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 t-designs 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 trapped-ion 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 multi-qubit 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 stabiliser-based 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 resource-theoretic questions in quantum computing.

Short CV

Publications

Here, you can find a list of my publications.
I am trying to keep it up-to-date, 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 gate-dependent noise, arXiv:2310.19947 (2023)
• Pascal Baßler, Markus Heinrich, and Martin Kliesch: Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time 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: Closed-form 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 time-optimal multi-qubit 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 Montealegre-Mora, Markus Heinrich, Jens Eisert, David Gross, and Ingo Roth: Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford 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 Jiménez-Alba, Sebastian Moeckel, and Martin Ammon: Surface States in Holographic Weyl Semimetals, Physical Review Letters 118, 201601 (2017). arXiv:1612.00836

PhD thesis

Markus Heinrich

On stabiliser techniques and their application to simulation and certification of quantum devices

University of Cologne, Germany, 2021

Download @ university library of Cologne

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, PGI-12, 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 t-designs with few non-Clifford resources. Quantum Rhineland Meeting, online (2020)
• Robustness of Magic and Symmetries of the Stabiliser Polytope. Workshop on Discrete Phase Space Methods For Quantum Fault-Tolerance, 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).