ABOUT ME
I am a researcher with interests in various subfields of quantum computing.
This encompasses classical simulation methods, stabiliser formalism and magic state model, characterisation and benchmarking protocols, and compilation of quantum circuits.
I am interested in the theory and construction of (approximate) unitary tdesigns and random quantum circuits.
Among others, unitary designs play an important role in many benchmarking and characterisation protocols.
From a practical point of view, exact unitary designs however have several disadvantages and hence the focus has shifted towards approximating them with random circuits.
Here, a thorough analysis of their convergence properties is key to guarantee the proper functioning of the protocol and, for instance, also plays an important role in quantum supremacy experiments.
I am currently working on adapting characterisation and benchmarking protocols to random circuits, thereby combining rigorous performance guarantees with minimal practical assumptions, making them more easily accessible to experimentalists.
Currently, I am working on a federally funded project on trappedion quantum computers which involves close collaboration with experimental and industrial partners.
Through this, I have become increasingly interested in the practical challenges of building quantum computers.
Moreover, I have started to work on gate set design and on compilation methods using multiqubit gates native to ion trap architectures.
During my PhD, I worked on advanced methods based on the stabiliser formalism and the Clifford group.
In particular, I have become interested in stabiliserbased simulation methods such as Wigner functions on discrete phase space and decompositions in stabiliser frames (e.g. robustness of magic, stabiliser extent, dyadic negativity).
I worked on the closely related resource theory of magic and I am interested in resourcetheoretic questions in quantum computing.
Short CV
05/2024  10/2024 
Visiting researcher in the Algorithms and Complexity group at CWI and QuSoft, Amsterdam, Netherlands. 
02/2021  present 
Postdoc in the group of Martin Kliesch @ Heinrich Heine University Düsseldorf & University of Technology Hamburg, Germany. 
02/2017  01/2021 
Institute for theoretical physics, University of Cologne, Germany.
PhD in theoretical physics (May 2021)
Thesis: On stabiliser techniques and their application to simulation and certification of quantum devices,
supervised by David Gross

10/2014  10/2016 
University of Jena, Germany.
Master's degree in physics
"Interfaces in Holographic Weyl Semimetals"

10/2009  09/2014 
University of Freiburg, Germany.
Bachelor's degree in mathematics
Bachelor's degree in physics

Publications
Here, you can find a list of my publications.
I am trying to keep it uptodate, but you also are welcome to check my papers on arXiv and my Google Scholar profile
 Raphael Brieger, Markus Heinrich, Ingo Roth, and Martin Kliesch: Stability of classical shadows under gatedependent noise, arXiv:2310.19947 (2023)
 Pascal Baßler, Markus Heinrich, and Martin Kliesch: Timeoptimal multiqubit gates: Complexity, efficient heuristic and gatetime bounds, Quantum 8, 1279 (2024) [open access]
 Markus Heinrich, Martin Kliesch, and Ingo Roth: Randomized benchmarking with random quantum circuits, arXiv:2212.06181 (2022)
 Mirko Arienzo, Markus Heinrich, Ingo Roth, and Martin Kliesch: Closedform analytic expressions for shadow estimation with brickwork circuits, Quantum Information and Computation 23, 961 (2023) [open access]
 Pascal Baßler, Matthias Zipper, Christopher Cedzich, Markus Heinrich, Patrick Huber, Michael Johanning, and Martin Kliesch: Synthesis of and compilation with timeoptimal multiqubit gates, Quantum 7, 984 (2023) [open access]
 Arne Heimendahl, Markus Heinrich, and David Gross: The axiomatic and the operational approaches to resource theories of magic do not coincide, Journal of Mathematical Physics 63, 112201 (2022). arXiv:2011.11651
 Jonas Haferkamp, Felipe MontealegreMora, Markus Heinrich, Jens Eisert, David Gross, and Ingo Roth: Efficient Unitary Designs with a SystemSize Independent Number of NonClifford Gates, Communications in Mathematical Physics 397, 995 (2023) [open access]
 Markus Heinrich and David Gross: Robustness of Magic and Symmetries of the Stabiliser Polytope, Quantum 3, 132 (2019) [open access]
 Markus Heinrich, Amadeo JiménezAlba, Sebastian Moeckel, and Martin Ammon: Surface States in Holographic Weyl Semimetals, Physical Review Letters 118, 201601 (2017). arXiv:1612.00836
PhD thesis
Conference talks
 General guarantees for randomized benchmarking with random quantum circuits. QIP Ghent, Belgium (2023). Youtube
 The axiomatic and the operational approaches to resource theories of magic do not coincide. QIP Munich, Germany (2021). Youtube
 Applying Symmetry Reduction Methods to the Robustness of Magic. The Mathematics of Quantum Information, Siegen, Germany (2019).
 Robustness of Magic and Symmetries of the Stabiliser Polytope. Modern Topics in Quantum Information. Natal, Brazil (2018). Youtube
 Using Stabilizer Symmetries to compute Resource Monotones. DPG Spring Conference, Erlangen, Germany (2018).
Other talks
 General guarantees for randomized benchmarking with random quantum circuits. QLunch, University of Copenhagen, Denmark (2023).
 General guarantees for randomized benchmarking with random quantum circuits. QuSoft seminar, University of Amsterdam/Centrum Wiskunde & Informatica, Netherlands (2023).
 General guarantees for randomized benchmarking with random quantum circuits. Quantum Computing Analytics seminar, PGI12, FZ Jülich, Germany (2023).
 General guarantees for randomized benchmarking with random quantum circuits. Eisert group seminar, FU Berlin, Germany (2023).
 General guarantees for randomized benchmarking with random quantum circuits. Gross group seminar, University of Cologne, Germany (2022).
 Classical simulation of quantum circuits. Quantum algorithms group seminar, Technology Innovation Institute Abu Dhabi, UAE (2021)
 Unitary tdesigns with few nonClifford resources. Quantum Rhineland Meeting, online (2020)
 Robustness of Magic and Symmetries of the Stabiliser Polytope. Workshop on Discrete Phase Space Methods For Quantum FaultTolerance, Bad Honnef, Germany. (2018).
 Robustness of Magic and Symmetries of the Stabiliser Polytope. CRC183 Workshop, Berlin, Germany. (2018).
 Robustness of Magic and Symmetries of the Stabiliser Polytope. Düsseldorf quantum information seminar, HHU Düsseldorf, Germany (2018).
 Robustness of Magic and Symmetries of the Stabiliser Polytope. IQOQI seminar, Vienna, Austria (2018).
 Correlated Noise and the Error Correction Threshold. CRC183 Workshop, Berlin, Germany. (2017).