QUROPE Quantum Information Processing and Communication in Europe

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, 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] on the other hand certain spin systems are shielded well enough from their environments such that room temperature operation seem feasible. 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.

Another solid basis for quantum information processing, which relies on new molecules engineered with features suitable for qubit encoding and entanglement, is provided by Single Molecular Magnets (SMMs). Current research activity focuses on the control of the coherent spin dynamics in molecular spin clusters, which implies the control of decoherence mechanisms both at synthetic level and in terms of modelling. While most of the experiments are currently performed on bulk crystals, the final goal of manipulating single molecular spins is drawing increasing attention towards the grafting of molecules at surfaces and the development of techniques for readout.

Research groups engaged in QIP research regarding impurity spins in solids in Europe include A. Briggs (Oxford, UK), P. Grangier (Orsay, FR), O. Guillot-Noël and P. Goldner (Paris, FR), W. Harneit (Berlin, DE), S. Kröll (Lund, SE), J.L. LeGouët (Orsay, FR), M. Mehring (Stuttgart, DE), K. Mølmer (Aarhus, DK), J.F. Roch (Cachan, FR), M. Stoneham (London, UK), D. Suter (Dortmund, DE), J. R. Hanson (Delft, NL), J. Wrachtrup (Stuttgart, DE). Research groups working on QIP with molecular spin clusters in Europe include D. Loss (Basel, CH), B. Barbara and W. Wernsdorfer (Grenoble, FR), M. Affronte and F. Troiani (Modena, IT), D. Gatteschi (Florence , IT), R. E. P. Winpenny and G. Timco (Manchester, UK).

B. State of the art

Impurity spins: 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:

• Magnetic resonance on single defects detected by charge transport and single spin state measurements by optical techniques.
• Multipartite entanglement on single defect spins as well as mutual coherent coupling between distant defect spins in diamond.
• Accurate preparation and readout of ensemble qubit states. Arbitrary single-qubit operations characterised by quantum state tomography with a fidelity >90% in rare earth crystals.
• The preparation of Bell states with electron and nuclear spin ensembles as well as a three qubit Deutsch-Jozsa algorithm has been achieved.
• A scalable architecture has been developed for N@C60 on Si and decoherence times have been measured to be up to 1 s.

Single molecular magnets: Quantum dynamics of spins in molecular clusters has been deeply studied by a number of fundamental works in the last decade. Decoherence and dephasing mechanisms have been investigated in assemblies: the intrinsic coherence times are expected to be longer than microseconds (preliminary experiments provide a lower bound of few tens of ns); similarly, the switching rates for one-qubit and two-qubit gates are estimated to be on the order of hundreds of picoseconds.

Recent important achievements are:

• Proposals for the implementation of the Grover’s algorithm in high spin SMMs [4], and of universal solid state quantum devices in antiferromagnetic spin clusters;
• Synthesis of specific molecules providing promising test-beds for scalable schemes [5];
• Entanglement of states belonging to different molecules inspired both synthesis of new molecular dimers and elaboration of specific quantum algorithms that exploit some features of molecular clusters.
• Spin qubits can be coupled to a superconducting microwave cavity that acts as a "quantum bus", as it is usually done for superconducting qubits.
• It has been demonstrated that the nuclear spin of an individual metal atom embedded in a single-molecule magnet can be read out electronically.

C. Strengths and weaknesses

Impurity spins: 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.

Single molecular magnets: The bottom-up approach used by supra-molecular chemistry offers simple and relatively cheap processes for the fabrication of quantum nanosized molecules exhibiting multi-functionality like the switchability of magnetic states with light, resonance at RF-MW radiation, etc. Moreover, the control on and the sharp definition of eigenstates and eigenvalues in magnetic molecules provides an extraordinary stimulus for the development of new quantum algorithms and schemes. In the latter case, the main issue would be to prove that single, isolated molecules behave not much differently from what is observed in experiments performed on assemblies of molecules.

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

Impurity spins: 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 and two qubit operations. Major efforts are concentrated in the US and Australia.
• Defects in diamond heads towards generation of coupled defect center arrays and incorporation into photonic structures. For this advanced nanoimplantation techniques as well as production of photonic cavities needs to be refined.
• For rare earth crystals short term goals include faster gate operations using pulses developed by optimal control theory, demonstration of two-qubit gates and the development of single ion readout capabilities for scaling up to several qubits.
• 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.

Single molecular magnets: The main goals can be summarized as follows:

• To engineer new molecular clusters for the optimization of the coherent dynamics of spins, and design, synthesize and characterize controlled molecular linkers between spin clusters;
• To set up experiments for the direct observation of coherent dynamics (for instance Rabi oscillations, spin echo experiments), and probe, understand and reduce the intrinsic decoherence mechanisms in specific cluster qubits;
• To develop computational schemes exploiting the features of molecular cluster qubits, and study different functionalities (f.i. switchability) of molecules useful for specific tasks in complex architectures of QIP. 

E. Long-term goals (10 years and beyond)

For impurity spins the main long-term challenges are

• Coupling of defects in wide band gap semiconductors to an optical cavity mode. Implantation of defects with nm accuracy in registry with control electrodes. Optical addressing of single defects within dense defect arrays;
• For rare earth ions, efforts should be joined with crystal growth research (inorganic chemistry) to create appropriate materials for larger scale systems. Techniques should also be developed for entangling remote systems to achieve full scalability;
• 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.

For single molecular magnets, the long-term challenges can be summarized as follows:

• Definition of reliable procedures for preparing, characterising and positioning (arrays of) molecular spin cluster qubits;
• Development of models and experimental methods for efficient read-out.

F. Key references

[1] B. Kane, “A silicon-based nuclear spin quantum computer”, Nature 393, 133 (1998)
[2] R. Hanson, D. Awschalom. "Coherent manipulation of single spins in semiconductors" Nature 453, 1043 (2008), P. Neumann et al. "Multipartite entanglement of single spins in diamond", Science 320, 1326 (2008)
[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] M.N. Leuenberger, D. Loss, “Quantum Computing in Molecular Magnets’’, Nature 410, 789 (2001)
[5] F. Troiani A. Ghirri, M. Affronte, P. Santini, S. Carretta, G. Amoretti, S. Piligkos, G. A. Timco, R. E. P. Winpenny, “Molecular engineering of antiferromagnetic rings for quantum Computation”, Phys. Rev. Lett. 94, 207208 (2005)