Stable organic radical qubits and their applications in quantum information science

Abstract

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

Graphical abstract

Figure 1

Introduction to stable organic radical qubits

Figure 2

Schemes of selected stable organic radical qubits

Figure 3

Influence of molecular structures on spin dynamics (A) g-Anisotropy mapped on a Bloch sphere calculated with EasySpin. (B) Illustration of spin-orbit coupling. (C) Illustration of spin diffusion barrier (inner circle). Green nuclei are within the spin diffusion barrier, and the red ones are out of it. (D) Influence of conjugation and steric hindrance on T₁ of various nitroxide radicals dissolved in sucrose octaacetate. Dotted and dashed lines represent contributions from the Raman process and thermally activated process, respectively, and solid lines represent their sums. Reproduced from Sato et al. with permission from Taylor & Francis, copyright 2007. (E) Influence of the number of chlorine atoms substituted on triphenylmethyl radicals on their T_m values. The triphenylmethyl radical was either dissolved in d₈-toluene solution or diluted in powders of hydrogenated diamagnetic analogues. 5CM is the same as PCTM (Figure 2). Reproduced from Dai et al. with permission from John Wiley & Sons, copyright 2018. (F) Influence of concentration of methyl groups in solution on the T_m of tempone radical. Reproduced from Zecevic et al. with permission from Taylor & Francis, copyright 1998.

Figure 4

Influence of temperature on spin dynamics (A) Temperature dependence of spin-lattice relaxation rate under various relaxation processes normalized to the 1/T₁ at 300 K. Simulations were performed based on corresponding equations in Table S1, and simulation parameters of Orbach, Raman, thermally activated, and local-mode processes are arbitrary. (B) Temperature dependence of T₁ and T_m for PtTTFtt and PtTTFtt+. Reproduced from McNamara et al. ©The Authors, some rights reserved; distributed under CC-BY-NC-ND 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/). (C) Temperature dependence of spin-lattice relaxation rate for d₂₄-OX063 with various concentrations. Reproduced from Chen et al. with permission from Royal Society of Chemistry, copyright 2016. (D) Temperature dependence of 1/T₁ and T_m for NIT-GNRs and NIT-polyphenylene. Reproduced from Slota et al. with permission from Springer Nature, copyright 2018.

Figure 5

Influence of Larmor frequency and pulse sequence on spin dynamics (A−D) Spin relaxation driven by (A) spin rotation, (B) modulation of g-anisotropy and A-anisotropy, (C) thermally activated process, and (D) dipolar interaction, respectively, with solvent nuclei under various tumbling times and Larmor frequencies. Simulations were performed based on the corresponding equations in Table S1, and simulation parameters are arbitrary. (E) FID, Hahn echo, and CPMG decay curves. Reproduced from Mirzoyan et al. with permission from John Wiley & Sons, copyright 2021. (F) Echo decay curves acquired by Hahn echo or CPMG sequences with various numbers of π_Y pulses for chemically modified carbon nanotubes. Reproduced from Chen et al.; distributed under CC-BY 4.0 (http://creativecommons.org/licenses/by/4.0/).

Figure 6

Integration of radical qubits in polymers and microporous materials (A–C) (A) Structures, (B) variable-temperature T₁ and T_m, and (C) Hahn echo decay curves (298 K) of C_n-LA_m block copolymers. Reproduced from Hou et al. with permission from John Wiley & Sons, copyright 2024. (D–F) (D) Structure of TAPPy-NDI, and (E and F) concentration and temperature dependencies of its T₁ and T_m. Reproduced from Oanta et al. with permission from American Chemical Society, copyright 2023. (G–I) (G) Structure, (H) inversion recovery curve (296 K), and (I) Hahn echo decay curve (296 K) of MgHOTP. Reproduced from Sun et al. with permission from American Chemical Society, copyright 2022. (J–L) (J) Structure, (K) variable-temperature electrical conductivity, and (L) variable-temperature T₁ and T_m of Ni₃(HATI_X)₂. Reproduced from Lu et al. with permission from American Chemical Society, copyright 2024.

Figure 7

Integration of radical qubits in thin films and SAMs (A and B) (A) Structure and (B) variable-temperature T₁ and T_m of thin films of the PCTM radical. Reproduced from Dai et al. with permission from John Wiley & Sons, copyright 2018. (C) Fabrication of TEMPO SAM on a gold surface. (D) Temperature dependencies of T₁ and T_m for the TEMPO SAM and a dilute solution of TEMPO (PTEMPO). (C and D) Reproduced from Tesi et al. distributed under CC-BY 4.0 (http://creativecommons.org/licenses/by/4.0/).

Figure 8

QIS applications of radical qubits (A–E) Molecular quantum logic gate. (A) The molecule containing two ¹⁵N- and ²H-substituted TEMPO radicals used for the CNOT gate implementation. (B) Schematic illustration of the CNOT gate. (C) Continuous wave (CW) EPR spectrum of the biradical molecule. The arrow points to the resonance field at which the CNOT gate is implemented. (D) Schematic energy diagram of four zero-field split electron spin states of the biradical molecule. (E) Manifestation of the CNOT gate through the Rabi oscillation. (C–E) reproduced from Nakazawa et al. with permission from John Wiley & Sons, copyright 2021. (F–H) Molecular quantum memory. (F) Conceptual illustration of quantum memory. (G) Avoided crossing in a 2D CW EPR spectrum of BDPA·Bz radicals showing the strong coupling between electron spins and the microwave cavity. (H) A spin echo that shows the retrieval of quantum information stored in the quantum memory for 1.4 μs. Reproduced from Lenz et al. distributed under CC-BY 4.0 (http://creativecommons.org/licenses/by/4.0/). (I–K) Molecular quantum sensing. (I) Conceptual illustration of quantum sensing harnessing hyperfine interaction between MOF-integrated radicals and nuclear spins of adsorbed ions. (J) CP-ESEEM spectra of MgHOTP in THF solutions with various concentrations of Li⁺. (K) CP-ESEEM spectra of MgHOTP in THF solutions consisting of both Li⁺ and Na⁺. Reproduced from Sun et al. with permission from American Chemical Society, copyright 2022.