- Quantum gravity I
- Quantum gravity II
- Cosmology
- Relativistic quantum information
- Quantum computing
- Communication engineering
- Shannon sampling theory/data compression
- Mathematical biology
- Radar signal design for maximum information return
- The Casimir effect in layered superconductors
- Combinatorics in quantum field theory
- Further interests: Consciousness

## Big question 1

Quantum computers have the potential to speed up certain computations far beyond what can be achieved with computing technology based solely on classical physics. This has been proven mathematically but the physical reasons for the speed-up are not yet clear.

## Basic idea 1

One type of calculation that can be sped up by quantum computers is data search. For example, a classical random search walk proceeds with a speed that relates the distance to the square root of the number of steps taken. Quantum computers can do a random walk that proceeds with a speed that is proportional to the number of steps and therefore much faster. In work with Renato Portugal, I showed that quantum walks can often be shown to be equivalent to the propagation of a wave in a medium, which explains why the propagation and therefore the search is with a constant speed.

## Big question 2

How to build quantum computers, given that their reliance on quantum effects makes them vulnerable to even the tiniest disturbances? How to make them resilient against errors?

## Basic idea 2

I have worked on the generalization of so-called quantum error correction algorithms that improve the resilience of quantum computers to noise. This work also yields new insight into the transfer of information from one system to another during a measurement process. This is work with David Kribs and my student, Cedric Beny. Cedric pioneered this study.

## Selected publications

- A. Kempf, R. Portugal, Group velocity of discrete-time quantum walks, Physical Review A79, 052317 (2009)
- C. Beny, A. Kempf, D. Kribs, Qantum Error Correction on Infinite-Dimensional Hilbert Spaces, quant-ph/0811.0421, J. Math. Phys. 50, 062108 (2009)
- C. Beny, A. Kempf, and D.W. Kribs, Generalization of Quantum Error Correction via the Heisenberg Picture, Phys. Rev. Lett. 98, 100502 (2007)
- C. Beny, A. Kempf, D.W. Kribs, Quantum error correction of observables, Phys. Rev. A76, 042303 (2007)