Here ions are confined in a linear Paul trap and are cooled by laser light. The ions repel each other due to Coulomb interaction and crystallize in linear, 2d, or 3d structures depending on the number of ions and the shape of the confining potential (see pictures of ion crystals above). Thanks to ultra-high vacuum conditions and the deep confining potential, the ions are well isolated from the environment and stay trapped for days. Quantum information is encoded in the ions’ electronic states and is manipulated by laser or microwave pulses. Also, the ions in the trap can exchange quantum information via their common motion or Rydberg interaction, which makes it possible to perform quantum calculations on an ion string.

There are several **advantages of trapped ion quantum computers over solid-state technologies** like superconducting systems

- Ions are made by nature. There is no variation in properties due to imprecise manufacturing processes.
- Each ion can encode one qubit. In principle, trapping more ions means more qubits.
- The quantum state of ion qubits is manipulated by laser light and read out by fluorescence detection. There is no need for complicated wiring.
- Ion trap quantum computers are operated at room temperature. Microkelvin temperatures are achieved by laser cooling not by technically demanding cryogenics.

The trapped ion approach has set several **highest level benchmarks for quantum computation**, in particular

- Qubit storage times can reach minutes or even hours [1].
- The record for lowest error two-qubit operations (<10-3) is held by trapped ion systems [2, 3].
- Multi-qubit operations can generate large entangled states with up to 20 ions [4, 5].
- Quantum simulations have been performed with up to 53 ion qubits [6].
- Fluorescence detection can determine the quantum state with an error <10-3 [7].

Trapped ions also have a leading role in the implementation of quantum algorithms [8, 9, 10] and quantum error correction [11, 12, 13]. As an example, trapped ions have been used in the first realization of an uncompiled, scalable version of Shor’s factorization algorithm [10].

## Our research

We are the **only group working on trapped ion quantum computers in Sweden**. We are developing techniques for fast and precise quantum calculations on large number of trapped ion qubits. Recently we have **realised a sub-microsecond quantum gate operation** on two trapped ion qubits [14]. By using larger ion crystals with more qubits we plan to further speed up these quantum gates by more than a factor of 10.

## References

[1] **Single-qubit quantum memory exceeding ten-minute coherence time**

Ye Wang, Mark Um, Junhua Zhang, Shuoming An, Ming Lyu, Jing -Ning Zhang, L.-M. Duan, Dahyun Yum, Kihwan Kim

Nature Photonics 11, 646–650 (2017).

[2] **High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits**

C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas

Phys. Rev. Lett. 117, 060504 (2016).

[3] **High-Fidelity Universal Gate Set for 9Be+ Ion Qubits**

J. P. Gaebler, T. R. Tan, Y. Lin, Y. Wan, R. Bowler, A. C. Keith, S. Glancy, K. Coakley, E. Knill, D. Leibfried, D. J. Wineland

Phys. Rev. Lett. 117, 060505 (2016).

[4] **Observation of Entangled States of a Fully Controlled 20-Qubit System**

Nicolai Friis, Oliver Marty, Christine Maier, Cornelius Hempel, Milan Holzäpfel, Petar Jurcevic, Martin B. Plenio, Marcus Huber, Christian Roos, Rainer Blatt, Ben Lanyon

Phys. Rev. X 8, 021012 (2018).

[5] **14-qubit entanglement: creation and coherence**

T. Monz, P. Schindler, J.T. Barreiro, M. Chwalla, D. Nigg, W.A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt

Physical Review Letters 106, 130506 (2011).

[6] **Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator**

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, C. Monroe

Nature 551, 601(2017).

[7] **High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit**

T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, and D. M. Lucas

Phys. Rev. Lett. 113, 220501 (2014).

[8] **Implementation of the semiclassical quantum Fourier transform in a scalable system**

J. Chiaverini, J. Britton, D. Leibfried, E. Knill, M. D. Barrett, R. B. Blakestad, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, T. Schaetz, D. J. Wineland

Science 308, 997 (2005).

[9] **A quantum information processor with trapped ions**

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. X. Wang, S. Quint, M. F. Brandl, V. Nebendahl, C. F. Roos, M. Chwalla, M. Hennrich and R. Blatt

New Journal of Physics 15, 123012 (2013).

[10] **Realization of a scalable Shor algorithm**

Thomas Monz, Daniel Nigg, Esteban A. Martinez, Matthias F. Brandl, Philipp Schindler, Richard Rines, Shannon X. Wang, Isaac L. Chuang, Rainer Blatt

Science 351, 1068 (2016).

[11] **Realization of quantum error correction**

J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton,W.M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, D. J. Wineland

Nature 432, 602 (2004).

[12] **Experimental repetitive quantum error correction**

P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt

Science 332, 1059-1061 (2011).

[13] **Quantum computations on a topologically encoded qubit**

D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hennrich, T. Monz, M. A. Martin-Delgado, R. Blatt

Science 345, 302 (2014).

[14] **Sub-microsecond entangling gate between trapped ions via Rydberg interaction**

Chi Zhang, Fabian Pokorny, Weibin Li, Gerard Higgins, Andreas Pöschl, Igor Lesanovsky, Markus Hennrich

arXiv:1908.11284.

## Our previous key results on quantum computation with trapped ions

A completely list of publications from the Quantum Optics and Spectroscopy Group at University of Innsbruck can be found here.

**A quantum information processor with trapped ions**

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. X. Wang, S. Quint, M. F. Brandl, V. Nebendahl,

C. F. Roos, M. Chwalla, M. Hennrich and R. Blatt

New Journal of Physics 15, 123012 (2013).

**14-qubit entanglement: creation and coherence**

T. Monz, P. Schindler, J.T. Barreiro, M. Chwalla, D. Nigg, W.A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt

Physical Review Letters 106, 130506 (2011).

**An open-system quantum simulator with trapped ions**

J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt

Nature 470, 486-491(2011).

**Universal digital quantum simulation with trapped ions**

B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro,

M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, C. F. Roos

Science 334, 57-61 (2011).

**Quantum simulation of dynamical maps with trapped ions**

P. Schindler, M. Müller, D. Nigg, J. T. Barreiro, E. A. Martinez, M. Hennrich, T. Monz, S. Diehl, P. Zoller, R. Blatt,

Nature Physics 9, 361–367 (2013).

**Quantum computations on a topologically encoded qubit**

D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hennrich, T. Monz, M. A. Martin-Delgado, R. Blatt

Science 345, 302 (2014).

**Experimental repetitive quantum error correction**

P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt

Science 332, 1059-1061 (2011).

**Demonstration of genuine multipartite entanglement with device-independent witnesses**

J. T. Barreiro, J.-D. Bancal, P. Schindler, D. Nigg, M. Hennrich, T. Monz, N. Gisin, R. Blatt

Nature Physics 9, 559–562 (2013).

**Experimental multiparticle entanglement dynamics induced by decoherence**

J.T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C.F. Roos, M. Hennrich, and R. Blatt

Nature Physics 6, 943–946 (2010).