Qubits

Plenary 7(5. N I Koroteev et al, e-mail address Koroteev nik.phys.iusu.su (CARS/CSRS, CAHRS, BioCARS). A survey of the many applications of what we call the Class II spectroscopies from third order and beyond. 2D and 3D Raman imaging. Coherence as stored infonuation, quantum infonuation (the qubit ). Uses tenus CARS/CSRS regardless of order. BioCARS is fourtli order in optically active solutions. 

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 2.11 Sample fragment of a quantum circuit illustrating the effect of some typical quantum gates a SWAP operation between the upper and centre qubits is effected through three consecutive controlled-NOT ...

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.

At least one qubit is different from all others and can be addressed individually this can be simply the final spin of a spin chain. 

Figure 2.13 The first 2" magnetic states of the system are assigned to combinations of n qubits. The rest of the spectrum is outside of the computational basis.

Considering any of these paradigms, a minimal goal for toy models would be to manipulate the quantum dynamics of a small number of spin levels , and that requires a known and controlled composition of the wavefunction, sufficient isolation and a method for coherent manipulation. As illustrated in Figure 2.13, the first few magnetic states of the system are labelled and thus assigned qubit values. The rest of the spectrum is outside of the computational basis, so one needs to ensure that these levels are not populated during the coherent manipulation. 

Combining Physical Qubit Implementations with Lanthanide Complexes... 

The use of trapped ions, or trapped atoms, as qubits [46, 47] is one of the most mature techniques. They have been used to achieve remarkable feats, mainly in the field of quantum simulation [48]. However, there is no clear link between this technology and molecular systems. 

Table 2.4 Some examples of physical qubits, with an estimation of their transversal relaxation times and error rate in one- or two-qubit gates (for details see [33] and references therein).

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... 

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... 

Figure 2.15 Proposed setup to effect two-qubit gates onto Mo12V2, a mixed-valence POM that combines two localized electrons on the lateral vanadyl groups with a variable number of delocalized electrons in the Keggin core.

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... 

A. and Barbara, B. (2007) Rare-earth solid-state qubits. Nat. Nanotechnol, 2, 39-42. 

Benjamin, S.C. (2004) Multi-qubit gates in arrays coupled by always-on interactions. New J. Phys., 6, 61, (1-17). 

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.,... 

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