Research

Areas of interest

My main motivation for research in Quantum Information Theory is to understand what is ultimately efficiently computable in the physical world? What constraints and opportunities do our best descriptions of the world, especially quantum mechanics, put on efficient computation? What exactly constitutes the border line between efficient classical and quantum computation (BPP vs. BQP)? For this reason I find it especially rewarding to study efficient classical simulations of quantum systems, as these pin down the borderline between what is (classically) tractable and what makes quantum mechanics hard to simulate.  Especially I enjoy studying

  • #P-complete counting problems,
  • partition functions,
  • tensor network contraction, and
  • (discrete) path integral approaches to quantum simulation

as closely related and different sides of the same coin.

Another area, where I feel the computational power of the quantum world vs. the classical world pinned down tightly, is the work of [Blier, Tapp, 2007], [Aaronson, et al., 2008] and [Beigi, 2008] on NP vs. QMA_log(2).  Essentially these results show how two unentangled copies of a log-sized quantum witness state can certify membership in NP to a very low complexity verifier. NP languages can thus be certified in very small Hilbert spaces, so I would find it interesting to characterize NP and furthermore P precisely within this framework, identifying the minimum quantum resources required to capture P and NP. Also the requirement for at least two unentangled copies is very peculiar and warrants further investigation.

Papers

For up-to-date citation counts and pre-prints, see my Google Scholar and arXiv pages.

  1. D. Hangleiter, J. Bermejo-Vega, M. Schwarz, J. Eisert, Anti-concentration theorems for schemes showing a quantum computational supremacy, 2017. arXiv:1706.03786
  2. J. Bermejo-Vega, D. Hangleiter, M. Schwarz, R. Raussendorf, J. Eisert, Architectures for quantum simulation showing quantum supremacy, 2017. arXiv:1703.00466
  3. M. Schwarz, O. Buerschaper, J. Eisert, Approximating local observables of projected entangled pair states, 2016. arXiv:1606.06301, CEQIP’16 poster, Seefeld’16 poster
  4. D. Hangleiter, M. Kliesch, M. Schwarz, J. Eisert, Direct certification of a class of quantum simulations, Quantum Sci. Technol. 2 (2017) 015004arXiv:1602.00703
  5. M. Schwarz, An exponential time upper bound for Quantum Merlin-Arthur games with unentangled provers, 2015. arXiv:1510.08447
  6. M. Schwarz, T.S. Cubitt, F. Verstraete, An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma, 2013. arXiv:1311.6474
  7. M. Schwarz, M. Van den Nest, Simulating Quantum Circuits with Sparse Output Distributions, 2013. Accepted for publication in Quantum Information and Computation, arXiv:1310.6749, ECCC TR13-154QIP’10 poster.
  8. M. Schwarz, T.S. Cubitt, K. Temme, F. Verstraete, D. Perez-Garcia, Preparing topological projected entangled pair states on a quantum computer, Phys. Rev. A, Vol. 88, 032321-1 (2013)arXiv:1211.4050
  9. T.S. Cubitt, M. Schwarz, A constructive commutative quantum Lovász Local Lemma, and beyond, 2011. arXiv:1112.1413, QIP’12 slides
  10. M. Schwarz, K. Temme, F. Verstraete, Preparing Projected Entangled Pair States on a Quantum Computer, Phys. Rev. Lett. 108, 110502 (2012), arXiv:1104.1410 , QIP’12 slides

Talks

  1. Towards new upper bounds for QMA(k). Workshop on QMA(2) and the Complexity of Entanglement (invited talk), Joint Center for Quantum Information and Computer Science, University of Maryland, United States, August 2, 2016.
  2. Simulating Quantum Circuits with Sparse Output DistributionsCentre for Quantum Information and Foundations Seminar (invited talk), Cambridge, United Kingdom, May 20, 2016. Dahlem Center for Complex Quantum Systems (seminar talk), Berlin, Germany, April 30, 2014.
  3. Preparing Projected Entangled Pair States on a Quantum Computer, Quantum Information Processing Workshop 2012, Montreal, Canada, December 21, 2011; Vienna Theory Lunch, Vienna University of Technology, Vienna, Austria, March 27, 2012

last updated: 2017-03-03