# Semiconductor quantum dots

## ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

### QUANTUM COMPUTING

#### SEMICONDUCTOR QUANTUM DOTS

A. Physical approach and perspectiveIII-V Semiconductor heterostructures (e.g. GaAs, InP, InAs, etc) form the backbone of today’s opto-electronics combining ultrafast electronics (e.g. HEMT), low-power optics together with the conversion between electronics and optics. The industrial development of this material class has also been fruitfully utilized in the field of QIPC. Employing nanofabrication and/or self-assembling techniques, quantum dots have been defined that can be addressed electrically and/or optically. The emerging field of quantum opto-electronics can provide an interface between solid state qubits and single-photon quantum optics.

Currently, quantum dot (QD) spin based quantum information processing (QIP) is pursued by 10 groups worldwide, 5 of which are located in Europe [L. Kouwenhoven (Delft, NL), K. Ensslin (ETH-Zurich, CH), G. Abstreiter (TU-Munich, DE), Ch. Bayer (Dortmund, DE) and A. Imamoglu (ETH-Zurich, CH)], as well as D. Loss (Basel, CH) on the theory side.

B. State of the artThe quantum dot qubits being developed in III-V semiconductors are based on the charge or spin properties of single electrons. Stable and reproducible quantum dots have been developed using split-gate techniques that can be loaded with exactly zero, one or two electrons. Electrical signals in the kHz to GHz range allow one to transfer reliably an individual electron from one quantum dot to another (Delft result). Circuits of such quantum dot devices form the basis for the Loss-DiVincenzo proposal (Basel result) exploiting the electron spin as the qubit degree of freedom. In this scheme the electron charge is used for manipulation of the carriers. The spin dynamics is largely decoupled from the charge motion and remains coherent over long time scales. An important aspect of the Loss-DiVincenzo proposal is the full on-off control over the two-qubit interaction. In split-gate quantum dots this control via the spin-spin exchange interaction can be realized simply by switching electrical gate voltages. Charged qubits were also discussed by the Oxford group, and served as a model for early implementations of quantum logic gates.

The current status in the field is the realization of highly controllable quantum dots in various labs. (The material and nanofabrication flexibility is certainly strong in this QIPC approach.) The spin qubit states as well as the two qubit superposition states are easily resolved in transport measurements. An all-electrical readout of individual spins (e.g. single shot measurements) has been realized (Delft result). An ensemble average provides values for the spin life time of the order of milliseconds. It is important to note that these values are measured in an electrical circuit with all components activated and thus they include the effects from a realistic back-action (Delft result).

Quantum dots are often referred to as artificial atoms. Some of the fundamental atom-like properties of optically active quantum dots, such as photon antibunching and presence of absorption/emission lines predominantly broadened by radiative recombination, have already been confirmed experimentally. In contrast to atoms and electrically-defined quantum dots discussed earlier, optically active quantum dots suffer from spatial and spectral inhomogeneity; i.e. each quantum dot has an energy and location that is a priori impossible to be determined with reasonable accuracy. This property has important but not necessarily negative consequences for their applications in quantum information processing.

Arguably, the most successful application of quantum dots in quantum information processing has been the realization of high-efficiency single-photon sources (first results from Imamoglu et al., now at ETH Zurich). The fact that quantum dots exhibit no center-of-mass motion and that they can be embedded in nano-cavity structures with ultra-small mode volumes, enabled generation of a train of optical pulses that never contain more than a single photon, with efficiency exceeding 30%. In addition to potential applications in unconditionally secure quantum key distribution, such a source could also be used to produce indistinguishable single- photon pulses that form the backbone of linear optics quantum information processing schemes.

Cavity QED has been a central element in many quantum optics based quantum computation proposals. Recently, three groups have reported the observation of strong-coupling regime for a single quantum dot embedded in a nano-cavity structure (Würzburg result). While these experiments relied on a random spatial and spectral coincidence between the quantum dot and cavity modes, recent advances in growth and processing have demonstrated that it is possible to deterministically locate a single quantum dot at the anti-node of a photonic crystal nano-cavity structure which is in turn spectrally resonant with the quantum dot exciton line (ETH Zurich result).

The progress in optical manipulation of quantum dot spins has been relatively slow. Deterministic charging of a single quantum dot with a single excess electron has been demonstrated by several groups. More recently, resonant laser transmission measurements on a single charged quantum dot have been used to demonstrate spin-selective optical absorption, or equivalently, Pauli-blocking of optical transitions (LMU and ETH-Zurich result).

C. Short-term goals (next 3-5 years)- Integrate electrically controlled single-qubit gates, two-qubit gates and single-shot read-out into a single device
- Demonstrate optically controlled single- and two-qubit gates
- Realize coupling between two distant spins on a chip, via striplines or on-chip cavities
- Interconvert between single electron spins and single-photon polarization (standing qubit to flying qubit conversion)
- Develop the ability to measure and/or control the nuclear spin bath, in order to retrieve the intrinsically long electron spin coherence times
- Extend system size from two qubits to three
- Implement simple quantum algorithms, error correction protocols, etc.
- Explore and compare alternative semiconductor materials for quantum dots

- Develop multi-qubit circuits in a scalable architecture
- Improve fidelity to the level needed for fault tolerance
- Demonstrate a quantum repeater (photon to spin to photon conversion)

[1] D. Loss and D. DiVincenzo, ‘‘Quantum computation with quantum dots’’, Phys. Rev. A 57, 120–126 (1998).

[2] J. M. Elzerman, R. Hanson, L. H. Willems Van Bereven, B. Witkamp, L. M. Vandersypen, and L. P. Kouwenhoven, ‘‘Single-shot read-out of an individual electron spin in a quantum dot’’, Nature 430, 431 (2004).

[3] M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, ‘‘Optically programmable electron spin memory using semiconductor quantum dots’’, Nature 432, 81 (2004).

[4] A. Högele, M. Kroner, S. Seidl, and K. Karrai, M. Atatüre, J. Dreiser, and A. Imamoglu, A. Badolato, B. D. Gerardot, and P. M. Petroff ‘‘Spin-selective optical absorption of singly charged excitons in a quantum dot’’, cond-mat/0410506, http://arxiv.org.

[5] J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Kelfysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, ‘‘Strong coupling in a single quantum dot-semiconductor microcavity system’’, Nature 432, 197 (2004).

[6] L. Childress, J. M. Taylor, A. S. Sorensen, M. D. Lukin, ‘‘Fault-tolerant Quantum Communication Based on Solid-state Photon Emitters’’, quant-ph/0410123, http://arxiv.org.