Spin qubits

Photons in quantum optical cavities also constitute excellent qubit candidates [52]. Resonant coupling of atoms with a single mode of the radiation field was experimentally achieved 25 years ago [53], and eventually the coherent coupling of quantum optical cavities with atoms or (simple) molecules was suggested as a means to achieve stable quantum memories in a hybrid quantum processor [54]. There might be a role to play for molecular spin qubits in this kind of hybrid quantum devices that combine solid-state with flying qubits. 

A wide variety of proof-of-principle systems have been proposed, synthesized and studied in the field of molecular spin qubits. In fact, due to the fast development of the field, several chemical quantum computation reviews using magnetic molecules as spin qubits have been published over the past decade, covering both experimental and theoretical results [67-69]. Only in a minority of experiments implementing non-trivial one- or two-qubit gates has been carried out, so in this aspect this family is clearly not yet competitive with other hardware candidates.1 Of course, the main interest of the molecular approach that makes it qualitatively different is that molecules can be chemically engineered to tailor their properties and acquire new functionalities. 

Before reviewing existing examples, a very brief explanation on the mechanisms of decoherence for molecular spin qubits is necessary more details are available elsewhere [67]. Broadly speaking, the three decoherence sources for these systems are spin bath decoherence, oscillator bath decoherence and pairwise dipolar decoherence, and can be regulated by a combination of temperature, magnetic field and chemical design of the system [70]. The spin bath mainly consists of nuclear spins, but in general it also includes any localized excitations that can couple to the 

1) Here we will focus on electron spin qubits and thus we will not be discussing NMR quantum computing, where molecules played a key role in the early successes of quantum information processing. 

Research on multi-qubit molecules starts with the synthesis and characterization of systems that seem to embody more than one qubit, for example, systems with weakly coupled electron spins. Indeed, many molecular structures include several weakly coupled magnetic ions [76-78]. On a smaller scale, the capability of implementing a Controlled-NOT quantum logic gate using molecular clusters 

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Mononuclear Lanthanide Complexes Use of the Crystal Field Theory to Design Single-Ion Magnets and Spin Qubits... 

On the other hand, lanthanides with 100% isotopical purity such as terbium or holmium are preferred to simplify the operation and minimize decoherence in spin qubits. In this respect, the existence, for some lanthanides, of a manifold of electronuclear states can provide additional resources for the implementation of multiple qubit states within the same molecule [31]. All atoms in the first coordination sphere should be oxygen, and the sample should be deuter-ated if the compound contains hydrogen, to avoid interaction with other nuclei spins. Again, POM chemistry has been shown to provide ideal examples of this kind. 

The final section deals with known examples of molecular spin qubits based on lanthanide SIMs. Distinction is made between single-qubit molecules and molecules which embody more than one qubit. This section includes some comments about decoherence in these molecular systems and strategies to control it. 

Quantum systems of any kind can in principle be candidates for quantum hardware, including different kinds of spin qubits we briefly review some of these in the next section. Much effort has been expended on the question of which physical systems are best suited for use in QIP, but no ultimate answer has been found so far. A much quoted list of conditions to build computers was established by DiVincenzo [35], but one has to note that some of these restrictions are specific to the quantum circuit paradigm. 

Figure 2.12 Section of an (-ABC—)n magnetic heteropolymer, or periodic array of spin qubits of three different types. Note than while both B sites are chemically equivalent.

J., van Slageren, J., Coronado, E. and Luis, F. (2012) Gd-based single-ion magnets with tunable magnetic anisotropy molecular design of spin qubits. Phys. Rev. Lett., 108, 247213. 

Baldovi, J. J., Clemente-Juan, J. M., Coronado, E., Gaita-Arino, A. and Gimenez-Saiz, C., (2014) Construction of a General Library for the Rational Design of Nanomagnets and Spin Qubits... 

Taylor, J.M., Zibrov, A.S., Jelezko, F., Lukin, M.D., Wrachtrup, J. and Hemmer, P.R. (2006) Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science, 314, 281—285. 

Morello, A., Stamp, P.C.E. and Tupitsyn, I. (2006) Pairwise decoherence in coupled spin qubit networks. Phys. Rev. 

H. (2013) Coherent manipulation of spin qubits based on polyoxometa-lates the case of the single ion magnet [GdW30P5On0]14-. Chem. Commun.,... 

Quantum Computing with Electron Spin Qubits... 

Single (or multiple) electrons or holes can be bound locally to a small semiconductor nanostructure or to a single impurity in a solid. The resulting discrete energy levels can be used to define a spin qubit. Coherent control and read-out... 

As an alternative to QDs, silicon can be doped with single atom impurities, in particular phosphorus, which acts as an electron donor. Donors can be implanted individually with a precision of about 10 nm. Either the 31P nuclear spin or the unpaired electron can be used as qubits [63, 64]. An advantage of silicon is its widespread use in current electronics, meaning that QC might profit from methods and technologies already developed for their classical cousins . Also, spins in silicon can attain extremely high coherence times experiments on 28 Si-enriched silicon show spin coherence times T2 exceeding 10 s [65]. The read-out and coherent manipulation of individual spin qubits in silicon have been recently achieved [66]. 

Some properties of these ions make them particularly appealing as solid state spin qubits. The fact that they can be diluted into diamagnetic crystals offers a simple method to optimize their quantum coherence. Similarly to trapped ions, they are simple each qubit is embodied by a single atom. Yet, their immediate... 

A different sequence of electromagnetic pulses can be used to directly monitor Rabi oscillations between the two spin qubit basis states (Figure 7.7). As expected,... 

Control of the Magnetic Anisotropy of Lanthanide Ions Chemical Design of Spin Qubits 7.3.2.1 Mononuclear Single Molecule Magnets... 

The synthesis of mononuclear molecular complexes, in which a single ion is wrapped by a shell of organic ligands, provides an alternative method for creating arrays of nearly isolated lanthanide spin qubits. The study of these materials was boosted by Ishikawa and coworkers [94] discovery of magnetic hysteresis in... 

Lanthanide ions offer several salient properties that make them especially attractive as qubit candidates (i) their magnetic states provide proper definitions of the qubit basis (ii) they show reasonably long coherence times (iii) important qubit parameters, such as the energy gap AE and the Rabi frequency 2R, can be chemically tuned by the design of the lanthanide co-ordination shell and (iv) the same molecular structure can be realized with many different lanthanide ions (e.g. with or without nuclear spin), thus providing further versatility for the design of spin qubits or hybrid spin registers. 

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