Molecular spin qubits

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. 

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... 

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. 

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. 

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... 

Various schemes for hybrid quantum processors based on molecular ensembles as quantum memories and optical interfaces have been proposed. In Ref. [17], a hybrid quantum circuit using ensembles of cold polar molecules with solid-state quantum processors is discussed. As described above, the quantum memory is realized by collective spin states (ensemble qubit), which are coupled to a high-Q stripline cavity via microwave Raman processes. This proposal combines both molecular ensemble and stripline resonator ideas. A variant of this scheme using collective excitations of rotational and spin states of an ensemble of polar molecules prepared in a dipolar... 

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