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Preparation of Weakly Coupled Spins within Molecules as 2qubit Quantum Gates

This article discusses the preparation of weakly coupled spins within molecules as 2-qubit quantum gates for quantum computing. It explores the requirements, strategies, and designs of molecular clusters and ligands for creating two-qubit quantum gates with low decoherence and switchable interactions.

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Preparation of Weakly Coupled Spins within Molecules as 2qubit Quantum Gates

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  1. QCPS-II 2010 Orlando Preparation of Weakly Coupled Spins within Molecules as 2qubit Quantum Gates Guillem Aromí Group of Magnetism and Functional Molecules (GMMF) Universitat de Barcelona

  2. QCPS-II 2010 Orlando The Challenge of Quantum Computing Q-bits: |0 & |1 TWO INEQUIVALENT Q-BITS Quantum Gates: x x Y x SWAP CNOT control y y F(x) x SWITCHABLE Q-BIT INTERACTION target M. A. Nielsen, I. L. Chuang, Quantum Computing and Quantum Information, Cambridge University Press, Cambridge, 2000.

  3. QCPS-II 2010 Orlando Requirements for Magnetic 2-qubit Quantum Gates 1. Exhibit two well defined q-bits 2. Possibility of initialize 3. Low decoherence (isolated from environment) 4. Readable 5. Q-gate operations ELECTRONIC SPINS 6. Chemically Stable M. N. Leuenberger, D. Loss, Nature 2001, 410, 789-793.

  4. QCPS-II 2010 Orlando Systems Proposed as two-qubits for QC Pairs of Metallic Wheels with Tunable Coupling J = 0 J0 Winpenny et al. Nature Nanotech., 2009, 4, 173

  5. QCPS-II 2010 Orlando What’s in our toolbox? Bis-β-diketonate Ligands H3L1 H4L2 H4L3 H5L4 H4L5 H2L6 Coord. Chem. Rev. 2008, 252, 964-989

  6. QCPS-II 2010 Orlando Types of Molecular ClusterPairs (MCPs) withBis-β-diketonates (L) Class C Class A Class B L aggregates themetals and links clusters L links clusters formedby other ligands L formstheclusters that are then linkedbyother ligands

  7. QCPS-II 2010 Orlando Class A Molecular Pairs of Clusterswith Ligand H4L3 Class A H4L3 L aggregates themetals and links clusters

  8. ΧMT / cm3Kmol−1 T / K QCPS-II 2010 Orlando HomometallicPair of Dimers J = −5.04 [Ni4(L3)2(py)6] [M-M···M-M] C. R. Chimie 2008, 11, 1117-1120

  9. QCPS-II 2010 Orlando Strategyfor Heterometallic Molecular ClusterPairs CuII = NiII = S ≠ 0 S ≠ 0

  10. QCPS-II 2010 Orlando SiteSelective Metal Distribution H4L3 Cu(AcO)2 / Ni(AcO)2 / NaH / py [Ni2Cu2(L3)2(py)6] Chem., Eur. J. 2009, 15, 11235 – 11243

  11. QCPS-II 2010 Orlando Magnetic Molecular ClusterPair S = 1/2 S = 1/2 J = −72.9 cm-1 θ = −0.5 K gNi = 2.46 gCu = 2.10 -Two weakly coupled, isolated S=1/2 spins -Both equivalent (not CNOT) Interaction not Switcheable (not SWAP) [Ni2Cu2(L3)2(py)6]

  12. QCPS-II 2010 Orlando Class B Molecular Pairs of Clusterswith Ligand H4L2 Class B H4L2 L links clusters formedby other ligands

  13. QCPS-II 2010 Orlando Class B Molecular Pairs of Clusterswith Ligand H4L2 [Mn4O2(AcO)6(dbm)2] Inorg. Chem. 2000, 39, 1501 [Mn3O(AcO)6(py)3]+ H4L2

  14. QCPS-II 2010 Orlando [Mn8O4(H2L2)2(RCO2)12(pz)2] RCO2- : 8.7 Å [(M4)···(M4)] Inorg. Chem. 2007, 46, 9045

  15. 3 Jbt 4 Jpyz Jtt Jbt 1 Jbb Jbt Jbt 2 T / K cMT / cm3 K mol−1 QCPS-II 2010 Orlando Magnetism of [Mn8O4(H2L2)2(AcO)12(pz)2] Inorg. Chem. 2007, 46, 9045

  16. QCPS-II 2010 Orlando Class B Magnetic Molecular Pairs of Clusters S = 2 -Two weakly coupled, isolated S=1/2 spins -Both equivalent (not CNOT) Interaction not Switcheable (not SWAP) S = 2

  17. QCPS-II 2010 Orlando Molecular Pairs of ClustersbySerendipity Class A+B [Mn14O4(OH)2(OMe)4(OAc)2(L)2(HL)4(H2L)2(MeOH)2]

  18. QCPS-II 2010 Orlando Molecular Pair of SMM’s S~2x5.5 SHMM SHMM SMM SMM

  19. QCPS-II 2010 Orlando Class C Molecular Pairs of Clusterswith Ligand H2L6 Class C H2L6 L formstheclusters that are then linkedbyother ligands

  20. QCPS-II 2010 Orlando Molecular Chainswith H2L6 as Building Blocks H2L6 Co(AcO)2 and Co(NO3)2 in MeOH [Co4(L6)2(MeOH)8]4+ [M-M-M-M] Aust. J. Chem. 2009, 62, 1130-1136

  21. QCPS-II 2010 Orlando Linkage of Metal-ChainstoBuild Molecular Pairs of Clusters of Class C (H2L6) + Co(AcO)2 and Co(NO3)2 in MeOH [Co8(OH)4(NO3)3(L6)4(bpy)4(H2O)](NO3)

  22. QCPS-II 2010 Orlando [Co8(OH)4(NO3)3(L6)4(bpy)4(H2O)](NO3) -Two weakly coupled clusters with potentially tunable interactions -Antiferromagnetic interactions cause an S = 0 on each cluster (not QuGate) Chem. Commun., 2011, 47, 707-709

  23. QCPS-II 2010 Orlando Design of Ligands to Prepare Asymmetric Asemblies Ln(NO3)3 or LnCl3 in pyridine H3L7 [Ln2(HL7)2(H2L7)(X)(solvents)x] [Gd2(HL7)2(H2L7)Cl(H2O)(py)] Inorg. Chem., 2010, 49, 6784–6786

  24. QCPS-II 2010 Orlando AsymmetricDinuclearLanthanides Ln= La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er,Tm, Yb, Lu

  25. QCPS-II 2010 Orlando MagneticProperties of [Tb2], [Gd2], [Eu2] Weak AF Coupling Stark Level Depopulation

  26. QCPS-II 2010 Orlando IsingHamiltonian of [Tb2(HL7)2(H2L7)Cl(py)2] H

  27. QCPS-II 2010 Orlando UltralowTemperatureMagneticStudies of [Tb2(HL7)2(H2L7)Cl(py)2] i) The total moment does not vanish at lowest temperature ii) There is a barrier to the reorientation of the total moment

  28. QCPS-II 2010 Orlando UltralowTemperatureSpecificHeat of [Tb2(HL7)2(H2L7)Cl(py)2] Specific Heat is consistent with Non-colinearity of the anisotropy axes of both ions in the dimer

  29. QCPS-II 2010 Orlando ConditionsfortheRealization of C-NOT Met |0,0 REALIZATION OF A CNOT!! |1,1 → |1,0 |1,0 → |1,1 |0,1 → |0,1 |0,0 → |0,0 |0,1 h |1,0 |1,1

  30. QCPS-II 2010 Orlando HeterometallicDinuclearLanthanides

  31. QCPS-II 2010 Orlando DinuclearComplexesCombining Ce and Tm

  32. QCPS-II 2010 Orlando HeterometallicDinuclearLanthanides‘at will’ Crystal structure of 33 complexes so far… CePr LaPr Pr2 PrNd PrSm PrEu PrGd PrTb PrHo PrYb PrDy PrLu CeY PrY LaEr LaTb LaY EuTb PrTm PrEr

  33. QCPS-II 2010 Orlando CONCLUSIONS Bis-β-diketonate ligands allowthesynthesis of Magnetic Molecular Pairs of Clusters An new Phenol/1,3-diketone/picolinicacid (H3L7) allowsaccess of unsymmetrical [Ln2]complexes of virtuallyanylanthanide. Some of whichmeettheconditionsfortherealization of a CNOT QuGate H3L7 seemstoallowthesynthesis of heterometallic [LnLn’] complexesforvirtuallyanypair of Lanthanides

  34. QCPS-II 2010 Orlando Acknowledgements University of Zaragoza Dr. Fernando Luis Dr. Olivier Roubeau Dr.MarcoEvangelisti University of Barcelona Dr. Leoní A. Barrios Dr. José Sánchez Dr. Carolina Sañudo David Aguilà Advanced Light Source (Berkeley, California) Dr. SimonTeat Generalitat de Catalunya

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