Qiskit quantum circuit compilation flow. In Int'l Conf. on Quantum Computing and Engineering. 2020. doi:10.1109/QCE49297.2020.00051.

[33]

S.-A. Wang, C.-Y. Lu, I-M. Tsai, and S.-Y. Kuo. An XQDD-based verification method for quantum circuits. In IEICE Trans. Fundamentals, 584–594. 2008. doi:10.1093/ietfec/e91-a.2.584.

[34]

Kaitlin N. Smith and Mitchell A. Thornton. Quantum logic synthesis with formal verification. In Int'l Midwest Symp. on Circuits and Systems, 73–76. 2019. doi:10.1109/MWSCAS.2019.8885132.

[35]

Xin Hong, Yuan Feng, Sanjiang Li, and Mingsheng Ying. Equivalence checking of dynamic quantum circuits. In Int'l Conf. on CAD. 2022. doi:10.1145/3508352.3549479.

[36]

Robert Wille, Lukas Burgholzer, and Michael Artner. Visualizing decision diagrams for quantum computing. In Design, Automation and Test in Europe. 2021. doi:10.23919/DATE51398.2021.9474236.

[37]

Yannick Stade, Lukas Burgholzer, and Robert Wille. Towards supporting QIR: Steps for adopting the quantum intermediate representation. In Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis. 2025. arXiv:2411.18682, doi:10.1145/3731599.3767546.

[38]

Lukas Burgholzer, Yannick Stade, Tom Peham, and Robert Wille. MQT Core: The backbone of the Munich Quantum Toolkit (MQT). Journal of Open Source Software, 10(108):7478, 2025. [PDF], doi:10.21105/joss.07478.

[39]

Robert Wille, Lucas Berent, Tobias Forster, Jagatheesan Kunasaikaran, Kevin Mato, Tom Peham, Nils Quetschlich, Damian Rovara, Aaron Sander, Ludwig Schmid, Daniel Schoenberger, Yannick Stade, and Lukas Burgholzer. The MQT handbook: A summary of design automation tools and software for quantum computing. In IEEE International Conference on Quantum Software (QSW). 2024. arXiv:2405.17543, doi:10.1109/QSW62656.2024.00013.