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A very exciting prospect in coordination chemistry is to manipulate spins within magnetic complexes for the realization of quantum logic operations. An introduction to the requirements for a paramagnetic molecule to act as a 2-qubit quantum gate is provided in this tutorial review. We propose synthetic methods aimed at accessing such type of functional molecules, based on ligand design and inorganic synthesis. Two strategies are presented: (i) the first consists in targeting molecules containing a pair of well-defined and weakly coupled paramagnetic metal aggregates, each acting as a carrier of one potential qubit, (ii) the second is the design of dinuclear complexes of anisotropic metal ions, exhibiting dissimilar environments and feeble magnetic coupling. The first systems obtained from this synthetic program are presented here and their properties are discussed.

A major challenge for realizing quantum computation is finding suitable systems to embody quantum bits (qubits) and quantum gates (qugates) in a robust and scalable architecture. An emerging bottom-up approach uses the electronic spins of lanthanides. Universal qugates may then be engineered by arranging in a molecule two interacting and different lanthanide ions. Preparing heterometallic lanthanide species is, however, extremely challenging. We have discovered a method to obtain [LnLn′] complexes with the appropriate requirements. Compound [CeEr] is deemed to represent an ideal situation. Both ions have a doubly degenerate magnetic ground state and can be addressed individually. Their isotopes have mainly zero nuclear spin, which enhances the electronic spin coherence. The analogues [Ce2], [Er2], [CeY], and [LaEr] have also been prepared to assist in showing that [CeEr] meets the qugate requirements, as revealed through magnetic susceptibility, specific heat, and EPR. Molecules could now be used for quantum information processing.

We show that a chemically engineered structural asymmetry in ½Tb 2 molecular clusters renders the two weakly coupled Tb 3þ spin qubits magnetically inequivalent. The magnetic energy level spectrum of these molecules meets then all conditions needed to realize a universal CNOT quantum gate. A proposal to realize a SWAP gate within the same molecule is also discussed. Electronic paramagnetic resonance experiments confirm that CNOT and SWAP transitions are not forbidden. DOI: 10.1103/PhysRevLett.107.117203 PACS numbers: 75.50.Xx, 03.67.Lx, 75.40.Gb, 85.65.+h Quantum computation [1,2] relies on the physical realization of quantum bits and quantum gates. The former can be in any of two distinguishable states, denoted here as spinup j *i and spin-down j +i, and also, as opposed to classical bits, in any arbitrary linear superposition of these. The latter involve controlled operations on two coupled qubits [1]. The universal controlled-NOT (CNOT) gate is the archetype of such a controlled operation. It flips the target qubit depending on the state of the control qubit [see Fig. 1(a)]. This definition implies that each of the two qubits should respond inequivalently to some external stimulus, e.g., electric or magnetic fields. A SWAP gate exchanges the states of both qubits; i.e., it takes j*i 1 j+i 2 to j+i 1 j*i 2 and vice versa.Solid-state candidates for these elements include superconducting circuits [3][4][5], spins in semiconductors [6][7][8], and molecular nanomagnets [9][10][11][12][13][14]. The last ones are attractive for scalability, since arrays of identical magnetic molecules can be prepared and grafted to solid substrates or devices via simple chemical methods [15,16]. The recent development of devices able to induce and readout the spin reversal of individual atoms [17][18][19] might also make feasible the coherent manipulation of one of these molecular qubits. State-of-the-art achievements with molecular nanomagnets include the measurement and minimization of single qubit decoherence rates [20][21][22] and the synthesis of mutually interacting qubit pairs [23,24]. However, the realization of a two-qubit quantum gate inside a molecular cluster remains an outstanding challenge [12,14]. Here, we show that ½Tb 2 molecular clusters display a magnetic asymmetry that should enable the realization of CNOT and SWAP gates.Lanthanide ions are promising candidates for encoding quantum information [25]. For the realization of a quantum gate, it seems therefore natural to look for molecules made of just two weakly coupled lanthanide qubits. However, the synthesis of asymmetric molecular dimers is not straightforward, as nature tends to make them symmetric. We propose a solution, sketched in Fig. 1(b), that exploits the ability of chemical design to finely tune the internal molecular structure. We synthesized a dinuclear complex of Tb 3þ ions, hereafter briefly referred to as ½Tb 2 , in which the metallic dimer is wrapped by three asymmetric organic ligands [26]. Each metal ion is in a different coordination enviro...

A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calculations, based on parameters of existing devices and molecular qubits. These results show that the proposal is feasible, provided that molecules with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the molecules, and the possibility of using their internal spin degrees of freedom.