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Organisation

# Quantum Matter and Quantum Information

This research priority area is focused on the experimental and theoretical study of Quantum Matter (QM) and applications in Quantum Information (QI).

The past 20 years have made it clear that the principles of the quantum theory offer unprecedented possibilities in the area of quantum information science. Quantum codes for cryptography cannot be broken. A quantum computer, if realized, has the potential of handling certain computational tasks at a speed superior to that of a classical computer.

### Challenges

The potential of quantum information science in turn formulates challenges for the study of quantum matter: not only do we wish to understand how quantum matter works’, we also want to learn how quantum materials and devices can be controlled and manipulated such that quantum information can be stored without leakage and that quantum algorithms can be implemented.

In the Science Park Amsterdam five research groups are active in the area of Quantum Matter and Quantum Information:

• At the Institute of Physics (IoP) the experimental groups Quantum Gases and Quantum Information
• Quantum Electron Matter at the van Waals Zeeman Institute (WZI)
• The group Low-D Quantum Condensed Matter and Quantum Information at the Institute for Theoretical Physics Amsterdam (ITFA).
• The group Quantum Computing, a joint venture between the Center for Mathematics and Computer Science (CWI) and the Institute for Logic, Language and Computation (ILLC)
• The Korteweg de Vries Institute for Mathematics (KdVI) houses the research group Quantum Geometry.

### Amsterdam Quantum Information Science

The reach of this collective of researchers is very large, stretching from experiments in quantum matter via theoretical physics to quantum information theory and mathematical foundations. Some years ago, in a grass-roots action, the researchers initiated an informal platform Amsterdam Quantum Information Science (AQIS). The research priority area QM&QI, which is acknowledged by the Faculty of Science, will further develop and structure the joint initiative.

Worldwide there are some very successful research institutes centered around the QM&QI research theme:

• IQC (Waterloo)
• IQOQI (Innsbruck/Vienna)
• JQI (NIST/Maryland)
• CQT (Singapore)
• INTRIQ (Montreal)
• IQI (CalTech)

### New materials and devices

Storing and processing information requires a physical device. If this device is a quantum mechanical system, novel possibilities for information science arise: unbreakable cryptographic codes and ultra-fast computational algorithms.

Exploiting these possibilities requires materials and devices whose quantum states can be controlled and manipulated with high accuracy. One candidate for this are systems of cold atomic matter: collections of a relative limited number of atoms that move slowly and can be manipulated with the help of electric and magnetic fields and (laser) light.

A second possibility is to use materials where electrons move in highly special and predictable manners. Examples of such solid state systems are 1-dimensional materials (quantum wires) or 2-dimensional electron gases. The latter possibility is realized in graphene (carbon in a 2-dimensional chicken wire configuration) and in a new family of materials known as topological insulators’.

### Fault tolerance

For effective handling of quantum information, an important requirement is fault tolerance: one needs to avoid events where quantum information leaks away or where unwanted switches of a quantum memory occur. One method to achieve fault tolerance is to select a device platform which is, to a high degree, robust against small perturbations.

A second strategy is via software: implementation of so-called error-correcting codes enable correction of a limited number of mistakes. A particularly elegant idea is to achieve fault-tolerance through a principle called topological protection.

### Ultracold atoms

At the WZI Walraven has pioneered experiments with ultracold atoms. The quantum gases group is developing the idea of storing information via cold atoms in an array of magnetic microtraps (Spreeuw, van Linden van den Heuvel).

### Ultracold gases

A particularly promising new direction is the study of ultracold gases in optical lattices, which can act as quantum registers and as quantum simulators that also shed light on quantum properties of electrons in the solid state.

### Topological insulators

The group of Golden, Goedkoop and de Visser focuses on topological insulators. The ITFA theory group has pioneered ideas of topological quantum computation (Bais, Schoutens) and supports the experimental studies of topological insulators (Schoutens, Turner) and experiments on ultra-cold atomic gases (Caux, van Druten

### Error-correcting codes

De CWI/ILLC group (Buhrman, de Wolf) are active in developing error-correcting codes for fault toleranceand address multiparty quantum communication complexity, entanglement, quantum algorithms, and quantum cryptography. This latter topic has high potential for innovation.

### Topological quantum field theory

The mathematical research at the KdVI/CWI is concerned with topological quantum field theory in relation to fault tolerant quantum computation and the mathematical description of topological insulators.

### Publications

Six publications with large impact since 2008 are :

1. E. Wille, F.M. Spiegelhalder, G. Kerner, D. Naik, A. Trenkwalder, G. Hendl, F. Schreck, R. Grimm, T.G. Tiecke, J.T.M. Walraven, S.J.J.M.F. Kokkelmans, E. Tiesinga and P.S. Julienne, “Exploring an ultra-cold fermi-fermi mixture: interspecies Feschbach resonances and scattering properties of Li-6 and K-40”, Phys. Rev. Lett. 100, 053201 (2008).
2. R. Ilan, E. Grosfeld, K. Schoutens and A. Stern, “Experimental signatures of non-Abelian statistics in clustered quantum Hall states”, Phys. Rev B79, 245305 (2009).
3. F. Massee, Y. Huang, R. Huisman, S. de Jong, J.B. Goedkoop and M.S. Golden, “Nanoscale superconducting gap variations and lack of phase separation in optimally doped BaFe1.86Co0.14As2”, Phys. Rev. B79, 220517R (rapid communication), (2009).
4. Faribault, P. Calabrese, J.S. Caux, “Quantum quenches from integrability: the fermionic pairing model”, J. Stat. Mech. - Theory and Exp, P03018 (2009).
5. H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Non-locality and Communication Complexity”, Rev. Mod. Phys. 82, 665-698 (2010).
6. E.M. Opdam and M.S. Solleveld, “Discrete series characters for affine Hecke algebras and their formal degrees”, Acta Mathematica 205, 105-187 (2010).