A 2023 blueprint (Chiesa, Roca, Chicco, de Ory, Gómez-León, Gomez, Zueco, Luis, Carretta; Phys. Rev. Applied 19, 064060) specifies a Molecular Spin Quantum Processor in which individual molecular nanomagnets act as multi-level spin qudits inside SQUID-tunable on-chip superconducting LC resonators, with local control lines and photon-mediated two-qudit gates. The architecture exists only on paper and in numerical simulations: its feasibility rests on materials and integration conditions that no synthesized molecule has yet met. The open problem is the design-synthesis realization of that blueprint: identify, synthesize, and integrate on chip molecular nanomagnets that simultaneously provide effective single-molecule spin-photon coupling of order 0.10.1–11 MHz (versus the ~kHz demonstrated so far), the inequivalent transition structure needed for spectral addressability and resonator tunability, placement and orientation of the addressed molecules at photon-field hot spots within the coupling range the design requires, and qudit coherence times compatible with gate sequences.

Background

A molecular nanomagnet (MNM) is a coordination molecule with a central magnetic ion or cluster shielded by organic ligands; chemists can tailor its spin SS, magnetic anisotropy, and environment with a precision unavailable in solid-state defects. Because an MNM with spin SS carries 2S+12S+1 low-energy spin levels, it naturally implements a qudit — a dd-level quantum unit with d>2d>2 that can embed several qubits and support quantum-error-correction codes designed at the chemical level. Circuit quantum electrodynamics (circuit QED) provides the wiring: a superconducting microwave resonator confines photons so that a spin placed in its magnetic field couples at rate gg, and a lumped-element LC resonator (a capacitor connected by a narrow wire inductor) can concentrate the photon vacuum magnetic field into a nanoscopic region, boosting gg. Inserting a dc SQUID (a superconducting loop of two Josephson junctions, tunable by magnetic flux) into the inductor makes the resonator frequency tunable by about 30% on nanosecond timescales, so different qudit transitions can be brought in and out of resonance one at a time. Zero-field-splitting anisotropy (a term DSz2DS_z^2 in the spin Hamiltonian) makes all energy gaps inequivalent, which is what allows each transition to be addressed selectively by resonant pulses or by resonator tuning.

The blueprint paper (Chiesa et al., Phys. Rev. Applied 19, 064060, 2023) assembles these ingredients into an elementary unit: two molecular spin qudits coupled to one SQUID-tunable LC resonator with nanoconstrictions and control transmission lines that generate local magnetic-field pulses. Single-qudit gates are driven classically; two-qudit gates use resonant photon exchange, which numerical simulations show to be faster and more faithful than the dispersive alternative; readout is via the resonator. The design is quantified: simulations assume an effective single-molecule transition coupling Gi0/2π≈1G_i^0/2\pi \approx 1 MHz (obtained from a bare S=1/2S=1/2 coupling of G/2π≃95G/2\pi \simeq 95 kHz at a 20 nm constriction in a 7.5 GHz low-impedance resonator, enhanced by the transition matrix elements of high-spin molecules) and coherence times T2T_2 of a few hundred microseconds. Against these targets the paper itself states the gap: experiments had achieved only G/2π≈1G/2\pi \approx 1–33 kHz for single spins near nanoconstrictions or in lumped-element resonators (e.g., Gimeno et al., ACS Nano 2020); depositing single molecules close enough to the constrictions is called "very challenging"; and reaching the assumed T2T_2 with qudits "needs still to be experimentally investigated". What has been demonstrated since — coherent collective coupling of molecular spin ensembles to lumped-element resonators, controlled orientation of vanadyl-porphyrin qudits via in-situ 2D-MOF nanosheet growth on multi-resonator chips (Gimeno et al., J. Phys. Chem. C 2025), coherent ensemble-photon control at millikelvin temperature (Bonizzoni et al., Nat. Commun. 2025), and high-fidelity qudit algorithms driven by classical pulses on ensembles (Chicco et al., JACS 2024; Rubín-Osanz et al., Nat. Commun. 2026) — is ensemble-level and drive-based, leaving the blueprint's molecule-by-molecule register unrealized.

Problem Statement

Which molecular nanomagnets can be synthesized, and how can they be integrated into superconducting circuitry, so that the blueprint of Chiesa et al. (Phys. Rev. Applied 19, 064060, 2023) is realized at its elementary-unit level? A satisfactory answer must specify chemically synthesizable molecular spin qudits — a deliberately positioned few-molecule register containing at least two qudits coupled to one resonator (the blueprint's elementary unit) — together with an on-chip integration and placement protocol for a SQUID-frequency-tunable lumped-element LC superconducting resonator chip such that, simultaneously: (1) the effective single-molecule spin-photon coupling on the addressed transitions is of order 0.10.1–11 MHz and large compared with the resonator and spin linewidths (the strong-coupling/cooperative regime for the individual unit, not only for a collective ensemble mode); (2) the molecular level structure provides the inequivalent, individually addressable transitions required for selective single-qudit drives, resonator-tuned matching, and local-field control of two-qudit gates; (3) the addressed molecules are located and oriented at the photon-field hot spots — within the tens of nanometres of the nanoconstrictions over which the design retains usable coupling — whether by deterministic placement or by selection of suitable molecules from a sparse statistical ensemble; and (4) qudit coherence times on chip are long enough — the blueprint assumes hundreds of microseconds — to support its simulated gate sequences, including a concrete prescription for at least one photon-mediated two-qudit gate between the molecular qudits. The question includes the chemical design space to be explored (high-spin clusters, lanthanide complexes with engineered gg-tensors such as Yb(trensal) analogues, clock-transition encodings) but asks for a concrete molecule-and-device realization: a synthesis-and-integration design with quantified predicted coupling, addressability, and coherence is acceptable, whereas merely restating the blueprint's simulation is not.

References

  1. A. Chiesa, S. Roca, S. Chicco, M. C. de Ory, A. Gómez-León, A. Gomez, D. Zueco, F. Luis, S. Carretta, "Blueprint for a Molecular-Spin Quantum Processor", Physical Review Applied 19, 064060 (2023). DOI: 10.1103/PhysRevApplied.19.064060; arXiv:2305.01688, https://arxiv.org/abs/2305.01688 (the arXiv preprint is titled "Blueprint of a Molecular Spin Quantum Processor")
  2. I. Gimeno, W. Kersten, M. C. Pallarés, P. Hermosilla, M. J. Martínez-Pérez, M. D. Jenkins, A. Angerer, C. Sánchez-Azqueta, D. Zueco, J. Majer, A. Lostao, F. Luis, "Enhanced Molecular Spin-Photon Coupling at Superconducting Nanoconstrictions", ACS Nano 14, 8707 (2020). DOI: 10.1021/acsnano.0c03167, https://doi.org/10.1021/acsnano.0c03167
  3. I. Gimeno, F. Luis, C. Marcuello, M. C. Pallarés, A. Lostao, M. Calero de Ory, A. Gomez, D. Granados, I. Tejedor, E. Natividad, A. Urtizberea, O. Roubeau, "Localized Nanoscale Formation of Vanadyl Porphyrin 2D MOF Nanosheets and Their Optimal Coupling to Lumped Element Superconducting Resonators", The Journal of Physical Chemistry C 129, 973 (2025). DOI: 10.1021/acs.jpcc.4c07265, https://doi.org/10.1021/acs.jpcc.4c07265
  4. S. Chicco, G. Allodi, A. Chiesa, E. Garlatti, C. D. Buch, P. Santini, R. De Renzi, S. Piligkos, S. Carretta, "Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits", Journal of the American Chemical Society 146, 1053 (2024). DOI: 10.1021/jacs.3c12008; arXiv:2309.05600, https://doi.org/10.1021/jacs.3c12008
  5. A. Chiesa, E. Macaluso, S. Carretta, "Quantum information processing with molecular nanomagnets: an introduction", Contemporary Physics 64, 253 (2023). DOI: 10.1080/00107514.2024.2381952; arXiv:2405.21000, https://doi.org/10.1080/00107514.2024.2381952
  6. S. Roca-Jerat, E. Macaluso, A. Chiesa, P. Santini, S. Carretta, "Simulating open quantum systems with molecular spin qudits", Materials Horizons 12, 3918 (2025). DOI: 10.1039/D4MH01512F, https://doi.org/10.1039/D4MH01512F
  7. C. Bonizzoni, D. Lamberto, S. Napoli, S. Günzler, D. Rieger, F. Santanni, A. Ghirri, W. Wernsdorfer, S. Savasta, M. Affronte, "Observation of perfect absorption in hyperfine levels of molecular spins with hermitian subspaces", Nature Communications 17, 470 (2025). DOI: 10.1038/s41467-025-67163-z; arXiv:2505.05966, https://doi.org/10.1038/s41467-025-67163-z
  8. M. Rubín-Osanz, L. Bersani, S. Chicco, G. Allodi, R. De Renzi, A. Mavromagoulos, M. D. Roy, S. Piligkos, E. Garlatti, S. Carretta, "Implementing the Quantum Fourier Transform on a molecular qudit with full refocusing and state tomography", Nature Communications 17, 6217 (2026). DOI: 10.1038/s41467-026-72390-z; arXiv:2512.15611, https://doi.org/10.1038/s41467-026-72390-z
  9. G. Gabarró-Riera, E. C. Sañudo, "Challenges for exploiting nanomagnet properties on surfaces", Communications Chemistry 7, 99 (2024). DOI: 10.1038/s42004-024-01183-6, https://doi.org/10.1038/s42004-024-01183-6
  10. M. Rubín-Osanz, D. Rodriguez, I. Gimeno, W. Kersten, N. González-Prato, M. C. Pallarés, S. Roca-Jerat, M. C. de Ory, M. Mas-Torrent, J. A. de Sousa, L. Tesi, D. Granados, J. Veciana, D. Zueco, A. Lostao, J. Schmiedmayer, I. Ratera, J. van Slageren, N. Crivillers, A. Gomez, F. Luis, "Optimizing magnetic coupling in lumped element superconducting resonators for molecular spin qubits", arXiv:2511.00857 (2025), https://arxiv.org/abs/2511.00857