Daniel Reitzner, PhD.

Research Portfolio

Research topics

Quantum walks

In quantum walks my main contributions in this area were in the quantum walks searches on symmetric graphs showcasing the utility of this approach. We extended the formalism for dimensionality reduction by identifying invariant subspaces. This allowed us to effectively describe speedups on many graphs utilizing their symmetries. With further extensions to the approach, we were able to describe also evolutions in noisy scenarios. I also co-authored a review paper on the topic of quantum-walk searches.

Quantum measurements

Quantum measurements is a topic where we explored many questions concerning compatibility of quantum measurements and extended structures. This exploration started with paper on Coexistence of qubit effects, where we provided an exhaustive description of when two qubit measurements can be jointly measurable. This turned out to be a topic of high interest as in the same year there were two other publications under the same title approaching the problem from different directions. Currently one now has three different options how to describe coexistence of qubits effects, if one needs them. On this path, we have found many new and interesting results, extended the notion to operations, other quantum devices, or studied noise robustness of incompatibility.

During my stay at Technische Universität München we have addressed a long-standing open problem of whether coexistence of effects is the same notion as joint measurability; it does not. The most recent result in this topic is one of a more practical setting that explores Anticipative measurements in hybrid quantum-classical computation . This result interestingly shows that the anticipation of posterior information on the outcome can increase probability of success for obtaining a correct result.

Practical quantum algorithms

Some results cannot be put in one of these two categories but extend these topics in one way or another. Within the topic of quantum measurements, we have published a paper on how to implement generalized quantum measurements (POVMs). There we present a constructive algorithm for such POVM implementation that in addition considers limitations of resources. Namely, we have looked at the possibility of reducing the number of necessary ancillary qubits to one. This meant that the partial measurements were limited to binary. The price for that to pay is the need to perform multiple such measurements in sequence. The paper thus explores not only the specific implementation but serves also as a probe to the boundaries set by the limited resources.

There are also other papers concerning this topic, dealing with practical asapects of quantum searches.

Benchmarking quantum computers

Comparison of quantum computers has many points of view, and it is impossible to choose a single number. Rather it is a problem that needs to include user preferences, application aims, as well as multitude of practical technological aspects. As a first step on this endeavour, we are publishing a white paper on the topic that includes many observations and recommendations.

Research supervision and leadership experience

Research output

Research output according to WoS:

List of publications

Peer-reviewed scientific articles

  1. D. Reitzner, J. Bouda, General measurements with limited resources and their application to quantum unambiguous state discrimination, Quantum Inf Process 23, 268 (2024)
  2. C.A. Galvis-Florez, D. Reitzner, S. Särkkä, Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Bellevue, WA, USA, pp. 111-119 (2023)
  3. D. Reitzner, Kvantové previazanie a Nobelova cena za fyziku 2022 (Quantum entanglement and Nobel prize in physics 2022), Pokroky matematiky, fyziky a astronomie, 68, 29–45 (2023)
  4. T. Heinosaari, D. Reitzner, A. Toigo, Anticipative measurements in hybrid quantum-classical computation, Phys. Rev. A 107, 032612 (2023)
  5. D. Reitzner, M. Hillery, Grover search under localized dephasing, Phys. Rev. A 99, 012339 (2019)
  6. T. Heinosaari, D. Reitzner, T. Rybár, M. Ziman, Incompatibility of unbiased qubit observables and Pauli channels, Phys. Rev. A 97, 022112 (2018)
  7. D. Reitzner, M. Hillery, D. Koch, Finding paths with quantum walks or quantum walking through a maze, Phys. Rev. A 96, 032323 (2017)
  8. C. Carmeli, T. Heinosaari, D. Reitzner, J. Schultz, A. Toigo, Quantum Incompatibility in Collective Measurements, Mathematics 4, 54 (2016)
  9. M. Sedlák, D. Reitzner, G. Chiribella, M. Ziman, Incompatible measurements on quantum causal networks, Phys. Rev. A 93, 052323 (2016)
  10. T. Heinosaari, J. Kiukas, D. Reitzner, J. Schultz, Incompatibility breaking quantum channels, J. Phys. A 48, 435301 (2015)
  11. T. Heinosaari, J. Kiukas, D. Reitzner, Noise Robustness of the Incompatibility of Quantum Measurements, Phys. Rev. A 92, 022115 (2015)
  12. P. Vrana, D. Reeb, D. Reitzner, M. M. Wolf, Fault-ignorant Quantum Search, New J. Phys. 16, 073033 (2014)
  13. D. Reitzner, M. Ziman, Two Notes on Grover’s Search: Programming and Discriminating, EPJ+ 129, 128 (2014)
  14. T. Heinosaari, J. Kiukas, D. Reitzner, Coexistence of effects from an algebra of two projections, J. Phys. A 47, 225301 (2014)
  15. T. Heinosaari, T. Miyadera, D. Reitzner, Strongly Incompatible Quantum Devices, Found. Phys. 44, 34 (2014)
  16. D. Reeb, D. Reitzner, M. M. Wolf, Coexistence does not imply Joint Measurability, J. Phys. A 46, 462002 (FT) (2013)
  17. M. Hillery, H. Zheng, E. Feldman, D. Reitzner, V. Bužek, Quantum walks as a probe of structural anomalies in graphs, Phys. Rev. A 85, 062325 (2012)
  18. D. Reitzner, D. Nagaj, V. Bužek, Quantum Walks, Acta Phys. Slovaca 61, 603 (2011)
  19. E. Feldman, M. Hillery, H.-W. Lee, D. Reitzner, H. Zheng, V. Bužek, Finding structural anomalies in graphs by means of quantum walks, Phys. Rev. A 82, 040301 (R) (2010)
  20. T. Heinosaari, M.A. Jivulescu, D. Reitzner, M. Ziman, Approximating incompatible von Neumann measurements simultaneously, Phys. Rev. A 82, 032328 (2010)
  21. M. Hillery, D. Reitzner, V. Bužek, Searching via walking: How to find a marked clique of a complete graph using quantum walks, Phys. Rev. A 81, 062324 (2010)
  22. T. Heinosaari, D. Reitzner, P. Staňo, M. Ziman, Coexistence of quantum operations, J. Phys. A 42, 365302 (2009)
  23. D. Reitzner, M. Hillery, E. Feldman, V. Bužek, Quantum Searches on Highly Symmetric Graphs, Phys. Rev. A 79, 012323 (2009)
  24. T. Heinosaari, D. Reitzner, P. Staňo, Notes on Joint Measurability of Quantum Observables, Found. Phys. 38, 1133 (2008)
  25. T. Heinosaari, P. Staňo, D. Reitzner, Approximate Joint Measurability of Spin Along Two Directions, Int. J. Quantum Inf. 6, 975 (2008)
  26. P. Staňo, D. Reitzner, T. Heinosaari, Coexistence of qubit effects, Phys. Rev. A 78, 012315 (2008)
  27. D. Reitzner, D. Horváth, Multicanonical sampling of vortex states in magnetic nanoelements, Physica A 379, 587 (2007)
  28. M. Gmitra, D. Horváth, D. Reitzner, The partitioning of magnetic configurations using the self-organized neural network, Czech. J. Phys. 54, 631 (2004)

Non-refereed scientific articles

  1. J.M. Lorenz, T. Monz, J. Eisert, D. Reitzner, F. Schopfer, F. Barbaresco, K. Kurowski, W. van der Schoot, T. Strohm, J. Senellart, C.M. Perrault, M. Knufinke, Z. Amodjee, M. Giardini, Systematic benchmarking of quantum computers: status and recommendations, preprint arXiv:2503.04905 [quant-ph] (2025) https://doi.org/10.48550/arXiv.2503.04905
  2. D. Reitzner, Comment on Afshar's experiments, preprint arXiv:quant-ph/0701152 (2007)

Theses

  1. D. Reitzner, Utilisation of Scattering Quantum Walks in Searches on Highly Symmetric Graphs, doctoral dissertation (monograph), Faculty of mathematics, physics and informatics, Comenius University (2010)
  2. D. Reitzner, Quantum Walk Searches, Rerum Naturalium Doctor (RNDr.) thesis, Faculty of mathematics, physics and informatics, Comenius University (2009)
  3. D. Reitzner, Monte Carlo Method in Construction of Large-scale Hamiltonians of Selected Spin Systems, Faculty of Science, Pavol Jozef Šafárik University (2006)

Audiovisual material, ICT software

  1. D. Reitzner, Video tutorials for online teaching during COVID period for PV275 Introduction to Quantum Computer Programming, Faculty of Informatics, Masaryk University in Brno, Czech Republic (2020)
  2. D. Reitzner, Python library for implementations of POVMs, in development