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.
Publications
- 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
- T.S. Cubitt, M. Schwarz, A constructive commutative quantum Lovász Local Lemma, and beyond, 2011. arXiv:1112.1413, QIP’12 slides
Talks
- 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
