= ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS =

QUANTUM COMPUTING

IMPURITY SPINS IN SOLIDS

A. Physical approach and perspective

Storage and processing of information can be carried out using individual atomic and molecular spins in condensed matter. Systems falling into this category include dopant atoms in semiconductors like phosphorous or deep donors in silicon or color centers in diamond, nitrogen or phosphorus atoms in molecules like C60 [4], rare earth ions in dielectric crystals and unpaired electrons at radiation induced defects or free radicals in molecular crystals. The main attraction of spins in low-temperature solids is that they can store quantum information for up to several thousand seconds [1]. Specific systems have been selected based on criteria like: dephasing time, optical access, single quantum state readout, and nanostructuring capabilities. While most of these systems are scalable in principle, technical progress in single quantum state readout, addressability and nanoengineering is necessary.

Research groups engaged in QIP research regarding impurity spins in solids in Europe include A. Briggs (Oxford, UK), P. Grangier (Orsay, F), O. Guillot-Noël and P. Goldner (Paris, F), S. Kröll (Lund, S), J.L. LeGouët (Orsay, F), W. Harneit (FU Berlin), M. Mehring (Stuttgart, D), K. Mølmer (Aarhus, DK), J.F. Roch (Cachan, F), M. Stoneham (London, UK), D. Suter (Dortmund, D), J. Twamley (Maynooth, IR), J. Wrachtrup (Stuttgart, D)

B. State of the art

Atomic and molecular spins in solids have received considerable attention as qubits. Already Kane's [1] proposal has underlined the basic challenges and opportunities of such systems in quantum computing. In the meantime a number of related systems like dilute rare earth ions, color centers, random deep donors in silicon with optically controlled spin and defects in wide and narrow band gap semiconductors have underlined their potential usefulness in QIP [2]. Most approaches use electron or nuclear spin degrees of freedom as quantum bits. The specific advantages of spin systems includes long decoherence times [3] and access to highly advanced methods for precise manipulation of quantum states. The experimental techniques that have made liquid state NMR the most successful QIP technique in terms of precise manipulation of quantum states so far are currently being transferred to solid-state systems. These systems may be able to overcome the scalability problems that plague liquid state NMR while preserving many of the advantages of today's liquid state work.

In detail the following landmark results have been achieved:

1. Magnetic resonance on single defects detected by charge transport and single spin state measurements by optical techniques.
2. Single and two qubit quantum gates on single defect spins in diamond.
3. For rare earth crystals preparation and readout of ensemble qubit states Rabi flops of a qubit, and qubit decoherence times on the order of seconds have been achieved. State control and quantum state tomography with a fidelity > 90% was shown.
4. The preparation of Bell states with electron and nuclear spin ensembles as well as a three qubit Deutsch-Jozsa algorithm has been achieved.
5. A scalable architecture has been developed for N@C60 on Si and decoherence times have been measured to be up to 1 s.

All of these are European achievements (point 3 was partly achieved in Australia).

C. Strengths and weaknesses

The strength of defect center QIP in solids are the long decoherence times of spins even under ambient conditions and the precise state control. Depending on the system, electrical as well as optical single spin readout has been shown (fidelity of 80%). Substantial progress in the nanopositioning of single dopants with respect to control electrodes has been achieved. Weaknesses are: Electrical and optical readout of spin states has been shown up to now for only a single type of defect. Nanopositioning of defects is still a major challenge (which has seen dramatic progress for phosphorus in silicon). However there are schemes, based on deep donors in Si, where nanopositioning is not needed. Instead the randomness is exploited so as to make maximum use of spatial and spectral selection to isolate qubits and their interactions. Manipulation and readout is optical. The situation is similar for rare earth crystals, but in this case a fully scalable scheme still needs to be developed.

D. Short-term goals (next 3-5 years)

Impurity systems form a bridge for transferring quantum control techniques between atomic and solid state systems. Close interaction between the atomic physics and solid state communities is a key ingredient for achieving this.

• The mid term perspectives for phosphorus in silicon are the demonstration of single spin readout by 2005 and two qubit operations by 2006. Major efforts are concentrated in the US and Australia.
• Optical readout of defects in diamond heads towards a three qubit system and demonstration of teleportation by 2006. For further scaling advanced nanoimplantation techniques need to be developed.
• For rare earth crystals the expected developments in the near future (1 year) includes a proposal of a scalable scheme and the demonstration of two-qubit gates in this scheme. On a time scale of a few years, scaling up to several qubits will be investigated. These require either new and partly untested materials or development of single ion readout.
• For N@C60, state readout for single spins should be demonstrated by 2006. For the scheme based on deep donors in Si or diamond, short term goals are demonstrations of all the key steps of fabrication, preparation, readout, and manipulation.

Excluding the first, all other goals are within reach of European laboratories.

E. Long-term goals (2010 and beyond)

• Coupling of defects in wide band gap semiconductors to an optical cavity mode. Implantation of defects with nm accuracy in registry with control electrodes. Improvement in optical detection efficiency by one order of magnitude to allow room temperature single-spin state read-out.
• For rare earth ions efforts should be joined with crystal growth research (inorganic chemistry) to create appropriate materials for larger scale systems. It can be expected that quantum computing in RE crystals will both contribute to and benefit from the development and knowledge base in the rare earth crystal area in general.
• Few-qubit device could be built on the basis of N@C60 by integrating nanopositioning of molecules with single-spin readout devices and control electronics.
• Few-qubit (up to perhaps 20 qubit) devices based on deep donors in silicon or silicon- compatible systems seem possible. Such devices should be linked into larger groups by flying qubits based largely on technology known from other fields. Achieving higher temperature is also of importance here.

F. Key references

[1] B. Kane, A silicon-based nuclear spin quantum computer, Nature 393, 133 (1998).

[2] S. Lloyd and C. Hammel, 'Unique' qubit approaches to QIP and QC, in "A Quantum Information Science and Technology Roadmap, Part 1: Quantum Computation", Version 2.0, section 6.8 and references therein; available from http://qist.lanl.gov.

[3] E. Yablonowitch, H.W. Jiang, H. Kosaka, H.D. Robinson, D.S. Rao, T. Szkopek Optoelectronic quantum telecommunications based on spins in semiconductors , Proc. IEEE 91, 761 (2003).

[4] W. Harneit, Phy. Rev. A 65, 032322 (2002); D. Suter, K. Lim, Phys. Rev. A 65, 052309 (2002); W. Harneit, C. Meyer, A. Weidinger, D. Suter, J. Twamley, phys. stat. sol.(b) 233, 453 (2002).

Category:ERA Quantiki Project