Monograph

Molecular approaches for quantum technologies

Optimization of electron spin-based quantum bits and quantum logic gates
  • Fabio Santanni,

Quantum computers provide a powerful resource to push the boundaries of current knowledge. At the core of their logical architecture are quantum bits and quantum logic gates. Electron spin can be used as a resource to encode logical operators, and, as such, magnetic molecules have proven to be a versatile platform for the realization of fundamental logical units. They offer the possibility of finely tuning desired quantum properties by exploiting targeted chemical approaches. This thesis book provides fundamental knowledge about quantum logical units, with a focus on magnetic molecules and electron spin dynamics. It reports on the various chemical approaches employed to advance beyond the current state-of-the-art in electron spin-based molecular quantum technologies.

  • Keywords:
  • Coordination Chemistry,
  • Molecular Magnetism,
  • Electron Spin Dynamics,
  • Molecular Qubits,
  • Quantum Inofrmation Science,
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Fabio Santanni

University of Florence, Italy - ORCID: 0000-0002-0506-8333

Fabio Santanni was born in Prato, Italy, in 1994. In 2022, he obtained the PhD title from the University of Florence, under the supervision of Prof. Roberta Sessoli, defending the dissertation that forms the basis of this thesis book. He is currently a research fellow at Trinity College Dublin, Ireland.
  1. Abragam, A. and Bleaney, B. (1970). Electron Paramagnetic Resonance of Transition Ions. Oxford: Clarendon Press.
  2. Adedoyin, J. A., Ambrosiano, J., Anisimov, P., Bärtschi, A., Casper, W., Chennupati, G., Coffrin, C.,Djidjev, H., Gunter, D., Karra, S., Lemons, N., Lin, S., Malyzhenkov, A., Mascarenas, D., Mniszewski, S., Nadiga, B., O’Malley, D., Oyen, D., Pakin, S., Prasad, L., Roberts, R., Romero, P., Santhi, N., Sinitsyn, N., Swart, P. J., Wendelberger, J. G., Yoon, B., Zamora, R., Zhu, W., Eidenbenz, S., Coles, P. J., Vuffray, M. and Lokhov, A. (2022). Quantum Algorithm Implementations for Beginners. ACM Transactions on Quantum Computing, 3, 1–92. DOI: 10.1145/3517340
  3. Aguilá, D., Barrios, L. A., Velasco, V., Roubeau, O., Repollés, A., Alonso, P. J., Sesé, J., Teat, S. J., Luis, F., and G. Aromí, G. (2014). Heterodimetallic [LnLn’] Lanthanide Complexes: Toward a Chemical Design of Two-Qubit Molecular Spin Quantum Gates. Journal of the American Chemical Society, 136, 14215–14222. DOI: 10.1021/ja507809w
  4. Albino, A., Benci, S., Tesi, L., Atzori, M., Torre, R., Sanvito, S., Sessoli, R., and Lunghi, A. (2019). First-Principles Investigation of Spin–Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits. Inorganic Chemistry, 58, 10260–10268. DOI: 10.1021/acs.inorgchem.9b01407
  5. Aleksandrowickz, G., Alexander, T., Panagiotis, B., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hernández, F. J., Carballo-Franquis, J., Chen, A., Chen, C.-F., Chow, J., M., … ,Zoufal, C. (2019). Qiskit: An open-source framework for quantum computing (0.7.2). Zenodo. 10.5281/zenodo.8190968 DOI: 10.5281/zenodo.2562111
  6. Amri, A., Hasan, K., Taha, H., Rahman, M. M., Herman, S., Andrizal, Awaltanova, E., Wantono, I., Kabir, H., Yin, C.-Y., Ibrahim, K., Bahri, S., Frimayanti, N., Hossain, M. A., and Jiang, Z.-T. (2019). Surface structural features and optical analysis of nanostructured Cu-oxide thin film coatings coated via the sol-gel dip coating method. Ceramics International, 45, 12888–12894. DOI: 10.1016/j.ceramint.2019.03.213
  7. Aravena, D. and Ruiz, E. (2020). Spin dynamics in single-molecule magnets and molecular qubits. Dalton Transactions, 49, 9916–9928 DOI: 10.1039/D0DT01414A
  8. Ardavan, A., Rival, O., Morton, J. J. L., Blundell, S. J., Tyryshkin, A. M., Timco, G. A., and Winpenny, R. E. P. (2007). Will Spin-Relaxation Times in Molecular Magnets Permit Quantum Information Processing? Physical Review Letters, 98, 057201. DOI: 10.1103/PhysRevLett.98.057201
  9. Ariciu, A.-M., Woen, D. H., Huh, D. N., Nodaraki, L. E., Kostopoulos, E. K., Goodwin, C. A. P., Chilton, N. F., McInnes, E. J. L., Winpenny, R. E. P., Evans, W. J., and Tuna, F. (2019). Engineering electronic structure to prolong relaxation times in molecular qubits by minimising orbital angular momentum. Nature Communications, 10, 3330. DOI: 10.1038/s41467-019-11309-3
  10. Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo, S., Brandao, L., Buell, D. A., Burkett, B., Chen, Y., Chen, Z.,Chiaro, B., Collins, R., …, and Martinis, J. M. (2019). Quantum supremacy using a programmable superconducting processor. Nature, 574, 505–510. DOI: 10.1038/s41586-019-1666-5
  11. Atzori, M. and Sessoli, R. (2019). The Second Quantum Revolution: Role and Challenges of Molecular Chemistry. Journal of the American Chemical Society, 141, 11339–11352. DOI: 10.1021/jacs.9b00984
  12. Atzori, M., Benci, S., Morra, E., Tesi, L., Chiesa, M., Torre, R., Sorace, L., and Sessoli, R. (2018). Structural Effects on the Spin Dynamics of Potential Molecular Qubits. Inorganic Chemistry, 57, 731–740. DOI: 10.1021/acs.inorgchem.7b02616
  13. Atzori, M., Chiesa, A., Morra, E., Chiesa, M., Sorace, L., Carretta, S., and Sessoli, R. (2018). A two-qubit molecular architecture for electron-mediated nuclear quantum simulation. Chemical Science, 9, 6183–6192. DOI: 10.1039/C8SC01695J
  14. Atzori, M., Garlatti, E., Allodi, G., Chicco, S., Chiesa, A., Albino, A., De Renzi, R., Salvadori, E., Chiesa, M., Carretta, S., and Sorace, L. (2021). Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit. Inorganic Chemistry, 11273–11286. DOI: 10.1021/acs.inorgchem.1c01267
  15. Atzori, M., Morra, E., Tesi, L., Albino, A., Chiesa, M., Sorace, L., and Sessoli, R. (2016). Quantum Coherence Times Enhancement in Vanadium(IV)-based Potential Molecular Qubits: the Key Role of the Vanadyl Moiety. Journal of the American Chemical Society, 138, 11234– 11244. DOI: 10.1021/jacs.6b05574
  16. Atzori, M., Tesi, L., Benci, S., Lunghi, A., Righini, R., Taschin, A., Torre, R., Sorace, L., and Sessoli, R. (2017). Spin Dynamics and Low Energy Vibrations: Insights from Vanadyl-Based Potential Molecular Qubits. Journal of the American Chemical Society, 139, 4338–4341 DOI: 10.1021/jacs.7b01266
  17. Atzori, M., Tesi, L., Morra, E., Chiesa, M., Sorace, L., and Sessoli, R. (2016). Room-Temperature Quantum Coherence and Rabi Oscillations in Vanadyl Phthalocyanine: Toward Multifunctional Molecular Spin Qubits. Journal of the American Chemical Society, 138, 2154–2157. DOI: 10.1021/jacs.5b13408
  18. Auwärter, W., Écija, D., Klappenberger, F., and Barth, J. V. (2015). Porphyrins at interfaces. Nature Chemistry, 7, 105–120. DOI: 10.1038/nchem.2159
  19. Bader, K, Winkler, M., and van Slageren, J. (2016). Tuning of molecular qubits: very long coherence and spin–lattice relaxation times. Chemical Communications, 52, 3623–3626. DOI: 10.1039/C6CC00300A
  20. Bader, K., Dengler, D., Lenz, S., Endeward, B., Jiang, S.-D., Neugebauer, P., and van Slageren, J. (2014). Room temperature quantum coherence in a potential molecular qubit. Nature Communications, 5,5304. DOI: 10.1038/ncomms6304
  21. Bal, M., Friedman, J. R., Suzuki, Y., Mertes, K. M., Rumberger, E. M., Hendrickson, D. N., Myasoedov, Y., Shtrikman, H., Avraham, N., and Zeldov, E. (2004). Photon-induced magnetization reversal in the Fe8 single-molecule magnet. Physical Review B, 70, 100408. DOI: 10.1103/PhysRevB.70.100408
  22. Barra, A. L., Caneschi, A., Cornia, A., Fabrizi de Biani, F., Gatteschi, D., Sangregorio, C., Sessoli, R., and Sorace, L. (1999). Single-Molecule Magnet Behavior of a Tetranuclear Iron(III) Complex. The Origin of Slow Magnetic Relaxation in Iron(III) Clusters. Journal of the American Chemical Society, 121, 5302–5310. DOI: 10.1021/ja9818755
  23. Barreiro, J. T., Wei, T.-C., and Kwiat, P. G. (2008). Beating the channel capacity limit for linear photonic superdense coding. Nature Physics, 4, 282–286. DOI: 10.1038/nphys919
  24. Bencini, A. and Totti, F. (2009). A Few Comments on the Application of Density Functional Theory to the Calculation of the Magnetic Structure of Oligo-Nuclear Transition Metal Clusters. Journal of Chemical Theory and Computation, 5, 144–154. DOI: 10.1021/ct800361x
  25. Bencini, A., and Gatteschi, D. (1990). EPR of Exchange Coupled Systems. Mineola, New York: Dover Publications, Inc.
  26. Bermudez, A., Xu, X., Nigmatullin, R., O’Gorman, J., Negnevitsky, V., Schindler, P., Monz, T., Poschinger, U. G., Hempel, C., Home, J., Schmidt-Kaler, F., Biercuk, B., Blatt, R., Benjamin, S. and Muller, M. (2017). Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum¨ Computation. Physical Review X, 7, 041061. DOI: 10.1103/PhysRevX.7.041061
  27. Biesinger, M. C., Lau, L. W., Gerson, A. R., and Smart, R. S. (2010). Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn. Applied Surface Science, 257, 887–898. DOI: 10.1016/j.apsusc.2010.07.086
  28. Bollinger, J. J., Prestage, J. D., Itano, W. M., and Wineland, D. J. (1985). Laser-Cooled-Atomic Frequency Standard. Physical Review Letters, 54, 1000–1003. DOI: 10.1103/PhysRevLett.54.1000
  29. Bonizzoni, C., Ghirri, A., and Affronte, M. (2018). Coherent coupling of molecular spins with microwave photons in planar superconducting resonators. Advances in Physics: X, 3, 1435305. DOI: 10.1080/23746149.2018.1435305
  30. Bonizzoni, C., Ghirri, A., Atzori, M., Sorace. L., Sessoli, R., and Affronte, M. (2017). Coherent coupling between Vanadyl Phthalocyanine spin ensemble and microwave photons: towards integration of molecular spin qubits into quantum circuits. Scientific Reports, 7, 13096. DOI: 10.1038/s41598-017-13271-w
  31. Bonizzoni, C., Ghirri, A., Santanni, F., Atzori, M., Sorace, L., Sessoli, R., and Affronte, M. (2020). Storage and retrieval of microwave pulses with molecular spin ensambles. Nature Physics Journal Quantum Information, 6. DOI: 10.1038/s41598-017-13271-w
  32. Borilovic, I., Alonso, P. J., Roubeau, O., and Aromí, G. (2020). A bis-vanadyl coordination complex as a 2-qubit quantum gate. Chemical Communications, 56, 3139–3142. DOI: 10.1039/C9CC09817H
  33. Bradley, C. E., Randall, J., Abobeih, M. H., Berrevoets, R. C., Degen, M. J., Bakker, M. A., Markham, M., Twitchen, D. J., and Taminiau, T. H. (2019). A Ten-Qubit Solid-State Spin Register with Quantum Memory up to One Minute. Physical Review X, 9, 031045. DOI: 10.1103/PhysRevX.9.031045
  34. Briganti, M., Lucaccini, E., Chelazzi, L., Ciattini, S., Sorace, L., Sessoli, R., Totti, F., and Perfetti, M. (2021). Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect. Journal of the American Chemical Society, 143, 8108–8115. DOI: 10.1021/jacs.1c02502
  35. Briganti, M., Santanni, F., Tesi, L., Totti, F., Sessoli, R., and Lunghi, A. A complete ab initio view of Orbach and Raman spin-lattice relaxation in a Dysprosium coordination compound. Journal of the American Chemical Society, 143, 13633–13645. DOI: 10.1021/jacs.1c05068
  36. Briggs, D. (1981). Book Review: Wanger, C. D., Riggs, W. M., Davis, L. E., Moulder, J. F., and Muilenberg, G. E. (1979). Handbook of X-ray Photoelectron Spectroscopy. Perkin-Elmer Corp., Physical Electronics Division, Eden Prairie, Minnesota, USA. Surface and Interface Analysis. DOI: 10.1002/sia.740030412
  37. Brustolon, M. and Giamello, E. (2009). Electron Paramagnetic Resonance: A Practitioner’s Toolkit. Hoboken: John Wiley and Sons, Inc. DOI: 10.1002/9780470432235
  38. Camargo, L. C., Briganti, M., Santana, F. S., Stinghen, D., Ribeiro, R. R., Nunes, G. G., Soares, J. F., Salvadori, E., Chiesa, M., Benci, S., Torre, R., Sorace, L., Totti, F., and Sessoli, R. (2021). Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case. Angewandte Chemie International Edition, 60, 2588–2593. DOI: 10.1002/anie.202009634
  39. Canarie, E. R., Jahn, S. M., and Stoll, S. (2020). Quantitative Structure-Based Prediction of Electron Spin Decoherence in Organic Radicals. The Journal of Physical Chemistry Letters, 11, 3396–3400. DOI: 10.1021/acs.jpclett.0c00768
  40. Candini, A., Lorusso, G., Troiani, F., Ghirri, A., Carretta, S., Santini, P., Amoretti, G., Muryn, C., Tuna, F., Timco, G., McInnes, E. J. L., Winpenny, R. E. P., Wernsdorfer, W., and Affronte, M. (2010). Entanglement in Supramolecular Spin Systems of Two Weakly Coupled Antiferromagnetic Rings (Purple-Cr7Ni). Physical Review Letters, 104, 037203. DOI: 10.1103/PhysRevLett.104.037203
  41. Carretta, S., Santini, P., Amoretti, G., Affronte, M., Ghirri, A., Sheikin, I., Piligkos, S., Timco, G. A., and Winpenny, R. E. P. (2005). Topology and spin dynamics in magnetic molecules. Physical Review B, 72, 060403. DOI: 10.1103/PhysRevB.72.060403
  42. Carretta, S., Zueco, D., Chiesa, A., Gómez-Léon, A., and Luis, F. (2021). A perspective on scaling up´ quantum computation with molecular spins. Applied Physics Letters, 118, 240501. DOI: 10.1063/5.0053378
  43. Carter, S. G., Sweeney, T. M., Kim, M., Kim, C. S., Solenov, D., Economou, S. E., Reinecke, T. R., Yang, L., Bracker, A. S., Gammon, D. (2013). Quantum control of a spin qubit coupled to a photonic crystal cavity. Nature Photonics, 7, 329–334. DOI: 10.1038/nphoton.2013.41
  44. Casimir, H., and du Pré, F. (1938). Note on the thermodynamic interpretation of paramagnetic relaxation phenomena. Physica, 5, 507–511. DOI: 10.1016/S0031-8914(38)80164-6
  45. Chandra Deb Nath, N., Yoo, K., and Lee, J.-J. (2018). Halogen-free guanidinium-based perovskite solar cell with enhanced stability. RSC Advances, 8, 17365–17372. DOI: 10.1039/C8RA00639C
  46. Chatterjee, A., Stevenson, P., De Franceschi, S., Morello, A., de Leon, N. P., and Kuemmeth, F. (2021), Semiconductor qubits in practice. Nature Reviews Physics, 3, 157–177. DOI: 10.1038/s42254-021-00283-9
  47. Chicco, S., Chiesa, A., Allodi, G., Garlatti, E., Atzori, M., Sorace, L., De Renzi, R., Sessoli, S., and Carretta, S. (2021). Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla. Chemical Science, 12, 12046–12055. DOI: 10.1039/D1SC01358K
  48. Chiesa, A., Cugini, F., Hussain, R., Macaluso, E., Allodi, G., Garlatti, E., Giansiracusa, M., Goodwin, C. A. P., Ortu, F., Reta, D., Skelton, J. M., Guidi, T., Santini, P., Solzi, M., De Renzi, R., Mills, D. P., Chilton, N. F., and Carretta, S. (2020). Understanding magnetic relaxation in single-ion magnets with high blocking temperature. Physical Review B, 101, 174402. DOI: 10.1103/PhysRevB.101.174402
  49. Chiesa, A., Petiziol, F., Macaluso, E., Wimberger, S., Santini, P., and Carretta, S. (2021). Embedded quantum-error correction and controlled-phase gate for molecular spin qubits. AIP Advances, 11, 025134. DOI: 10.1063/9.0000166
  50. Chilton, N. F., Collison, F., McInnes, E. J. L., Winpenny, R. E. P., and Soncini, A. (2013). An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes. Nature Communications, 4, 2551. DOI: 10.1038/ncomms3551
  51. Christoforidis, K. C., Louloudi, M., Milaeva, E. R., Sanakis, Y., and Deligiannakis, Y. (2007). EPR study of a novel [Fe–porphyrin] catalyst. Molecular Physics, 105, 2185–2194. DOI: 10.1080/00268970701749260
  52. Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W., and Lloyd, S., Experimental realization of a quantum algorithm. Nature, 393, 143–146. DOI: 10.1038/30181
  53. Cimatti, I., Bondí, L., Serrano, G., Malavolti, L., Cortigiani, B., Velez-Fort, E., Betto, D., Ouerghi, A., Brookes, N. B., Loth, S., Mannini, M., Totti, F., and Sessoli, R. (2019). Vanadyl phthalocyanines on graphene/SiC(0001): toward a hybrid architecture for molecular spin qubits. Nanoscale Horizons, 4, 1202–1210. DOI: 10.1039/C9NH00023B
  54. Clarke, J. and Wilhelm, F. K. (2008). Superconducting quantum bits. Nature, 453, 1031–1042. DOI: 10.1038/nature07128
  55. Cole, K. S., and Cole, R. H. (1941). Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics. The Journal of Chemical Physics, 9, 341–351. DOI: 10.1063/1.1750906
  56. Collett, C. A., Santini, P., Carretta, S., and Friedman, J. R. (2020). Constructing clock-transition-based two-qubit gates from dimers of molecular nanomagnets. Physical Review Research, 2, 032037. DOI: 10.1103/PhysRevResearch.2.032037
  57. Collison, D. and Powell, A. K. (1990). Electron spin resonance studies of ”FeO6”tris chelate complexes: models for the effects of zero-field splitting in distorted S = 5/2 spin systems. Inorganic Chemistry, 29, 4735–4746. DOI: 10.1021/ic00348a030
  58. Colston, K. J., Dille, S. A., Mogesa, B., Astashkin, A. V.,. Brant, J. A., Zeller, M., and Basu, P. (2019). Design, Synthesis, and Structure of Copper Dithione Complexes: Redox-Dependent Charge Transfer. European Journal of Inorganic Chemistry, 2019, 4939–4948. DOI: 10.1002/ejic.201901222
  59. Das, P. K., Chatterjee, S., Samanta, S., and Dey, A. (2012). EPR, Resonance Raman, and DFT Calculations on Thiolate- and Imidazole-Bound Iron(III) Porphyrin Complexes: Role of the Axial Ligand in Tuning the Electronic Structure. Inorganic Chemistry, 51, 10704–10714. DOI: 10.1021/ic3016035
  60. De Vroomen, A., Lijphart, E., Prins, D., Marks, J., and Poulis, N. (1972). Electron spin-lattice relaxation of the Zeeman and interaction systems in CuCs2(SO4)2·6H2O. Physica, 61, 241–249. DOI: 10.1016/0031-8914(72)90070-5
  61. Delfs, C., Gatteschi, D., Pardi, L., Sessoli, R., Wieghardt, K., and Hanke, D. (1993). Magnetic properties of an octanuclear iron(III) cation. Inorganic Chemistry, 32, 3099–3103 DOI: 10.1021/ic00066a022
  62. Deutsch, D.E. (1989). Quantum computational networks. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 425, 73–90. DOI: 10.1098/rspa.1989.0099
  63. Devoret, M. H. and Schoelkopf, R. J. (2013). Superconducting Circuits for Quantum Information: An Outlook. Science, 339, 1169–1174. DOI: 10.1126/science.1231930
  64. Diamond, S., Fatemi, V., Hays, M., Nho, H., Kurilovic, P., Connolly, T., Joshi, V. R., Serniak, R., Frunzio, L., Glazman, L. I., and Devoret, M. H. (2022). Distinguishing Parity-Switching Mechanisms in a Superconducting Qubit. PRX Quantum, 3, 040304. DOI: 10.1103/PRXQuantum.3.040304
  65. DiVincenzo, D. P. (1998). Real and realistic quantum computers. Nature, 393, 113–114. DOI: 10.1038/30094
  66. DiVincenzo, D. P. (2000). The Physical Implementation of Quantum Computation. Fortschritte der Physik, v48, 771–783. DOI: 10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E
  67. Drago, R. S. (1992). Physical Methods for Chemists. Gainesville: Saunders College Publishing.
  68. Du, J.-L., Eaton, G. R., and Eaton, S. S. (1995). Temperature and Orientation Dependence of ElectronSpin Relaxation Rates for Bis(diethyldithiocarbamato)copper(II). Journal of Magnetic Resonance, Series A, 117, 67–72. DOI: 10.1006/jmra.1995.9971
  69. Eaton, G. R. and Eaton, S. S. (2011). Multifrequency Electron Spin-Relaxation Times, in Multifrequency Electron Paramagnetic Resonance (Misra, S. K., eds.), pp. 719–753, Weinheim: Wiley-VCH Verlag GmbH and Co. KGaA. DOI: 10.1002/9783527633531.ch17
  70. Eaton, S. S. and Eaton, G. R. (2002). Relaxation Times of Organic Radicals and Transition Metal Ions, in Distance Measurements in Biological Systems by EPR (Berliner, L. J., Eaton, G. R., and Eaton, S. S., eds.), 29–154. New York: Springer New York. DOI: 10.1007/b111467
  71. Edmonds, A. M., D’Haenens-Johansson, U. F. S., Cruddace, R. J., Newton, M. E., Fu, K.-M. C., Santori, C., Beausoleil, R. G., Twitchen, D. J., and Markham, M. L. (2012). Production of oriented nitrogen-vacancy color centers in synthetic diamond. Physical Review B, 86,035201. DOI: 10.1103/PhysRevB.86.035201
  72. Eichhorn, T. R., McLellan, C. A., and Bleszynski Jayich, A. C., (2019). Optimizing the formation of depth-confined nitrogen vacancy center spin ensembles in diamond for quantum sensing. Physical Review Materials, 3, 113802. DOI: 10.1103/PhysRevMaterials.3.113802
  73. Escalera-Moreno, L., Baldoví, J. J., Gaita-Ariño, A., and Coronado, E. (2018). Spin states, vibrations and spin relaxation in molecular nanomagnets and spin qubits: a critical perspective. Chemical Science, 9, 3265–3275. DOI: 10.1039/C7SC05464E
  74. Escalera-Moreno, L., Gaita-Ariño, A., and Coronado, E. (2019). Decoherence from dipolar interspin interactions in molecular spin qubits. Physical Review B, 100, 064405. DOI: 10.1103/PhysRevB.100.064405
  75. Fábregas Ibáñez, L., Jeschke, G., and Stoll, S. (2020). DeerLab: a comprehensive software package for analyzing dipolar electron paramagnetic resonance spectroscopy data. Magnetic Resonance, 1, 209–224. DOI: 10.5194/mr-1-209-2020
  76. Fataftah, M. S., Bayliss, S. L., Laorenza, D. W., Wang, X., Phelan, B. T., Wilson, C. B., Mintun, P. J., Kovos, B. D., Wasielewski, M. R., Han, S., Sherwin, M. S., Awschalom, D. D., and Freedman, D. E. (2020). Trigonal Bipyramidal V3+ Complex as an Optically Addressable Molecular Qubit Candidate. Journal of the American Chemical Society, 142, 20400–20408. DOI: 10.1021/jacs.0c08986
  77. Ferrando-Soria, J., Moreno Pineda, E., Chiesa, A., Fernandez, A., Magee, A. A., Carretta, S., Santini, P., Vitorica-Yrezabal, I. J., Tuna, F., Timco, G. A., McInnes, E. J. L., and Winpenny, R. E. P. (2016). A modular design of molecular qubits to implement universal quantum gates. Nature Communications, 7, 11377. DOI: 10.1038/ncomms11377
  78. Ferreira, G. J. and Loss, D. (2013). Magnetically Defined Qubits on 3D Topological Insulators. Physical Review Letters, 111, 106802. DOI: 10.1103/PhysRevLett.111.106802
  79. Finazzo, C., Calle, C., Stoll, S., Van Doorslaer, S., and Schweiger, A. (2006). Matrix effects on copper(ii)phthalocyanine complexes. A combined continuous wave and pulse EPR and DFT study. Physical Chemistry Chemical Physics, 8, 1942, 2006. DOI: 10.1039/b516184c
  80. Friis, N., Marty, O., Maier, C., Hempel, C., Holzäpfel, M., Jurcevic, P., Plenio, M. B., Huber, M., Roos, C., Blatt, R., and Lanyon, B. (2018). Observation of Entangled States of a Fully Controlled 20-Qubit System. Physical Review X, 8, 021012. DOI: 10.1103/PhysRevX.8.021012
  81. Fukui, N., Kim, T., Kim, D., and Osuka, A. (2017). Porphyrin Arch-Tapes: Synthesis, Contorted Structures, and Full Conjugation. Journal of the American Chemical Society, 139, 9075– 9088. DOI: 10.1021/jacs.7b05332
  82. Gaita-Ariño, Luis, F., Hill, S., and Coronado, E. (2019). Molecular spins for quantum computation. Nature Chemistry, 11, 301–309. DOI: 10.1038/s41557-019-0232-y
  83. Garlatti, E., Tesi, L., Lunghi, A., Atzori, M., Voneshen, D. J., Santini, P., Sanvito, S., Guidi, T., Sessoli, R., and Carretta, S. (2020). Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory. Nature Communications, 11, 1751. DOI: 10.1038/s41467-020-15475-7
  84. Gatteschi, D., Sessoli, R., and Villain, J. (2006). Molecular Nanomagnets. Oxford: Oxford University Press. DOI: 10.1093/acprof:oso/9780198567530.001.0001
  85. Georgeot, B. and Mila, F. (2010). Chirality of Triangular Antiferromagnetic Clusters as a Qubit. Physical Review Letters, 104, 200502. DOI: 10.1103/PhysRevLett.104.200502
  86. Ghirri, A., Bonizzoni, C., Gerace, D., Sanna, S., Cassinese, A., and Affronte, M. (2015). YBa2Cu3O7 microwave resonators for strong collective coupling with spin ensembles. Applied Physics Letters, 106, 184101. DOI: 10.1063/1.4920930
  87. Giménez-Santamarina, S., Cardona-Serra, S., Clemente-Juan, J. M., Gaita-Ariño, A., and Coronado, E. (2020). Exploiting clock transitions for the chemical design of resilient molecular spin qubits. Chemical Science, 11, 10718–10728. DOI: 10.1039/D0SC01187H
  88. Giovannetti, R. (2012). The Use of Spectrophotometry UV-Vis for the Study of Porphyrins, in Macro To Nano Spectroscopy (Uddin J., eds), 87–108. InTech. DOI: 10.5772/38797
  89. Godfrin, W., Ferhat, A., Ballou, R., Klyatskaya, S., Ruben, M., Wernsdorfer, W., and Balestro, F (2017). Operating Quantum States in Single Magnetic Molecules: Implementation of Grover’s Quantum Algorithm. Physical Review Letters, 119, 187702. DOI: 10.1103/PhysRevLett.119.187702
  90. Goldberg, I. (2005). Crystal engineering of porphyrin framework solids. Chemical Communications, 10, 1243. DOI: 10.1039/b416425c
  91. Goodwin, C. A. P., Ortu, F., Reta, D., Chilton, N. F., and Mills, D. P. (2017). Molecular magnetic hysteresis at 60 kelvin in dysprosocenium. Nature, 548, 439–442. DOI: 10.1038/nature23447
  92. Graham, M. J., Yu, C.-J., Krzyaniak, M. D., Wasielewski, M. R., and Freedman, D. E. (2017). Synthetic Approach to Determine the Effect of Nuclear Spin Distance on Electronic Spin Decoherence. Journal of the American Chemical Society, 139, 3196–3201. DOI: 10.1021/jacs.6b13030
  93. Graham, M. J., Yu, C.-J., Krzyaniak, M. D., Wasielewski, M. R., Freedman, D. E. (2017). Synthetic Approach To Determine the Effect of Nuclear Spin Distance on Electronic Spin Decoherence. Journal of the American Chemical Society, 139, 3196–3201. DOI: 10.1021/jacs.6b13030
  94. Graham, M. J., Zadrozny, J. M., Fataftah, M. S., and Freedman, D. E. (2017). Forging Solid-State Qubit Design Principles in a Molecular Furnace. Chemistry of Materials, 29, 1885–1897. DOI: 10.1021/acs.chemmater.6b05433
  95. Grezes, C., Kubo, Y., Julsgaard, B., Umeda, T., Isoya, J., Sumiya, H., Abe, H., Onoda, S., Ohshima, T., Nakamura, K., Diniz, I., Auffeves, A., Jacques, V., Roch, J.-F., Vion, D., Esteve, D., Moelmer, K., and Bertet, P. (2016). Towards a spin-ensemble quantum memory for superconducting qubits. Comptes Rendus Physique, 17, 693–704. DOI: 10.1016/j.crhy.2016.07.006
  96. Grezes,C., Julsgaard, B., Kubo, Y., Stern, M., Umeda, T., Isoya, J., Sumiya, H., Abe, H., Onoda, S., Ohshima, T., Jacques, V., Esteve, J., Vion, D., Esteve, D., Mølmer, K., and Bertet , P. (2014). Multimode Storage and Retrieval of Microwave Fields in a Spin Ensemble. Physical Review X, 4, 021049. DOI: 10.1103/PhysRevX.4.021049
  97. Grimme, S. (2012). Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory. Chemistry - A European Journal, 18, 9955–9964. DOI: 10.1002/chem.201200497
  98. Grover, L. K. (1997). Quantum Computers Can Search Arbitrarily Large Databases by a Single Query. Physical Review Letters, 79, 4709–4712. DOI: 10.1103/PhysRevLett.79.4709
  99. Haljan, P. C., Lee, P. J., Brickman, K.-A., Acton, M., Deslauriers, L., and Monroe, C. (2005). Entanglement of trapped-ion clock states. Physical Review A, 72, 062316. DOI: 10.1103/PhysRevA.72.062316
  100. Hardy, Y. and Steeb, W. (2001). Classical and Quantum Computing. Basel: Birkhäuser Basel. DOI: 10.1007/978-3-0348-8366-5
  101. Haroche, S. and Raimond, J.-M. (2006). Exploring the Quantum: Atoms, Cavities, and Photons. Oxford Graduate Texts, Oxford: Oxford University Press. DOI: 10.1093/acprof:oso/9780198509141.001.0001
  102. Henfling, S., Kultaeva, A., Pöppl, A., Klose, J., Kersting, B., Domasevitch, K. V., and Krautscheid, H. (2021). Proton and Electron Transfer in the Formation of a Copper Dithiolene-Based Coordination Polymer. Inorganic Chemistry, 60, 9008–9018. DOI: 10.1021/acs.inorgchem.1c00914
  103. Hiroto, S., Miyake, Y., and Shinokubo, H. (2017). Synthesis and Functionalization of Porphyrins through Organometallic Methodologies. Chemical Reviews,117,2910–3043. DOI: 10.1021/acs.chemrev.6b00427
  104. Hoffmann, S. K., Goslar, J., Lijewski, S., and Zalewska, A. (2013). EPR and ESE of CuS4 complex in Cu(dmit)2: g-Factor and hyperfine splitting correlation in tetrahedral Cu–sulfur complexes. Journal of Magnetic Resonance, 236, 7–14. DOI: 10.1016/j.jmr.2013.08.009
  105. Holevo, A. S. (2019). Quantum Systems, Channels, Information. Berlin/Boston: De Gruyter. DOI: 10.1515/9783110642490
  106. Hoshino, A., Takenaka, Y., and Miyaji, H. (2003). Redetermination of the crystal structure of α-copper phthalocyanine grown on KCl. Acta Crystallographica Section B Structural Science, 59, 393–403. DOI: 10.1107/S010876810300942X
  107. Hou, J., Wang, Y., Eguchi, K., Nanjo, C., Takaoka, T., Sainoo, T., Arafune, R., Awaga, K., and Komeda, T. (2020). Enhanced magnetic spin–spin interactions observed between porphyrazine derivatives on Au(111). Communications Chemistry, 3, 36. DOI: 10.1038/s42004-020-0282-5
  108. Jackson, C. E., Lin, C.-Y., Johnson, S. H., van Tol, J., and Zadrozny, J. M. (2019). Nuclear-spin-pattern control of electron-spin dynamics in a series of V(IV) complexes. Chemical Science, 10, 8447–8454. DOI: 10.1039/C9SC02899D
  109. Jacobsen H., and Donahue, J. P. (2008). Computational Study of Iron Bis(dithiolene) Complexes: Redox Non-Innocent Ligands and Antiferromagnetic Coupling. Inorganic Chemistry, 47, 10037–10045. DOI: 10.1021/ic801277r
  110. Jain, S. K., Yu, C.-J., Wilson, C. B., Tabassum, T., Freedman, D. E., and Han, S. (2021). Dynamic Nuclear Polarization with Vanadium(IV) Metal Centers. Chem, 7, 421–435. DOI: 10.1016/j.chempr.2020.10.021
  111. Jaquinod, L., Siri, O., and Khoury, R. G. (2001). Linear fused oligoporphyrins: potential molecular wires with enhanced electronic communication between bridged metal ions. Chemical Communications, 12, 1261–1262. DOI: 10.1039/a801676c
  112. Jenkins, M. D., Zueco, D., Roubeau, O., Aromí G., Majer, J., and Luis, F. (2016). A scalable architecture for quantum computation with molecular nanomagnets. Dalton Transactions, 45, 16682–16693. DOI: 10.1039/C6DT02664H
  113. Jiang, S.-D., Wang, B.-W., Su, G., Wang, Z.-M., and Gao, S. (2010). A Mononuclear Dysprosium Complex Featuring Single-Molecule-Magnet Behavior. Angewandte Chemie International Edition, 49, 7448–7451. DOI: 10.1002/anie.201004027
  114. Jin, L.-M., Chen, L., Yin, J.-J., Guo, C.-C., and Chen, Q.-Y. (2005). A Facile and Potent Synthesis of meso, meso-Linked Porphyrin Arrays Using Iodine(III) Reagents. European Journal of Organic Chemistry, 2005, 3994–4001. DOI: 10.1002/ejoc.200500255
  115. Jin, Z., Liu, C., Qi, K., and Cui, X. (2017). Photo-reduced Cu/CuO nanoclusters on TiO2 nanotube arrays as highly efficient and reusable catalyst. Scientific Reports, 7, 39695. DOI: 10.1038/srep39695
  116. Johann, R. and Wolmershäuser, G. (1997). 1,3,2-Dithiazolylium Cations with Various Anions; Syntheses and Solid State Structures. Phosphorus, Sulfur, and Silicon and the Related Elements, 124, 233–242. DOI: 10.1080/10426509708545628
  117. Johansson, J., Nation, P., and Nori, F. (2012). QuTiP: An open-source Python framework for the dynamics of open quantum systems. Computer Physics Communications, 183, 1760–1772. DOI: 10.1016/j.cpc.2012.02.021
  118. Johnson, M. A. I., Madzik, M. T., Hudson, F. E., Itoh, K. M.., Jakob, A. M., Jamieson, D. N., Dzurak, A., and Morello, A. (2022). Beating the Thermal Limit of Qubit Initialization with a Bayesian Maxwell’s Demon. Physical Review X, 12, 041008. DOI: 10.1103/PhysRevX.12.041008
  119. Joshi, G., Kubasek, J., Nikolov, I., Sheehan, B., Costa, T. A., Allão Cassaro, R. A., and Friedman, J. R. (2020). Adjustable coupling and in situ variable frequency electron paramagnetic resonance probe with loop-gap resonators for spectroscopy up to X-band. Review of Scientific Instruments, 91, 023104. DOI: 10.1063/1.5133074
  120. Kadish, K. M., Sazou, D., Araullo, C., Liu, Y. M., Saoiabi, A., Ferhat, M., and Guilard, R. (1998). Electrochemistry of vanadyl porphyrins in dimethylformamide. Inorganic Chemistry, 27, 2313– 2320. DOI: 10.1021/ic00286a019
  121. Kahn, O. (1993). Molecular Magnetism. Orsay: VCH Publishers, Inc.
  122. Kane, B. E. (1998). A silicon-based nuclear spin quantum computer. Nature, 393, 133–137. DOI: 10.1038/30156
  123. Kato, K., Furukawa, K., Mori, T., and Osuka, A. (2018). Porphyrin-Based Air-Stable Helical Radicals. Chemistry - A European Journal, 24, 572–575. DOI: 10.1002/chem.201705291
  124. Kim, D. and Osuka, A. (2003). Photophysical Properties of Directly Linked Linear Porphyrin Arrays. The Journal of Physical Chemistry A, 107, 8791–8816. DOI: 10.1021/jp030490s
  125. Koo, J., Kim, I., Kim, Y., Cho, D., Hwang, I.-C., Mukhopadhyay, R. D., Song, H., Ko, Y. H., Dhamija, A., Lee, H., Hwang, W., Kim, S., Baik, M.-H., and Kim, K. (2020). Gigantic Porphyrinic Cages. Chem, 6, 3374–3384. DOI: 10.1016/j.chempr.2020.10.002
  126. Kurizki, G., Bertet, P., Kubo, Y., Mølmer, K., Petrosyan, D., Rabl, P., and Schmiedmayer, J. (2015). Quantum technologies with hybrid systems. Proceedings of the National Academy of Sciences, 112, 3866–3873. DOI: 10.1073/pnas.1419326112
  127. Larsen, F. K., McInnes, E. J. L., Mkami, H. E., Overgaard, J., Piligkos, S., Rajaraman, G., Rentschler, E., Smith, A. A., Smith, G. M., Boote, V., Jennings, M., Timco, G. A., and Winpenny, R. E. P. (2003). Synthesis and Characterization of Heterometallic {Cr7M} Wheels. Angewandte Chemie International Edition, 42, 101–105. DOI: 10.1002/anie.200390034
  128. Le Bellac, M. (2006). A Short Introduction to Quantum Information and Quantum Computation. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511755361
  129. Leuenberger, M. N. and Loss, D. (2001). Quantum computing in molecular magnets. Nature, 410, 789–793. DOI: 10.1038/35071024
  130. Li, W.-S. and Aida, T. (2009). Dendrimer Porphyrins and Phthalocyanines. Chemical Reviews, 109, 6047–6076. DOI: 10.1021/cr900186c
  131. Liddle, S. T. and van Slageren, J. (2015). Improving f-element single molecule magnets. Chemical Society Reviews, 44, 6655–6669. DOI: 10.1039/C5CS00222B
  132. Linstead, R. P. (1934). 212. Phthalocyanines. Part I. A new type of synthetic colouring matters. Journal of the Chemical Society, 1016–1017. DOI: 10.1039/JR9340001016
  133. Liu, J., Mrozek, J., Ullah, A., Duan, Y., Baldoví, J. J., Coronado, E., Gaita-Ariño, A., and Ardavan, A. (2021). Quantum coherent spin-electric control in a molecular nanomagnet at clock transitions. Nature Physics, 17, 1205–1209. DOI: 10.1038/s41567-021-01355-4
  134. Lloyd, S. (1995). Almost Any Quantum Logic Gate is Universal. Physical Review Letters, 75, 346–349. DOI: 10.1103/PhysRevLett.75.346
  135. Lockyer, S. J., Chiesa, A., Timco, G. A., McInnes, E. J. L., Bennett, T. S., Vitorica-Yrezebal, I. J., Carretta, S., and Winpenny, R. E. P. (2021). Targeting molecular quantum memory with embedded error correction. Chemical Science, 12, 9104–9113. DOI: 10.1039/D1SC01506K
  136. Luis, F., Repollés, A., Martínez-Pérez, M. J., Aguilà, D., Roubeau, O., Zueco, D., Alonso, P.J., Evangelisti, M., Camón, A., Sesé, J., Barrios, L. A., and Aromí, G. (2011). Molecular Prototypes for Spin-Based CNOT and SWAP Quantum Gates. Physical Review Letters, 107, 117203. DOI: 10.1103/PhysRevLett.107.117203
  137. Lunghi, A. and Sanvito, S. (2019). How do phonons relax molecular spins?. Science Advances, 5, eaax7163. DOI: 10.1126/sciadv.aax7163
  138. Lunghi, A. and Sanvito, S. (2020). Multiple spin–phonon relaxation pathways in a Kramer single-ion magnet. The Journal of Chemical Physics, 153, 174113. DOI: 10.1063/5.0017118
  139. Lunghi, A. and Sanvito, S. (2020). The Limit of Spin Lifetime in Solid-State Electronic Spins. The Journal of Physical Chemistry Letters, 11, 6273–6278. DOI: 10.1021/acs.jpclett.0c01681
  140. Lunghi, A., Totti, F., Sanvito, S., and Sessoli, R. (2017). Intra-molecular origin of the spin-phonon coupling in slow-relaxing molecular magnets. Chemical Science, 8, 6051–6059. DOI: 10.1039/C7SC02832F
  141. Macaluso, E., Rubín, M., Aguilà, D., Chiesa, A., Barrios, L. A., Martínez, J. I., Alonso, P. J., Roubeau, O., Luis, F., Aromí, G., and Carretta, S. (2020). A heterometallic [LnLn’Ln] lanthanide complex as a qubit with embedded quantum error correction. Chemical Science, 11, 10337–10343. DOI: 10.1039/D0SC03107K
  142. Mądzik, M. T., Asaad, S., Youssry, A., Joecker, B., Rudinger, K. M., Nielsen, E., Young, K. C., Proctor, J. T., Baczewski, A. D., Laucht, A., Schmitt, V., Hudson, F. E., Itoh, K. M., Jakob, A. M., Johnson, B. J., Jamieson, D. N., Dzurak, A. S., Ferrie, C., Blume-Kohout, R., and Morello, A. (2022). Precision tomography of a three-qubit electron-nuclear quantum processor in silicon Nature, 601, 348–353. DOI: 10.1038/s41586-021-04292-7
  143. Malavolti, L., Briganti, M., Hänze, M., Serrano, G., Cimatti, I., McMurtrie, C., Otero, E., Ohresser, P., Totti, F., Mannini, M., Sessoli, R., and Loth, S. (2018). Tunable Spin–Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules. Nano Letters, 18, 7955–7961. DOI: 10.1021/acs.nanolett.8b03921
  144. Manousakis, J., Altland, A., Bagrets, D., Egger, R., and Ando, Y. (2017). Majorana qubits in a topological insulator nanoribbon architecture. Physical Review B, 95, 165424. DOI: 10.1103/PhysRevB.95.165424
  145. McAuslan, D. L., Bartholomew, J. G., Sellars, M. J., and Longdell, J. J. (2012). Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials. Physical Review A, 85, 032339. DOI: 10.1103/PhysRevA.85.032339
  146. Miyoshi, Y., Kubo, M., Fujinawa, T., Suzuki, Y., Yoshikawa, H., and Awaga, K. (2007). Electrochromism and Stable n-Type Doping of Highly Oriented Thin Films of Tetrakis(thiadiazole)porphyrazine. Angewandte Chemie International Edition, 46, 5532–5536. DOI: 10.1002/anie.200700702
  147. Mørkved, E. H., Neset, S. M., Kjøsen, H., Hvistendahl, G., Mo, F., Balzarini, J., Fransson, B., Ragnarsson, U., and Francis, G. W. (1994). Template Assisted Cyclotetramerisations of 1,2,5-Thiadiazole-3,4dicarbonitrile. Acta Chemica Scandinavica, 48, 912–916. DOI: 10.3891/acta.chem.scand.48-0912
  148. Morris J. L., and Rees, C. W. (1987). Organic heterocyclothiazenes. Part 3. Synthesis and structure of 1,3,5,2,4-trithiadiazepines. Journal of the Chemical Society, Perkin Transactions 1, 211. DOI: 10.1039/p19870000211
  149. Morris, J. L., Rees, C. W., and Rigg, D. J. (1985). 1,3,5,2,4-Trithiadiazepine. Journal of the Chemical Society, Chemical Communications, 7, 396. DOI: 10.1039/c39850000396
  150. Morrish, A. H. (1965). The Physical Principles of Magnetism. New York: Wiley-IEEE Press. DOI: 10.1002/9780470546581
  151. Morton, J. J. L., Tyryshkin, A. M., Brown, R. M., Shankar, S., Lovett, B. W., Ardavan, A., Schenkel, T., Haller, E. E., Ager, J. W., and Lyon, S. A. (2008). Solid-state quantum memory using the 31P nuclear spin. Nature, 455, 1085–1088. DOI: 10.1038/nature07295
  152. Moseley, D.H., Stavretis, S. E., Thirunavukkuarasu, K., Ozerov, M., Cheng, Y., Daemen, L. L., Ludwig, J., Lu, Z., Smirnov, D., Brown, C. M., Pandey, A., Ramirez-Cuesta, A. J., Lamb, A. C., Atanasov, M., Bill, E., Neese, F., and Xue, Z.-L. (2018). Spin–phonon couplings in transition metal complexes with slow magnetic relaxation. Nature Communications, 9, 2572. DOI: 10.1038/s41467-018-04896-0
  153. Mueller, W. H., and Dines, M. (1969). Dithioheterocycles from ethane-1,2-disulfenyl chloride. Journal of Heterocyclic Chemistry, 6, 627–630. DOI: 10.1002/jhet.5570060505
  154. Nakamura, T., Sasamori, K., Kodama, T., Kikuchi, K., and Fujita, W. (2013). Preparation, Crystal Structure, and Magnetic Properties of a New Dithiolene Ligand, 1,3,2-Dithiazole-4-thione-5thiolate, and its Metal Complex. Chemistry - An Asian Journal, 8, 348–350. DOI: 10.1002/asia.201200912
  155. Nelson, J. N., Zhang, J., Zhou, J., Rugg, B. K., Krzyaniak, M. D., and Wasielewski, M. R. (2020). NOT gate operation on a photogenerated molecular electron spin-qubit pair. The Journal of Chemical Physics, 152, 014503. DOI: 10.1063/1.5128132
  156. Nielsen, M. A. (2010). Superdense Coding: How to Send Two Bits Using One Qubit. Nielsen, M. A. (2010). https://youtu.be/w5rCn593Dig
  157. Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511976667
  158. Niu, D. -Z., Yao, L., Min, X., and Zou, H. (2011). Crystal structure of cis-bis[1-hydroxypyridine-2(1H)thionato-S,O]copper(II),Cu(C5H4NOS2)2, Zeitschrift für Kristallographie - New Crystal Structures, 226. DOI: 10.1524/ncrs.2011.0234
  159. ollett, C., Ellers, K.-I., Russo, N., Kittilstved, K., Timco, G. A., Winpenny, R. E. P. and Friedman, J. R. (2019). A Clock Transition in the Cr7Mn Molecular Nanomagnet. Magnetochemistry, 5, 4. DOI: 10.3390/magnetochemistry5010004
  160. Orbach, R. (1961). Spin-lattice relaxation in rare-earth salts. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 264, 458–484. DOI: 10.1098/rspa.1961.0211
  161. Osuka, A. and Shimidzu, H. (1997). meso, meso-Linked Porphyrin Arrays. Angewandte Chemie International Edition, 36, 135–137. DOI: 10.1002/anie.199701351
  162. Ouyang, Q., Zhu, Y.-Z., Zhang, C.-H., Yan, K.-Q., Li, Y.-C., and Zheng, J.-Y. (2009). An Efficient PIFA Mediated Synthesis of Fused Diporphyrin and Triply/Singly Interlacedly Linked Porphyrin Array. Organic Letters, 11, 5266–5269. DOI: 10.1021/ol902198w
  163. Peisach, J., and Blumberg, W. (1974). Structural implications derived from the analysis of electron paramagnetic resonance spectra of natural and artificial copper proteins. Archives of Biochemistry and Biophysics, 165, 691–708. DOI: 10.1016/0003-9861(74)90298-7
  164. Perfetti, M. (2017). Cantilever torque magnetometry on coordination compounds: from theory to experiments. Coordination Chemistry Reviews, 348, 171–186. DOI: 10.1016/j.ccr.2017.08.013
  165. Perfetti, M., Lucaccini, E., Sorace, L., Costes, J. P., and Sessoli, R. (2015). Determination of Magnetic Anisotropy in the LnTRENSAL Complexes (Ln = Tb, Dy, Er) by Torque Magnetometry. Inorganic Chemistry, 54, 3090–3092. DOI: 10.1021/acs.inorgchem.5b00288
  166. Perlovich, G. L., Golubchikov, O. A., and Klueva, M. E. (2000). Thermodynamics of porphyrin sublimation. Journal of Porphyrins and Phthalocyanines, 4, 699–706. DOI: 10.1002/1099-1409(200012)4:8<699::AID-JPP284>3.0.CO;2-M
  167. Pla, J. J., Tan, K. Y., Dehollain, J. P., Lim, W. H., Morton, J. J. L., Jamieson, D. N., Dzurak, A. S., and Morello, A. (2012). A single-atom electron spin qubit in silicon. Nature, 489, 541–545. DOI: 10.1038/nature11449
  168. Pla, J. J., Tan, K. Y., Dehollain, J. P., Lim, W. H., Morton, J. J. L., Jamieson, D. N., Dzurak, A. S., and Morello, A. (2012). A single-atom electron spin qubit in silicon. Nature, 489, 541–545. DOI: 10.1038/nature11449
  169. Pla, J. J., Tan, K. Y., Dehollain, J. P., Lim, W. H., Morton, J. J. L., Zwanenburg, F. A., Jamieson, D. N., Dzurak, A. S., and Morello, A. (2013). High-fidelity readout and control of a nuclear spin qubit in silicon. Nature, 496, 334–338. DOI: 10.1038/nature12011
  170. Rembold, P., Oshnik, N., Müller, M. M., Montangero, S., Calarco, T., and Neu, E. (2020). Introduction to quantum optimal control for quantum sensing with nitrogen-vacancy centers in diamond. AVS Quantum Science, 2, 024701. DOI: 10.1116/5.0006785
  171. Reta, D., Kragskow, J. G. C., and Chilton, N. F. (2021). Ab Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule Magnets. Journal of the American Chemical Society, 143, 5943–5950 DOI: 10.1021/jacs.1c01410
  172. Rigamonti, L., Cornia, A., Nava, A., Perfetti, M., Boulon, M.-E., Barra, A.-L., Zhong, X., Park, K., and Sessoli, R. (2014). Mapping of single-site magnetic anisotropy tensors in weakly coupled spin clusters by torque magnetometry. Physical Chemistry Chemical Physics, 16, 17220. DOI: 10.1039/C4CP02462A
  173. Rubín-Osanz, M., Lambert, F., Shao, F., Rivìere, E., Guillot, R., Suaud, N., Guihéry, N., Zueco, D., Barra, A.-L., Mallah, T., and Luis, F. (2021). Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni( II ). Chemical Science, 12, 5123–5133. DOI: 10.1039/D0SC05856D
  174. Ryan, A. A. and Senge, M. O. (2013). Synthesis and Functionalization of Triply Fused Porphyrin Dimers. European Journal of Organic Chemistry, 2013, 3700–3711. DOI: 10.1002/ejoc.201201622
  175. Santanni, F., Albino, A., Atzori, M., Ranieri, D., Salvadori, E., Chiesa, M., Lunghi, A., Bencini, A., Sorace, L., Totti, F., and Sessoli, R. (2021). Probing Vibrational Symmetry Effects and Nuclear Spin Economy Principles in Molecular Spin Qubits. Inorganic Chemistry, 60,140–151. DOI: 10.1021/acs.inorgchem.0c02573
  176. Santini, P., Carretta, S., and Amoretti, G. (2016). Magnetic Molecules as Spin Qubits. in Molecular Magnetic Materials (Sieklucka, B. and Pinkowicz, D. edts.), pp. 103–129. Weinheim: Wiley-VCH Verlag GmbH and Co. KGaA DOI: 10.1002/9783527694228.ch5
  177. Sato, K., Nakazawa, S., Rahimi, R., Ise, T., Nishida, S., Yoshino, T., Mori, N., Toyota, K., Shiomi, D., Yakiyama, Y., Morita, Y., Kitagawa, M., Nakasuji, K., Nakahara, M., Hara, H., Carl, P., Hofer, P., and Takui, T. (2009). Molecular electron-spin quantum computers and quantum information processing: pulse-based electron magnetic resonance spin technology applied to matter spin-qubits. Journal of Materials Chemistry, 19, 3739. DOI: 10.1039/b819556k
  178. Schild, D. (2008). X-ray Photoelectron Spectroscopy in Hydrogen Technology: Mobile and Portable Applications (Léon, A., ed), pp. 575–601. Berlin, Heidelberg: Springer Berlin Heidelberg. DOI: 10.1007/978-3-540-69925-5
  179. Schissler, C., Schneider, E. K., Felker, B., Weis, P., Nieger, M., Kappes, M. M., and Bräse, S. (2021). A Synthetic Strategy for Cofacial Porphyrin-Based Homo- and Heterobimetallic Complexes. Chemistry – A European Journal, 27, 3047–3054. DOI: 10.1002/chem.202002394
  180. Schweiger, A. and Jeschke, G. (2001). Principles of pulse electron paramagnetic resonance. Oxford: Oxford University Press. DOI: 10.1093/oso/9780198506348.001.0001
  181. Sessoli, R., Gatteschi, D., Caneschi, A., and Novak, M. A. (1993). Magnetic bistability in a metal-ion cluster. Nature, 365, 141–143. DOI: 10.1038/365141a0
  182. Shevchenko, O. A., Melnikov, A. R., Tararyshkin, S. V., Getmanov, Y. V., Serednyakov, S. S., Bykov, E. V., Kubarev, V. V., Fedin, M. V., and Veber, S. L. (2019). Electronic Modulation of THz Radiation at NovoFEL: Technical Aspects and Possible Applications. Materials, 12, 3063. DOI: 10.3390/ma12193063
  183. Shiddiq, M., Komijani, D., Duan, Y., Gaita-Ariño, A., Coronado, E., and Hill, S. (2016). Enhancing coherence in molecular spin qubits via atomic clock transitions. Nature, 531, 348–351. DOI: 10.1038/nature16984
  184. Shimizu, D. and Osuka, A. (2018). A Benzene-1,3,5-Triaminyl Radical Fused with ZnII-Porphyrins: Remarkable Stability and a High-Spin Quartet Ground State. Angewandte Chemie International Edition, 57, 3733–3736. DOI: 10.1002/anie.201801080
  185. Sleator, T. and Weinfurter, H. (1995). Realizable Universal Quantum Logic Gates. Physical Review Letters, 74, 4087–4090. DOI: 10.1103/PhysRevLett.74.4087
  186. Smith, J. M., Meynell, Bleszynski Jayich, A. C., and Meijer, J. (2019). Colour centre generation in diamond for quantum technologies. Nanophotonics, 8, 1889–1906. DOI: 10.1515/nanoph-2019-0196
  187. Soeteman, J., Bevaart, L., and van Duyneveldt, A. (1974). The direct and Raman spin-lattice relaxation process in YbCl3·6H2O. Physica, 74, 126–134. DOI: 10.1016/0031-8914(74)90188-8
  188. Souza, A. M., Álvarez, G. A., and Suter, D. (2012). Robust dynamical decoupling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370, 4748–4769. DOI: 10.1098/rsta.2011.0355
  189. Standley, K. J. and Vaughan, R. A. (1969). Electron Spin Relaxation Phenomena in Solids. Boston: Springer US. DOI: 10.1007/978-1-4899-6539-4
  190. Stoll, S. and Schweiger, A. (2006). EasySpin, a comprehensive software package for spectral simulation and analysis in EPR. Journal of Magnetic Resonance, 178, 42–55. DOI: 10.1016/j.jmr.2005.08.013
  191. Stuzhin, P. A., Bauer, E. M., and Ercolani, C. (1998). Tetrakis(thiadiazole)porphyrazines. 1. Syntheses and Properties of Tetrakis(thiadiazole)porphyrazine and Its Magnesium and Copper Derivatives. Inorganic Chemistry, 37, 1533–1539. DOI: 10.1021/ic9609259
  192. Suzuki, Y., Fujimori, M.,Yoshikawa, H., and Awaga, K. (2004). Packing Motifs and Magneto-Structural Correlations in Crystal Structures of Metallo-Tetrakis(1,2,5-thiadiazole)porphyrazine Series, MTTDPz (M = H2, Fe, Co, Ni, Cu, Zn). Chemistry - A European Journal, 10, 5158– 5164. DOI: 10.1002/chem.200400394
  193. Tacchino, F., Chiesa, A., Sessoli, R., Tavernelli, I., and Carretta, S. (2021). A proposal for using molecular spin qudits as quantum simulator of light-matter interactions. Chemical Science, 9, 10266–10275. DOI: 10.1039/D1TC00851J
  194. Tennant, W. C., Walsby, C. J., Claridge, R. F. C., and McGavin, D. G. (2000). Rotation matrix elements and further decomposition functions of two-vector tesseral spherical tensor operators; their uses in electron paramagnetic resonance spectroscopy. Journal of Physics: Condensed Matter, 12, 9481–9495. DOI: 10.1088/0953-8984/12/45/310
  195. Tesi, L., Lunghi, A., Atzori, M., Lucaccini, E., Sorace, L., Totti, F., and Sessoli, R. (2016). Giant spin–phonon bottleneck effects in evaporable vanadyl-based molecules with long spin coherence. Dalton Transactions, 45, 16635–16643. DOI: 10.1039/C6DT02559E
  196. Thiele, S., Balestro, F., Ballou, R., Klyatskaya, S., Ruben, M., and Wernsdorfer, W. (2014). Electrically driven nuclear spin resonance in single-molecule magnets. Science, 344, 1135–1138. DOI: 10.1126/science.1249802
  197. Timco, G. A., Carretta, S., Troiani, F., Tuna, F., Pritchard, R. J., Muryn, C. A., McInnes, E. J. L., Ghirri, A., Candini, A., Santini, P., Amoretti, G., Affronte, M., and Winpenny, R. E. P. (2009). Engineering the coupling between molecular spin qubits by coordination chemistry. Nature Nanotechnology, 4, 173–178. DOI: 10.1038/nnano.2008.404
  198. Timco, G. A., Carretta, S., Troiani, F., Tuna, F., Pritchard, R. J., Muryn, C. A., McInnes, E. J. L., Ghirri, A., Candini, A., Santini, P., Amoretti, G., Affronte, M., and Winpenny, R. E. P. (2009). Engineering the coupling between molecular spin qubits by coordination chemistry. Nature Nanotechnology, 4, 173–178. DOI: 10.1038/nnano.2008.404
  199. Timco, G. A., Faust, T. B., Tuna, F., and Winpenny, R. E. P. (2011). Linking heterometallic rings for quantum information processing and amusement. Chemical Society Reviews, 40, 3067. DOI: 10.1039/c0cs00151a
  200. Timco, G. A., McInnes, E. J. L., Pritchard, R. G., Tuna, F., and Winpenny, R. E. P. (2008). Heterometallic Rings Made From Chromium Stick Together Easily. Angewandte Chemie International Edition, 47, 9681–9684. DOI: 10.1002/anie.200803637
  201. Trauzettel, B., Bulaev, D. V., Loss, D., and Burkard, G. (2007). Spin qubits in graphene quantum dots. Nature Physics, 3, 192–196. DOI: 10.1038/nphys544
  202. Troiani, F. and Affronte, M. (2011). Molecular spins for quantum information technologies. Chemical Society Reviews, 40, 3119. DOI: 10.1039/c0cs00158a
  203. Troiani, F., Ghirri, A., Affronte, M., Carretta, S., Santini, P., Amoretti, G., Piligkos, S., Timco, G. A., and Winpenny, R. E. P. (2005). Molecular Engineering of Antiferromagnetic Rings for Quantum Computation. Physical Review Letters, 94, 207208. DOI: 10.1103/PhysRevLett.94.207208
  204. Tsuda, A and Osuka, A. (2001). Fully Conjugated Porphyrin Tapes with Electronic Absorption Bands That Reach into Infrared. Science, 293, 79–82. DOI: 10.1126/science.1059552
  205. Uhrig, G. S. (2007). Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences. Physical Review Letters, 98, 100504. DOI: 10.1103/PhysRevLett.98.100504
  206. Ullah, A., Cerdá, J., Baldoví, J. J., Varganov, S. A., Aragó, J., and Gaita-Ariño, G. (2019). In Silico Molecular Engineering of Dysprosocenium-Based Complexes to Decouple Spin Energy Levels from Molecular Vibrations. The Journal of Physical Chemistry Letters, 10, 7678–7683. DOI: 10.1021/acs.jpclett.9b02982
  207. Urtizberea, A., Natividad, E., Alonso, P. J., Andrés, M. A., Gascón, I., Goldmann, M., and Roubeau, O. (2018). A Porphyrin Spin Qubit and Its 2D Framework Nanosheets. Advanced Functional Materials, 28, 1801695. DOI: 10.1002/adfm.201801695
  208. Van Vleck, J. H. (1940). Paramagnetic Relaxation Times for Titanium and Chrome Alum. Physical Review, 57, 426–447. DOI: 10.1103/PhysRev.57.426
  209. Vance, C. T., Welch, J. H., and Bereman, R. D. (1989). Syntheses, characterization and structural studies of copper complexes of the 1,2-dithiolene ligand, 5,6-dihydro-1,4-dithiin-2,3-dithiolate. Inorganica Chimica Acta, 164, 191–200. DOI: 10.1016/S0020-1693(00)83222-3
  210. Vasyukov, V. N. (2011). Manifestation of non-centrality effect in the EPR spectrum of Fe3+ ion in the polycrystalline materials. Journal of Physics: Conference Series, 324, 012024. DOI: 10.1088/1742-6596/324/1/012024
  211. Veldhorst, M., Yang, C. H., Hwang, J. C. C., Huang, W., Dehollain, J. P., Muhonen, J. T., Simmons, S., Laucht, A., Hudson, F. E., Itoh, K. M., Morello, A., and Dzurak, A. S., (2015). A two-qubit logic gate in silicon. Nature, 526, 410–414, 2015. DOI: 10.1038/nature15263
  212. Volkov, M. Y. and Salikhov, K. M. (2011). Pulse Protocols for Quantum Computing with Electron Spins as Qubits. Applied Magnetic Resonance, 41, 145–154. DOI: 10.1007/s00723-011-0297-2
  213. von Kugelgen, S., Krzyaniak, M. D., Gu, M., Puggioni, D., Rondinelli, J. M., Wasielewski, M. R., and Freedman, D. E. (2021). Spectral Addressability in a Modular Two Qubit System. Journal of the American Chemical Society, 143, 8069–8077. DOI: 10.1021/jacs.1c02417
  214. Waldherr, G., Wang, Y., Zaiser, S., Jamali, M., Schulte-Herbrüggen, T., Abe, H., Ohshima, T., Isoya, J., Du, J. F., Neumann, P., and Wrachtrup, J. (2014). Quantum error correction in a solid-state hybrid spin register. Nature, 506, 204–207. DOI: 10.1038/nature12919
  215. Wang, Y., Hou, J., Eguchi, K., Nanjo, C., Takaoka, T., Sainoo, Y., Awaga, K., and Komeda, T. (2020). Structural, Electronic, and Magnetic Properties of Cobalt Tetrakis (Thiadiazole) Porphyrazine Molecule Films on Au(111). ACS Omega, 5, 6676–6683. DOI: 10.1021/acsomega.9b04453
  216. Warner, M., Din, S., Tupitsyn, I. S., Morley, G. W., Stoneham, A. M., Gardener, J. A., Wu, Z., Fisher, A. J., Heutz, S., Kay, C. W. M., and Aeppli, G. (2013). Potential for spin-based information processing in a thin-film molecular semiconductor. Nature, 503, 504–508. DOI: 10.1038/nature12597
  217. Wasielewski, M. R., Forbes, M. D. E., Frank, N. L., Kowalski, K., Scholes, G. D., Yuen-Zhou, J., Baldo, M. A., Freedman, D. E., Goldsmith, R. H., Goodson, T., Kirk, M. L., McCusker, J. K., Ogilvie, J. P., Shultz, D. A., Stoll, S. and Whaley, K. B. (2020). Exploiting chemistry and molecular systems for quantum information science. Nature Reviews Chemistry, 4, 490–504, 2020. DOI: 10.1038/s41570-020-0200-5
  218. Wedge, C. J., Timco, G. A., Spielberg, E. T., George, R. E., Tuna, F., Rigby, S., McInnes, E. J. L., Winpenny, R. E. P., Blundell, S. J., and Ardavan, A. (2012). Chemical Engineering of Molecular Qubits. Physical Review Letters, 108, 107204. DOI: 10.1103/PhysRevLett.108.107204
  219. Werninghaus, M., Egger, D. J., Roy, F., Machnes, S., Wilhelm, F. K., and Filipp, S. (2021). Leakage reduction in fast superconducting qubit gates via optimal control. Nature Physics Journal Quantum Information, 7, 14. DOI: 10.1038/s41534-020-00346-2
  220. Westfall, L. and Leider, A. (2020). Superdense coding step by step. in Advances in Information and Communication (Arai, K. and Bhatia, R. eds.), pp. 357–372. Springer Nature Switzerland AG DOI: 10.1007/978-3-030-12385-7
  221. Wili, N., Richert, S., Limburg, B., Clarke, S. J., Anderson, H. L., Timmel, C. R., and Jeschke, G. (2019). ELDOR-detected NMR beyond hyperfine couplings: a case study with Cu(II)-porphyrin dimers. Physical Chemistry Chemical Physics, 21, 11676–11688. DOI: 10.1039/C9CP01760G
  222. Willke, P., Paul, W., Natterer, F. D., Yang, K., Bae, Y., Choi, T., Fernández-Rossier, J., Heinrich, A. J., and Lutz, C. P. (2018). Probing quantum coherence in single-atom electron spin resonance. Science Advances, 4, eaaq1543. DOI: 10.1126/sciadv.aaq1543
  223. Wojnar, M. K., Laorenza, D. W., Schaller, R. D., and Freedman, D. E. (2020). Nickel(II) Metal Complexes as Optically Addressable Qubit Candidates. Journal of the American Chemical Society, 142, 14826–14830. DOI: 10.1021/jacs.0c06909
  224. Wolfowicz, G., Tyryshkin, A. M., George, R. E., Riemann, H., Abrosimov, N. V., Becker, P., Pohl, H. J., Thewalt, M. L. W., Lyon, S. A., and Morton, J. J. L. (2013). Atomic clock transitions in silicon-based spin qubits. Nature Nanotechnology, 8, 561–564. DOI: 10.1038/nnano.2013.117
  225. Wu, H., George, R. E., Wesenberg, J. H., Mølmer, K., Schuster, D. I., Schoelkopf, R. J., Itoh, K. M., Ardavan, A., Morton, J. J. L., and Briggs, G. A. D. (2010). Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble. Physical Review Letters, 105, 140503. DOI: 10.1103/PhysRevLett.105.140503
  226. Wu, Y., Wang, Y., Qin, X., Rong, X., and Du, J. (2019). A programmable two-qubit solid-state quantum processor under ambient conditions. Nature Physics Journal Quantum Information, 5, 9. DOI: 10.1038/s41534-019-0129-z
  227. Yamabayashi, T., Atzori, M., Tesi, L., Cosquer, G., Santanni, F., Boulon, M.-E., Morra, E., Benci, S., Torre, R., Chiesa, M., Sorace, L., Sessoli, R., and Yamashita, M. (2018). Scaling Up Electronic Spin Qubits into a Three-Dimensional Metal–Organic Framework. Journal of the American Chemical Society, 140, 12090–12101. DOI: 10.1021/jacs.8b06733
  228. Yang, K., Phark, S.-H., Bae, Y., Esat, T., Willke, P., Ardavan, A., Heinrich, A. J., and Lutz, C. P. (2021). Probing resonating valence bond states in artificial quantum magnets. Nature Communications, 12, 993. DOI: 10.1038/s41467-021-21274-5
  229. Yu, C.-J., Krzyaniak, M. D., Fataftah, M. S., Wasielewski, M. R., and Freedman, D. E. (2019). A concentrated array of copper porphyrin candidate qubits. Chemical Science, 10, 1702– 1708. DOI: 10.1039/C8SC04435J
  230. Zadrozny, J. M., Niklas, J., Poluektov, O. G., and Freedman, D. E (2015). Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit. ACS Central Science, 1, 488–492. DOI: 10.1021/acscentsci.5b00338
  231. Zhang, X., Wolf, C., Wang, Y., Aubin, H., Bilgeri, T., Willke, P., Heinrich, A., and Choi, T. (2022). Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions. Nature Chemistry, 14, 59–65. DOI: 10.1038/s41557-021-00827-7
  232. Zhang, Y.-H., Ruan, W.-J., Li, Z.-Y., Wu, Y., and Zheng, J.-Y. (2005). DFT study on the influence of meso-phenyl substitution on the geometric, electronic structure and vibrational spectra of free base porphyrin. Chemical Physics, 315, 201–213. DOI: 10.1016/j.chemphys.2005.04.004
  233. Zheng, T.-C., Burkart, M., and Richardson, D. E. (1999). A general and mild synthesis of thioesters and thiols from halides. Tetrahedron Letters, 40, 603–606. DOI: 10.1016/S0040-4039(98)02545-3
  234. Zou, X., Fan, H., Tian, Y., Zhang, M., and Yan, X. Chemical bath deposition of Cu2O quantum dots onto ZnO nanorod arrays for application in photovoltaic devices. RSC Advances, 5, 30, 23401–23409. DOI: 10.1039/C4RA13776K
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Book Title

Molecular approaches for quantum technologies

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Optimization of electron spin-based quantum bits and quantum logic gates

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Fabio Santanni

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2025

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