^{SENIOR RESEARCHER}

Quantum Architectures and Computation Group (QuArC)

Microsoft Research

One Microsoft Way

Redmond, WA 98052, USA

E-mail: martinro@microsoft.com

Phone: (425) 706-3473

I am a Senior Researcher at Microsoft Research Redmond and member of the Quantum Architectures and Computation (QuArC) group. Prior to joining MSR, I was a Senior Research Staff Member at NEC Laboratories America (2005-2013) and the leader of NEC's Quantum IT group. I was a post-doctoral fellow at the Institute for Quantum Computing, Waterloo, Canada (2003-2004). I received my Ph.D. degree from the University of Karlsruhe, Germany (2001). My research is centered around quantum algorithms, quantum error-correction, quantum circuits, and digital signal processing.

I am passionate about finding new examples of problems for which a quantum computer *dramatically* outperforms any classical computer. In particular, I am interested in problems where an exponential speedup compared to the best known classical algorithm can be achieved by using a quantum computer. Not many such problems are currently known, arguably the most well-known cases are Shor's algorithms for factoring and dlog and the simulation of a wide range of quantum mechanical systems on a quantum computer. A problem that I like in particular is the so-called hidden shift problem in which one has to identify an unknown offset in the argument of a function. I showed that for certain Boolean functions that are used in cryptography, such hidden shift problems can be solved efficiently, a result which was subsequently generalized to broader classes of functions.

Starting in 2011, I changed my research area almost completely and started to work on quantum programming languages, quantum circuit synthesis, and more generally, a compiler system that can break down higher-level algorithms into elementary gate sequences and that can perform resource estimation for a variety of physical machine descriptions.

- M. Grassl, B. Langenberg, M. Roetteler, and R. Steinwandt, Applying Grover's algorithm to AES: quantum resource estimates, no. MSR-TR-2015-89, December 2015.
- A. Bocharov, S. X. Cui, M. Roetteler, and K. M. Svore, Improved quantum ternary arithmetics, no. MSR-TR-2015-90, December 2015.
- V. Kliuchnikov, A. Bocharov, M. Roetteler, and J. Yard, A framework for approximating qubit unitaries, no. MSR-TR-2015-80, 13 October 2015.
- Alex Parent, Martin Roetteler, and Krysta M. Svore, Reversible circuit compilation with space constraints, no. MSR-TR-2015-75, 2 October 2015.
- A. D. Bookatz, M. Rötteler, and P. Wocjan, Improved bounded-strength decoupling schemes for local Hamiltonians, no. MSR-TR-2015-69, September 2015.
- M. Grassl and M. Rötteler, Quantum MDS codes over small fields, in
*Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT'15), Hong Kong*, IEEE – Institute of Electrical and Electronics Engineers, June 2015. - A. Bocharov, M. Rötteler, and K. M. Svore, Efficient synthesis of probabilistic quantum circuits with fallback, in
*Physical Review A*, vol. 91, pp. 052317, May 2015. - Alex Bocharov, Martin Roetteler, and Krysta M. Svore, Efficient Synthesis of Universal Repeat-Until-Success Circuits, in
*Physical Review Letters*, vol. 114, no. 080502, American Physical Society, 27 February 2015. - M. Rötteler and R. Steinwandt, A note on quantum related-key attacks, in
*Information Processing Letters*, vol. 115, pp. 40–44, 26 August 2014. - M. Rötteler and R. Steinwandt, A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2 n), in
*Quant. Inform. & Comp.*, vol. 14, no. 9&10, pp. 888-900, Rinton Press, July 2014.