# Quantum Computation with Trapped Ions

##### Today computers are indispensable even in our daily life. Each year engineers create more powerful computers simply by making them smaller. Can this continue for ever? With the current rate of miniaturization in about 20 years single atoms will be used for storage and manipulation of information. For such small objects, however, our usual intuition fails, since they do not follow classical, but quantum mechanical rules. Is it still possible to build a computer based on these strange, new quantum laws?

Already in 1982, Richard Feynman pronounced the idea that certain calculations could be performed much more efficiently with quantum mechanical than with classical computers. In 1994, the first computational problem was proved to be solvable substantially faster with a "quantum algorithm" (the Shor algorithm) compared to a classical one. Nevertheless, the physics and mathematics behind this is little known to most people, and experimental exploration of this fascinating subject has just started. Our approach is based on well controlled laser beams and a series of calcium ions, confined to a space of less than a hair wide.

*Linear ion trap: By applying voltages to the trap electrodes, a string of ions can be held in the trap *

*for several days. The lower picture shows a string*

of 6 Calcium 40 ions taken with a ordinary CCD camera.

of 6 Calcium 40 ions taken with a ordinary CCD camera.

Our group has demonstrated the basic principles of such a quantum computer. Currently, we are working with up to eight ionized Calcium atoms suspended in free space by electromagnetic forces. Each atom represents one quantum bit (qubit). In contrast to classical bits, a qubit can take any value between 0 and 1, so that it contains partially both values at the same time. Due to this property it is possible to calculate an algorithm for both values in parallel. Thus loosely speaking, quantum computers can solve different tasks simultaneously. For certain tasks - like simulation of complicated quantum processes - even a 40-bit quantum computer would be much more powerful than any existing classical computer.

*Sketch of the experimental setup. The quantum state of the trapped ions is manipulated by laser pulses and finally detected by measuring the ion's fluorescence on a CCD camera. Absence and presence of fluorescence signal the qubit's "0" and "1" states, respectively. *

In our prototype quantum computer, we use lasers to manipulate quantum information encoded in the atoms. The atomic states evolve according to the chosen strength and frequency of the laser pulse. Also, lasers serve to read out the qubits: depending on their state, the atoms either emit light or remain dark which can be readily detected with a CCD-camera. One of the biggest challenges is to control the interaction between these tiny quantum bits. Similarly to classical computing, for quantum computers there exists a small set of (quantum) gates with which every quantum algorithm can be realized. Using two trapped ions, we have demonstrated an important quantum gate, the controlled-NOT operation (F. Schmidt-Kaler et al.) which - together with single qubit gates - constitutes such a set of gates. We have realized the quantum mechanical equivalent to the Toffoli gate - a controlled-controlled-NOT gate (T. Monz et al.). This gate could become an essential element for implementing quantum error correction (QEC).

## Exploring quantum physics

Quantum computing techniques are also very useful tools for exploring the strange rules of quantum physics. We have created entangled states of up to eight ions (H. Häffner et al.). Here, the state of a single particle is completely undetermined even though the state of the whole system is well-defined. These states are used to investigate fundamental properties of quantum physics like, for example, the collapse of the wave function induced by measurements. Also, we can demonstrate the non-local nature of quantum theory, i.e. the fact that the quantum state of an object can be inextricably linked to the quantum state of another (distant) object. This property plays a key role in quantum state teleportation.

*A closer look at the quantum computing setup showing a box of mu-metal for magnetic shielding, inside the vacuum vessel housing the ion trap and laser beam steering optics around.** *

## Quantum teleportation with ions

Quantum state teleportation is a scheme that solves the task of transferring an unknown quantum state from one location to another. First achieved with entangled photons, it is also applicable to atomic quantum states. In our implementation (M. Riebe et al.) based on three ions, we show that the quantum information encoded in one ion is deterministically transferred to another ion at any time. Although the teleportation distance is currently limited to 10 micrometers, the development of segmented ion traps with complex electrode structures will overcome this limitation and increase the distance over which quantum information can be communicated.

* Schematic of the teleportation of a quantum state.*

## Entanglement swapping with ions

A similar protocol as for quantum teleportation can be used to entangle two ions that have never interacted before. Such deterministic entanglement swapping (M. Riebe et al.) was recently show by our group (C. F. Roos et al. and H. Häffner et al.). Entanglement swapping is of particular significance for the next generation of quantum computers where it could be used to entangle and link qubits in distant regions of the quantum processor.

## Quantum computation with logical qubits

A quantum computer can encode logical information in superpositions of quantum states. The information is contained in the relative probabilities of the two states of the qubits, but also their respective phase. Environmental effects like magnetic field fluctuations or laser instabilities can result in dephasing, and therefore loss, of quantum information. However, special states - the so called decoherence free subspace (DFS) - are insensitive to dephasing. We have shown encoding of qubits within that subspace (M. Chwalla et al.), storing information in a way that is only limited by the lifetime of the qubit states. Currently, we are working on techniques to use such robust encoding for calculating arbitrary algorithms

* View into the vacuum chamber with the ion trap inside.*

## Project members

(Lintrap Group picture)

- Roman Stricker (Master's student)
- Alexander Erhard (PhD student)
- Esteban Martinez (PhD student)
- Daniel Nigg (PhD student)
- Thomas Monz (Postdoc)
- Philipp Schindler (project leader)
- Rainer Blatt (group leader)

Former members: Julio Barreiro, Michael Chwalla, Stefan Quint