Molecular Prototypes for Spin-Based CNOT and SWAP Quantum Gates

Abstract

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...

Direct measurement of dysprosium(III)˙˙˙dysprosium(III) interactions in a single-molecule magnet

“…Electrostatic optimization of the oblate m J ¼ ± 15 / 2 electron density 24 provides the same result (8.6°difference to CASSCF) and confirms that this orientation is due to the short terminal Dy-O bond of 2.248(3) Å (c.f. 2.349(3)-2.384(3) Å for the bridging oxygen atoms), identical to the motif in the recently described homoleptic [Dy 3 (hq) 9 ] 25 . The first excited doublet is well separated from the ground state (B100 cm À 1 ) and has dominant m J ¼ ± 13 / 2 character with its main magnetic axis (g z ) almost colinear with that of the ground doublet.…”

“…A diverse range of applications has been envisioned for lanthanide (Ln) containing molecules, including use as qubits for quantum information processing 9,10 and prototype devices such as molecular spin valves 11 and transistors 1 have been reported. These advances have been very rapid since the initial report that a terbium phthalocyanine compound could function as a single-molecule magnet (SMM) 12 .…”

Using the Singly Deprotonated Triethanolamine to Prepare Dinuclear Lanthanide(III) Complexes: Synthesis, Structural Characterization and Magnetic Studies

“…Thus, Ln III 2 complexes are highly desirable [10][11][12][13][14][15][16][17][18][19][20]. Another interesting area to which dinuclear lanthanide(III) complexes (and also mononuclear ones) are relevant is quantum computation; Ln III ions are promising candidates for encoding quantum information [21,22]. For the realization of a quantum gate, asymmetric dinuclear molecules composed of two weakly coupled Ln III qubits are promising [21].…”

“…Another interesting area to which dinuclear lanthanide(III) complexes (and also mononuclear ones) are relevant is quantum computation; Ln III ions are promising candidates for encoding quantum information [21,22]. For the realization of a quantum gate, asymmetric dinuclear molecules composed of two weakly coupled Ln III qubits are promising [21]. However, the synthesis of asymmetric molecular dimers is not straightforward, as nature tends to make them symmetric.…”

Supramolecular Complexes for Quantum Simulation

“…These are characterized by a S = 1/2 ground state, and coherence times above 10 µs have been demonstrated on properly engineered variants [12]. Rabi oscillations within the computational doublet (corresponding to single-qubit gates) have already been performed on ensembles of MNMs [13][14][15], as well as two-qubit operations in dimers of permanently coupled molecular qubits [16,17]. However, an important and much more challenging step towards the realization of a digital quantum simulator is the physical implementation of two-qubit entangling gates on a scalable architecture.…”