The Rise of Single-Ion Magnets as Spin Qubits

Recent studies revealed that magnetic molecules with single spin centers showed exciting phenomena related to quantum information processing, such as long quantum coherence times and Rabi oscillations. In this review, we go over these phenomena according to the essential metal ions, from which we can see the development of single-ion magnets as spin qubits is booming, especially quantum coherence times have been significantly enhanced from nanoseconds to hundreds of microseconds in a short period. Hence, the correlations between the molecular structures and quantum coherence are becoming clearer. In this regard, some chemical approaches to designing better spin qubits have been discussed.


Introduction
Single-ion magnets (SIMs) are a kind of molecular magnets that contain only one spin center surrounded by organic ligands [1][2][3][4][5], and show potential applications for high-density information storage, molecular spintronic devices and quantum information processing (QIP) units [6][7][8][9].In this review, we will focus on the topic of SIMs for QIP applications.
For classical computation, the data are encoded in binary digits (bits), each of which is a well-defined state (0 or 1).In contrast, qubits take the advantage of superposition of quantum microstates.The basic set for qubits is |ψ> = α|0> + β|1>.Hence, a qubit can be either |1> or |0>, or any arbitrary superposition of these two states [10][11][12].The key point for being a good qubit is to have long transverse relaxation time T 2 .Moreover, the spin-lattice relaxation time T 1 , which describes transitions from, say, |1> to |0>, is also very important because to observe the Rabi oscillations both T 1 and T 2 must be long enough.Because the period of coherent Rabi oscillations 1/Ω R , induced by an external stimulus (usually microwaves) between different qubit states, is actually used to evaluate the quality of a quantum system, the coherence time divided by half of the Rabi period, which is defined as Q M = 2Ω R T 2 (Q M is the qubit figure of merit) and represented by the number of coherent single-qubit operations, is useful to evaluate the performance of spin qubit.Only when the Q M is large enough, can the material then be used for QIP [13].Other than the long coherence times, the possibility of building quantum logical gates is also very important [14].
Up to date, suitable physical carriers for qubits are found in ion traps [15,16], photons [17], nuclear spins [18], superconducting circuits [19,20], spin-based systems [21], atomic impurities in solids [22,23] and coordination molecules [12,[24][25][26][27].Among those candidates, the coordination molecules are extremely exciting due to the ready chemical design and detailed magneto-structural correlations.Specifically, the primary factors influencing the quantum decoherence such as the magnitude of spins, spin-orbit coupling effects and nuclear spin bath, and other peripheral factors such as the donor atoms of the coordinating ligands and solvent molecules can be systematically clarified, which can in turn guide the design of better molecular qubits [28][29][30][31][32][33][34].Previously, such examples were only demonstrated by molecules with multi-metal centers [12,34].More recently, new systems based on single-ion magnetic molecules were identified with even better performance owing to the well isolated environment.More excitingly, quantum logic gates such as the Controlled-NOT (CNOT) gate based on multiqubit can be readily achieved by chemical linkage of molecules [35][36][37][38] and quantum state can be read out by a single nuclear spin in TbPc 2 [39,40].Here below, we discussed these exciting topics according to the comprising metal centers, highlighting their advantages for QIP applications.

Single-Ion Magnetic Molecules with Transition Metal Centers
As the valence electrons for 3d transition metals locate in outer d orbits, the ligands coordinating to the transition metals have great impact on the electronic structure of the central cations, which then significantly influence the property of quantum coherence.The story starts from the simplest spin-1/2 systems such as V(IV) and Cu(II) ions with only two-level states, spin-up and spin-down.

V(IV) Based Spin Qubits
Pioneering work searching for potential spin qubits started from the V(IV) ion with small spin-1/2 state and large nuclear spin I = 7/2 (see Table 1).The first example is the complex (Bu 4 N) 2 [V(C 8 S 8 ) 3 ] 1 [41], in which the V(IV) ion is coordinated to six S ions, providing a nuclear spin free peripheral environment (Figure 1a).The hyperfine coupling of the electron spin and nuclear spin produces multiple states detected by electron paramagnetic resonance (EPR) spectrum (Figure 1b).Eight separate transitions were found to be potentially available for quantum information processing.The coherence time T 2 is 1.2 µs at 80 K (performed on a 1 mM solution of 1 in butyronitrile).Rabi oscillations are observed by transient nutation experiments (Figure 1d), and the Rabi frequencies yielded from the nutation data at 3486 Oe at corresponding microwave power (B 1 ) attenuations, namely are 28.1 MHz, 17.6 MHz, and 10.2 MHz for 3 dB, 7 dB, and 11 dB.
clarified, which can in turn guide the design of better molecular qubits [28][29][30][31][32][33][34].Previously, such examples were only demonstrated by molecules with multi metal centers [12,34].More recently, new systems based on single-ion magnetic molecules were identified with even better performance owing to the well isolated environment.More excitingly, quantum logic gates such as the Controlled-NOT (CNOT) gate based on multiqubit can be readily achieved by chemical linkage of molecules [35][36][37][38] and quantum state can be read out by a single nuclear spin in TbPc2 [39,40].Here below, we discussed these exciting topics according to the comprising metal centers, highlighting their advantages for QIP applications.

Single-Ion Magnetic Molecules with Transition Metal Centers
As the valence electrons for 3d transition metals locate in outer d orbits, the ligands coordinating to the transition metals have great impact on the electronic structure of the central cations, which then significantly influence the property of quantum coherence.The story starts from the simplest spin-1/2 systems such as V(IV) and Cu(II) ions with only two-level states, spin-up and spin-down.

V(IV) Based Spin Qubits
Pioneering work searching for potential spin qubits started from the V(IV) ion with small spin-1/2 state and large nuclear spin I = 7/2 (see Table 1).The first example is the complex (Bu4N)2[V(C8S8)3] 1 [41], in which the V(IV) ion is coordinated to six S ions, providing a nuclear spin free peripheral environment (Figure 1a).The hyperfine coupling of the electron spin and nuclear spin produces multiple states detected by electron paramagnetic resonance (EPR) spectrum (Figure 1b).Eight separate transitions were found to be potentially available for quantum information processing.The coherence time T2 is 1.2 μs at 80 K (performed on a 1 mM solution of 1 in butyronitrile).Rabi oscillations are observed by transient nutation experiments (Figure 1d), and the Rabi frequencies yielded from the nutation data at 3486 Oe at corresponding microwave power (B1) attenuations, namely are 28.1 MHz, 17.6 MHz, and 10.2 MHz for 3 dB, 7 dB, and 11 dB.2a-d), were prepared to test the electronic donating ability on the quantum coherence times [42].The similar S 6 coordination environment is maintained.Interestingly, the longest T 2 was found for 2 of 4 µs at 80 K, indicating the weaker donating ability is better since the donating ability sequence is C 8 S 8 2− < β-C 3 S 5 2− < α-C 3 S 5 2− < C 3 S 4 O 2− .In addition, the solvent effect on quantum coherence was investigated.Several solvents including some deuterated ones such as PrCN, PrCN/DMF, DMF/Tol, d 7 -DMF/d 8 -Tol and CS 2 were chosen and found they have little effect on T 1 .In contrast, T 2 is significantly affected, e.g., T 2 for complex 2 in CS 2 is 1.18 µs (120 K), which is about 10 times longer than that in PrCN (0.108 µs, 120 K).Moreover, T 2 is temperature-dependent.At 10 K T 2 of 2 in CS 2 solution is enhanced to 675 (7) µs, even longer than some prominent solid-state qubits [43,44].Remarkably, Rabi oscillations were observed for all four complexes (Figure 2e), and Q M for 2 was found to be 36,000, which is very high among molecule-based spin qubits.Hence, this series of V(IV) complexes indicates the spin qubits are significantly affected by nuclear spin bath.Subsequently, a series of V(IV) complexes (Ph4P)2[V(C8S8)3] 2, (Ph4P)2[V(β-C3S5)3] 3, (Ph4P)2[V(α-C3S5)3] 4, and (Ph4P)2[V(C3S4O)3] 5, based on carbonsulfides (Figure 2a-d), were prepared to test the electronic donating ability on the quantum coherence times [42].The similar S6 coordination environment is maintained.Interestingly, the longest T2 was found for 2 of 4 μs at 80 K, indicating the weaker donating ability is better since the donating ability sequence is C8S8 2− < β-C3S5 2− < α-C3S5 2− < C3S4O 2− .In addition, the solvent effect on quantum coherence was investigated.Several solvents including some deuterated ones such as PrCN, PrCN/DMF, DMF/Tol, d7-DMF/d8-Tol and CS2 were chosen and found they have little effect on T1.In contrast, T2 is significantly affected, e.g., T2 for complex 2 in CS2 is 1.18 μs (120 K), which is about 10 times longer than that in PrCN (0.108 μs, 120 K).Moreover, T2 is temperature-dependent.At 10 K T2 of 2 in CS2 solution is enhanced to 675 (7) μs, even longer than some prominent solid-state qubits [43,44].Remarkably, Rabi oscillations were observed for all four complexes (Figure 2e), and QM for 2 was found to be 36,000, which is very high among molecule-based spin qubits.Hence, this series of V(IV) complexes indicates the spin qubits are significantly affected by nuclear spin bath.The second class of mononuclear V(IV) based spin qubits contains the VO 2+ unit with distinct short V=O double bond (about 1.6 Å), which is much shorter than other coordination bonds bound to the central V(IV) ions in a typical square pyramidal geometry.Such strong bond is believed to be responsible for a special d-orbital splitting which leaves the dxy orbital being in the lowest place in energy levels and well separated from the other orbitals.This is evident in the complex VO(dpm)2 6 (dpm − = dipivaloylmethanate) (Figure 3a) [45] whose V=O bond length is 1.59 Å, while other V-O single bonds averages at 1.96 Å. AC magnetic susceptibility study gives out-of-phase signals up to 80 K for frequencies lower than 10 kHz, which is the highest one among all reported molecular magnets.The relaxation time T1 at 80 K reached 13.42 μs (Figure 3d).By pulsed EPR spectroscopy, the coherence time was detected.When complex 6 was dissolved in CH2Cl2-toluene (1 mM), T2 reaches 2.1 μs at 80 K, and with 1:10 dispersion of diamagnetic TiO(dpm)2, this T2 can be further preserved up to 220 K. T1 was also determined by pulsed EPR spectroscopy, which gave the consistent results for AC magnetic susceptibility study, conforming that the two techniques are actually probing the same process.Complexes VO(acac)2 7 and VO(dbm)2 8)(acac − = acetylacetonate, and dbm − = dibenzoylmethanate) (Figure 3b,c) share a similar coordination environment to 6 [46].The V=O bond distances are 1.585 Å and 1.578 Å for 7 and 8, respectively.Both of 7 and 8 show out-ofphase AC signals under a static magnetic field of 0.2 T up to 40 K, which is associated with a giant spin-phonon bottleneck effect.Moreover, a pronounced crystal size dependence of the relaxation time was observed in complexes 6-8.The second class of mononuclear V(IV) based spin qubits contains the VO 2+ unit with distinct short V=O double bond (about 1.6 Å), which is much shorter than other coordination bonds bound to the central V(IV) ions in a typical square pyramidal geometry.Such strong bond is believed to be responsible for a special d-orbital splitting which leaves the d xy orbital being in the lowest place in energy levels and well separated from the other orbitals.This is evident in the complex VO(dpm) 2 6 (dpm − = dipivaloylmethanate) (Figure 3a) [45] whose V=O bond length is 1.59 Å, while other V-O single bonds averages at 1.96 Å. AC magnetic susceptibility study gives out-of-phase signals up to 80 K for frequencies lower than 10 kHz, which is the highest one among all reported molecular magnets.The relaxation time T 1 at 80 K reached 13.42 µs (Figure 3d).By pulsed EPR spectroscopy, the coherence time was detected.When complex 6 was dissolved in CH 2 Cl 2 -toluene (1 mM), T 2 reaches 2.1 µs at 80 K, and with 1:10 dispersion of diamagnetic TiO(dpm) 2 , this T 2 can be further preserved up to 220 K. T 1 was also determined by pulsed EPR spectroscopy, which gave the consistent results for AC magnetic susceptibility study, conforming that the two techniques are actually probing the same process.Complexes VO(acac) 2 7 and VO(dbm) 2 8) (acac − = acetylacetonate, and dbm − = dibenzoylmethanate) (Figure 3b,c) share a similar coordination environment to 6 [46].The V=O bond distances are 1.585 Å and 1.578 Å for 7 and 8, respectively.Both of 7 and 8 show out-of-phase AC signals under a static magnetic field of 0.2 T up to 40 K, which is associated with a giant spin-phonon bottleneck effect.Moreover, a pronounced crystal size dependence of the relaxation time was observed in complexes 6-8.
a Reported T2 values at the highest temperatures; b Best T2 values; c Reported temperature for Rabi oscillations.
Another mononuclear V(IV) based spin qubits with short V=O bond (1.58 Å) is the complex VOPc 9 (Pc = Phthalocyanine) (Figure 4a) [31,48].Together with its d 1 electron configuration, this molecule makes a perfect two level system for spin qubit.Moreover, the out-of-phase signals of AC magnetic susceptibility for the frequency of 10 kHz can be observed up to 40 K under an applied static magnetic field of 0.2 T.An extraordinarily long T1 (2.4 s at 7 K) was obtained by Q-band EPR measurements in 0.5 mM D2SO4-solution, and T2 is 20 μs at 20 K under the same condition [31].When VOPc is mixed with the isostructural diamagnetic host TiOPc in molar ratio of 1:1000, quantum coherence could be detected up to room temperature.T1 of 1.1 μs at 300 K was obtained by inversion recovery experiments and by echo decay experiments, echo decay traces (Figure 4b) were detected up to room temperature with T2 of 0.83 μs.Hence, for the first time, Rabi oscillation at room temperatures was detected in a solid state molecular system (Figure 4c).Besides, the quantum states of this electron spins based system can be efficiently initialized with high thermal stability, representing a promising qubit.Another mononuclear V(IV) based spin qubit with short V=O bond (1.58 Å) is the complex VOPc 9 (Pc = Phthalocyanine) (Figure 4a) [31,48].Together with its d 1 electron configuration, this molecule makes a perfect two level system for spin qubit.Moreover, the out-of-phase signals of AC magnetic susceptibility for the frequency of 10 kHz can be observed up to 40 K under an applied static magnetic field of 0.2 T.An extraordinarily long T 1 (2.4 s at 7 K) was obtained by Q-band EPR measurements in 0.5 mM D 2 SO 4 -solution, and T 2 is 20 µs at 20 K under the same condition [31].When VOPc is mixed with the isostructural diamagnetic host TiOPc in molar ratio of 1:1000, quantum coherence could be detected up to room temperature.T 1 of 1.1 µs at 300 K was obtained by inversion recovery experiments and by echo decay experiments, echo decay traces (Figure 4b) were detected up to room temperature with T 2 of 0.83 µs.Hence, for the first time, Rabi oscillation at room temperatures was detected in a solid state molecular system (Figure 4c).Besides, the quantum states of this electron spins based system can be efficiently initialized with high thermal stability, representing a promising qubit.More recently, a new mononuclear V(IV) complex (Ph4P)2[VO(α-C3S5)2] 10 was reported, which enhances the quantum coherence by strong V=O double bond [47].As shown in Figure 5a, the structure of 10 is similar to 4 except for the apical O atom.For comparison, the dynamic magnetism of both complexes were studied.Under a static magnetic field of 0.2 T, complex 4 displays slow magnetic relaxations below 10 K; while for complex 10, the temperature is raised up to 40 K. Their quantum coherences were detected by continuous wave and pulsed EPR measurements on diluted samples.For   More recently, a new mononuclear V(IV) complex (Ph 4 P) 2 [VO(α-C 3 S 5 ) 2 ] 10 was reported, which enhances the quantum coherence by strong V=O double bond [47].As shown in Figure 5a, the structure of 10 is similar to 4 except for the apical O atom.For comparison, the dynamic magnetism of both complexes was studied.Under a static magnetic field of 0.2 T, complex 4 displays slow magnetic relaxations below 10 K; while for complex 10, the temperature is raised up to 40 K. Their quantum coherences were detected by continuous-wave and pulsed EPR measurements on diluted samples.More recently, a new mononuclear V(IV) complex (Ph4P)2[VO(α-C3S5)2] 10 was reported, which enhances the quantum coherence by strong V=O double bond [47].As shown in Figure 5a, the structure of 10 is similar to 4 except for the apical O atom.For comparison, the dynamic magnetism of both complexes were studied.Under a static magnetic field of 0.2 T, complex 4 displays slow magnetic relaxations below 10 K; while for complex 10, the temperature is raised up to 40 K. Their quantum coherences were detected by continuous wave and pulsed EPR measurements on diluted samples.For

Cu(II) Based Single-Ion Spin Qubits
Except for V(IV), Cu(II) is another ion with spin-1/2 state.Several examples of mononuclear Cu(II) complexes have been reported as potential single-ion spin qubits (Table 2).The first one is CuPc 11 (Figure 6a) [31,49].By organic-molecular-beam deposition, complex 11 and free phthalocyanine are able to assemble a monoatomic layer onto the layer of perylene-3,4,9,20-tetracarboxylic dianhydride.With the Hahn echo sequence, T 2 for 11 was determined to be 1 µs at 80 K.Moreover, Rabi oscillations of a 0.1% CuPc:H 2 Pc were clearly observed at 5 K (Figure 6c) [49].The impact of solvent deuteration on electron spin relaxation has been investigated by dissolving 11 in H 2 SO 4 and D 2 SO 4 [31].For D 2 SO 4 , T 2 is about 41 µs at 7 K, which is five times longer than those in H 2 SO 4 (Figure 6b).The ligand effect on the quantum coherence times was also investigated using complexes CuPc Cl 12 and CuPc F 13.All the three complexes share a similar T 2 value of 40 µs at 7 K, indicating the ligand field effect is little in this series [31].Except for V(IV), Cu(II) is another ion with spin-1/2 state.Several examples of mononuclear Cu(II) complexes have been reported as potential single-ion spin qubits (Table 2).The first one is CuPc 11 (Figure 6a) [31,49].By organic-molecular-beam deposition, complex 11 and free phthalocyanine are able to assemble a monoatomic layer onto the layer of perylene-3,4,9,20-tetracarboxylic dianhydride.With the Hahn echo sequence, T2 for 11 was determined to be 1 μs at 80 K.Moreover, Rabi oscillations of a 0.1% CuPc:H2Pc were clearly observed at 5 K (Figure 6c) [49].The impact of solvent deuteration on electron spin relaxation has been investigated by dissolving 11 in H2SO4 and D2SO4 [31].For D2SO4, T2 is about 41 μs at 7 K, which is five times longer than those in H2SO4 (Figure 6b).The ligand effect on the quantum coherence times was also investigated using complexes CuPc Cl 12 and CuPc F 13.All the three complexes share a similar T2 value of 40 μs at 7 K, indicating the ligand field effect is little in this series [31].(PPh4)2[Cu(mnt)2] 14 (mnt 2− = maleonitriledithiolate or 1,2-dicyanoethylene-1,2-dithiolate) is another high-performance single-ion spin qubit that displays long quantum coherence times at room temperature [50].The Cu(II) ion in 14 is coordinated to four S ions in a square planner geometry (Figure 7a).The H atoms in this complex can be fully replaced by deuterium and its Ni analogy is diamagnetic, allowing a magnetic dilution study.At 294 K, electron spin echo-detected EPR measurements of the highly diluted sample (0.0001% of 14 in (PPh4)2[Ni(mnt)2]) gave T1 of 0.48 μs and T2 of 0.6 μs (Figure 7b).Towards lower temperatures with 0.01% deuterated 14 in deuterated (PPh 4 ) 2 [Cu(mnt) 2 ] 14 (mnt 2− = maleonitriledithiolate or 1,2-dicyanoethylene-1,2-dithiolate) is another high-performance single-ion spin qubit that displays long quantum coherence times at room temperature [50].The Cu(II) ion in 14 is coordinated to four S ions in a square planner geometry (Figure 7a).The H atoms in this complex can be fully replaced by deuterium and its Ni analogy is diamagnetic, allowing a magnetic dilution study.At 294 K, electron spin echo-detected EPR measurements of the highly diluted sample (0.0001% of 14 in (PPh 4 ) 2 [Ni(mnt) 2 ]) gave T 1 of 0.48 µs and T 2 of 0.6 µs (Figure 7b).Towards lower temperatures with 0.01% deuterated 14 in deuterated (PPh 4 ) 2 [Ni(mnt) 2 ], T 2 is prolonged to 68 µs at 7 K.Moreover, Rabi-like oscillations of the echo intensities were clearly observed by nutation measurements of the same sample at 15 K with a merit Q M ≈ 3400.a Reported T2 values at the highest temperatures; b Best T2 values; c Reported temperature for Rabi oscillations.
The other Cr(III) based single-ion spin qubits is K3[Cr(C2O4)3] 16 (Figure 9a) [33].The |D| value of 16 is about 0.7 cm −1 and the E value is about 0.06 cm −1 [52].The inherent scalability and tunability engendered by zero-field splitting are illustrated in Figure 9b.The transitions between the multiple MS pairs can be used as qubits, which is in accordance with the study of complex 15 [51].T2 for 16 is about 1.27 μs at 22 K, obtained by two-pulse Hahn echo sequence on 1 mM solutions of 16 in 1:1 (v/v) H2O/glycerol (Figure 9c) [33].
The other Cr(III) based single-ion spin qubit is K 3 [Cr(C 2 O 4 ) 3 ] 16 (Figure 9a) [33].The |D| value of 16 is about 0.7 cm −1 and the E value is about 0.06 cm −1 [52].The inherent scalability and tunability engendered by zero-field splitting are illustrated in Figure 9b.The transitions between the multiple M S pairs can be used as qubits, which is in accordance with the study of complex 15 [51].T 2 for 16 is about 1.27 µs at 22 K, obtained by two-pulse Hahn echo sequence on 1 mM solutions of 16 in 1:1 (v/v) H 2 O/glycerol (Figure 9c) [33].A series of analogous complexes K ] 21 and 16 were used to study the influence of spin-spin and spin-orbit couplings on quantum coherence [33].Complexes 19, 16 and 17 possess spin states of s = 1/2, 3/2, and 5/2 with the same coordination environment, which gives an opportunity to understand the impact of spin magnitude on quantum coherence (Figure 10a).At low temperature, T 2 value for 19 is the longest one (3.44 µs at 5 K and 2.01 µs at 14 K), followed by 16 (2.79µs at 5 K and 1.86 µs at 14 K) and then 17 (1.83µs at 5 K and 0.81 µs at 14 K).This result indicates a larger spin increases the intermolecular dipolar interaction and hence enhances the decoherence rate [53][54][55].However, at a higher temperature (22 K), T 2 for becomes the longest, reaching 1.27 µs, which may also indicate spin magnitude can be varied without significantly compromising T 2 in certain conditions as long as it is appropriate for signal detection.As the spin states for complexes 18, 20, 21 are all 1/2, and the free ion SOC effects on T 2 can be compared.T 2 for those three complexes are in the order Fe(III) < Ru(III) < Os(III), which is coincident with the increase of SOC constants, namely 464 cm −1 , 880 cm −1 , and 3100 cm −1 for 18, 20 and 21 (Figure 10a and Table 3) [56][57][58].Rabi oscillations and pulse sequence for a solution of 19 at 5 K, H dc = 2812 G, and relative B 1 of 2.0 was observed (Figure 10b).Note that 21 is the only Os complex regarded as potential qubit.[33].Complexes 19, 16 and 17 possess spin states of s = 1/2, 3/2, and 5/2 with the same coordination environment, which give an opportunity to understand the impact of spin magnitude on quantum coherence (Figure 10a).At low temperature, T2 value for 19 is the longest one (3.44 μs at 5 K and 2.01 μs at 14 K), followed by 16 (2.79μs at 5 K and 1.86 μs at 14 K) and then 17 (1.83μs at 5 K and 0.81 μs at 14 K).This result indicates a larger spin increases the intermolecular dipolar interaction and hence enhances the decoherence rate [53][54][55].However, at a higher temperature (22 K), T2 for 16 becomes the longest, reaching 1.27 μs, which may also indicate spin magnitude can be varied without significantly compromising T2 in certain conditions as long as it is appropriate for signal detection.As the spin states for complexes 18, 20, 21 are all 1/2 and the free ion SOC effects on T2 can be compared.T2 for those three complexes are in the order Fe(III) < Ru(III) < Os(III), which is coincident with the increase of SOC constants, namely 464 cm −1 , 880 cm −1 , and 3100 cm −1 for 18, 20 and 21 (Figure 10a and Table 3) [56][57][58].Rabi oscillations and pulse sequence for a solution of 19 at 5 K, Hdc = 2812 G, and relative B1 of 2.0 was observed (Figure 10b).Note that 21 is the only Os complex regarded as potential qubit.Another Fe(III) based single-ion spin qubit is the complex (Ph4P)3[Fe(C5O5)3] 22 (Figure 11a) [59,60].Variable-frequency CW EPR measurements at low temperatures (5 K) and high frequencies (208 GHz) on this trigonally distorted six-coordinate iron(III) complexes with O6 coordination environments reveal a sharp resonance near g = 2.00 and negative D value of −0.30 cm −1 .To evaluate the spin qubit viability of 22, its diamagnetic analogy (Ph4P  Another Fe(III) based single-ion spin qubit is the complex (Ph 4 P) 3 [Fe(C 5 O 5 ) 3 ] 22 (Figure 11a) [59,60].Variable-frequency CW EPR measurements at low temperatures (5 K) and high frequencies (208 GHz) on this trigonally distorted six-coordinate iron(III) complexes with O 6 coordination environments reveal a sharp resonance near g = 2.00 and negative D value of −0.30 cm −1 .To evaluate the spin As far as we know, few mononuclear Mn and Co complexes were reported as potential spin qubits.The only investigation of these two ions was found in complexes MnPc (23) and CoPc (24), which were used to reveal the influences of central ion on quantum coherence behavior of complexes 9, 11-13 [31].Pulsed Q-band EPR spectroscopy was measured on 0.5 mM D2SO4 solution of complexes 9, 11, 23 and 24 because they have the same ligand Pc.T1 for those complexes were found to be in the order of 23 (0.69 ms) < 24 (11.1 ms) < 11 (103 ms) < 9 (2.4 s) at 7 K, which is in accord with the conclusion that smaller SOC effects generate longer spin-lattice relaxation times [33,61].The T2 values at 7 K are 22 μs, 41 μs, 14 μs and 9.44 μs for 9, 11, 23 and 24, respectively.As far as we know, few mononuclear Mn and Co complexes were reported as potential spin qubits.The only investigation of these two ions was found in complexes MnPc (23) and CoPc (24), which were used to reveal the influences of central ion on quantum coherence behavior of complexes 9, 11-13 [31].Pulsed Q-band EPR spectroscopy was measured on 0.5 mM D 2 SO 4 solution of complexes 9, 11, 23 and 24 because they have the same ligand Pc.T 1 for those complexes were found to be in the order of 23 (0.69 ms) < 24 (11.1 ms) < 11 (103 ms) < 9 (2.4 s) at 7 K, which is in accord with the conclusion that smaller SOC effects generate longer spin-lattice relaxation times [33,61].The T 2 values at 7 K are 22 µs, 41 µs, 14 µs and 9.44 µs for 9, 11, 23 and 24, respectively.

Single-Lanthanide Polyoxometalates as Spin Qubits
Though the magnetism of free Gd(III) ion is very isotropic, Gd(III) complexes with special coordination environments can behave as single-molecule magnets at very low temperatures [70,77].The tungsten-based polyoxometalates are such ligand beds for Gd(III) ions.Compounds [Gd(P 5 W 30 O 110 )] 12− (25) and [Gd(W 5 O 18 P) 2 ] 9− (GdW 10 ) (Figure 12) show slow magnetic relaxation behaviors below 300 mK.The relaxation times for GdW 10 follow the activated behavior with an energy barrier of 2.2 K.However, for 25, relaxation times depend weakly on temperature and show a strong deviation from the expected thermally activated behavior.Qualitative fitting of their EPR data proves that the magnetic anisotropy is raised by mixing ground and excited states, resulting in easy-axial magnetic anisotropy for GdW 10 and an easy-plane magnetic anisotropy for 25.This difference further influences their application as spin qubits.Pulsed X-band EPR experiments give coherence figure of merit Q M > 50 for 25 with observation of Rabi oscillations at 5 K, proving the possibility of spin qubits [71].
Another single-lanthanide polyoxometalate for spin qubit is the complex [Ho(W 5 O 18 P) 2 ] 9− (26) [72,73], an analogy of GdW 10 with a different lanthanide center.The Ho(III) ion is encapsulated between two W 5 O 18 POM units that provide a square-antiprismatic coordination geometry with D 4d symmetry (Figure 13a).By high-frequency and X-band EPR measurements, the hyperfine-split m J = ±4 ground states can be observed (Figure 13b).The tunneling gap is about 9 GHz, which make 26 suitable for spin qubits [72].The dilution study of 26 was carried out on Na 9 [Ho x Y (1-x) (W 5 O 18 ) 2 ]•nH 2 O, where x ranges from 0.001 to 0.25 [73].For x = 0.001, a long T 2 of 8.4 µs was detected together with T 1 of 20 µs at 5 K (Figure 13c).Interestingly, T 2 remains at higher concentrations for a long period (about 8.0 µs for x = 0.01 and 0.7 µs for x = 0.1) at 5 K.The main contribution to those narrow resonances is found to be a Gaussian distribution in the B 4  4 parameter.Thus, by exploiting optimal operating points or atomic clock transitions between hyperfine states, quantum coherence times could be significantly protected regardless of spin concentrations [73].

Tb(III) Based Nuclear-Spin Qubits
TbPc2 27, one of the high-performance SIMs, has also been identified as one promising qubit for several reasons [39,40,74,75].(I) The synthesis of this complex is facile and controllable with various

Tb(III) Based Nuclear-Spin Qubits
TbPc2 27, one of the high-performance SIMs, has also been identified as one promising qubit for several reasons [39,40,74,75].(I) The synthesis of this complex is facile and controllable with various

Tb(III) Based Nuclear-Spin Qubits
TbPc 2 27, one of the high-performance SIMs, has also been identified as one promising qubit for several reasons [39,40,74,75].(I) The synthesis of this complex is facile and controllable with various functional groups [78]; (II) The magnetic properties are robust, which can be retained after sublimation at 820 K on a copper surface [64]; (III) The two Pc ligands have a conjugated p system, which can easily conduct electrons; while the valence state for Tb(III) is very stable, so that the current flow does not damage the complex [39]; (IV) The flat Pc ligands help graft the complexes on various surfaces, including gold, carbon nanotube, graphite, etc.With all these characteristics, it is possible to make 27 a spintronic devices (Figure 14a).Magnetic studies of 27 reveal a strong uniaxial magnetic anisotropy with ground J = 6 state separated from the excited states by an energy gap of more than 400 cm −1 [1,79].With the nuclear spin I = 3/2, strong hyperfine coupling between the ground state and the nuclear spin makes the ground states split into four sub-states (Figure 14b), which can be functionalized as quantum microstates.The coherence time T 2 for 27 is about 64.0 µs with isotope-dependent relaxation times, while T 1 is more than 10 s.Moreover, Rabi oscillations are observed (Figure 14c,d) [40].functional groups [78]; (II) The magnetic properties are robust, which can be retained after sublimation at 820 K on a copper surface [64]; (III) The two Pc ligands have a conjugated p system, which can easily conduct electrons; while the valence state for Tb(III) is very stable, so that the current flow does not damage the complex [39]; (IV) The flat Pc ligands help graft the complexes on various surfaces, including gold, carbon nanotube, graphite, etc.With all these characteristics, it is possible to make 27 a spintronic devices (Figure 14a).Magnetic studies of 27 reveal a strong uniaxial magnetic anisotropy with ground J = 6 state separated from the excited states by an energy gap of more than 400 cm −1 [1,79].With the nuclear spin I = 3/2, strong hyperfine coupling between the ground state and the nuclear spin makes the ground states split into four sub-states (Figure 14b), which can be functionalized as quantum microstates.The coherence time T2 for 27 is about 64.0 μs with isotopedependent relaxation times, while T1 is more than 10 s.Moreover, Rabi oscillations are observed (Figure 14c,d) [40].

Yb(III) Based Spin Qubits
For Yb(III) ions, the ground state is a Kramers doublet with J = 7/2, which can be approximated as an effective spin-1/2 system at low temperatures [76].Its isotopes include I = 1/2 ( 171 Yb), I = 5/2 ( 173 Yb) and 0 for the others.To detect the quantum coherence of Yb(trensal) 28 (H 3 trensal = 2,2 ,2"-tris(salicylideneimino)triethylamine), sample of 7% 28 in diamagnetic Lu(trensal) was prepared for EPR measurements (Figure 15a) [76].Fitting the echo-detected field-swept (EDFS) X-band pulsed EPR spectrum gave both spin-lattice relaxation times T 1 and quantum coherence times T 2 (Figure 15c).The T 1 values are in accord with ac susceptibility studies on bulk 28, which exhibits strong temperature dependence behavior and can be described by a power law [80].On the contrary, T 2 is weakly temperature dependent and reaches 0.5 µs at 3 K.Clear oscillatory behavior was observed at 5 K (Figure 15d).The peak widths show little difference for all isotopes, but for the damping, the oscillations at "I = 0 lines" are much stronger than other isotopes.Besides, more than 70 Rabi oscillations can be observed extending to 4 µs.Together with the coherence figure of merit Q M of about 40, complex 28 is an excellent candidate for QIP.EPR measurements (Figure 15a) [76].Fitting the echo-detected field-swept (EDFS) X-band pulsed EPR spectrum gave both spin-lattice relaxation times T1 and quantum coherence times T2 (Figure 15c).The T1 values are in accord with ac susceptibility studies on bulk 28, which exhibits strong temperature dependence behavior and can be described by a power law [80].On the contrary, T2 is weakly temperature dependent and reaches 0.5 μs at 3 K.Clear oscillatory behavior was observed at 5 K (Figure 15d).The peak widths show little difference for all isotopes, but for the damping, the oscillations at "I = 0 lines" are much stronger than other isotopes.Besides, more than 70 Rabi oscillations can be observed extending to 4 μs.Together with the coherence figure of merit QM of about 40, complex 28 is an excellent candidate for QIP.

Conclusions and Perspectives
From the above analyses, we can see the practice of SIMs for spin qubits is still in its infancy, especially for lanthanide based SIMs, yet many exciting results have been achieved in the field.These

Conclusions and Perspectives
From the above analyses, we can see the practice of SIMs for spin qubits is still in its infancy, especially for lanthanide based SIMs, yet many exciting results have been achieved in the field.These include: (i) long quantum coherence times (e.g., complex 2 exhibits T 2 = 657 µs at 7 K; complex 10 exhibits T 2 = 1 µs for at room-temperature; while T 1 reaches 10 s for TbPc 2 at low temperatures); (ii) Rabi oscillations are well observed in many well isolated molecules; (iii) electrically read-out of a single nuclear spin using a molecular spintronic device was achieved; (iv) chemical linkage for CNOT gate operations was demonstrated.Last but not least, the decoherence-structural correlation of SIMs is becoming clearer, which is extremely encouraging for chemists who are working on this field because this knowledge may help to design better spin qubits.The key points can be summarized as follows.Firstly, the quantum states must exist, which may arise from hyperfine coupling of the electron spin and nuclear spin or the spin orbital coupling with a proper energy gap (reasonably between 2 and 20 GHz).Secondly, the ligands, especially the atoms directly coordinated to the metal center, would significantly influence the electronic structure of the center ions.Nuclear spin free atoms are often favorable in this area, such as C and S. Besides, if there is an H atom in the ligands, deuteration often helps to protect the quantum coherence.Finally, the concentration, which is often adjusted by solvents or diamagnetic analogy, is also crucial.Nuclear spin free solvents (e.g., CS 2 ) can effectively enhance the coherence time.Since all these factors are chemically controllable, it is very encouraging for chemists to design high performance single spin qubits based on the toolbox of synthetic chemistry.Only if the quantum coherence time is long enough at room temperature can the realization of QIP for daily usage be expected.

Figure 1 .
Figure 1.(a) Molecular structure of [V(C8S8)3] 2− in 1 (Green, V; yellow, S; gray, C) and energies of spin states with increasing applied dc field for 1 oriented; (b) Echo-detected, field-swept, X-band spectrum of a 1 mM solution of 1 in butyronitrile at 20 K (blue line); (c) Integrated echo intensity as a function of delay time (τ) for 1 under an applied dc field of 3486 Oe at 80 K with graphical depiction of Hahnecho pulse sequence.Inset: Temperature dependence of T2 for 1; (d) Rabi oscillations collected on a 1 mM solution of 1 at 20 K, Hdc = 3486 Oe, and 11 dB attenuation of B1 (adapted with permission from [41]).

Figure 1 .
Figure 1.(a) Molecular structure of [V(C 8 S 8 ) 3 ] 2− in 1 (Green, V; yellow, S; gray, C) and energies of spin states with increasing applied dc field for 1 oriented; (b) Echo-detected, field-swept, X-band spectrum of a 1 mM solution of 1 in butyronitrile at 20 K (blue line); (c) Integrated echo intensity as a function of delay time (τ) for 1 under an applied dc field of 3486 Oe at 80 K with graphical depiction of Hahn-echo pulse sequence.Inset: Temperature dependence of T 2 for 1; (d) Rabi oscillations collected on a 1 mM solution of 1 at 20 K, H dc = 3486 Oe, and 11 dB attenuation of B 1 (adapted with permission from [41]).

Figure 2 .
Figure 2. Molecular structures of 2-5 (a-d) (Green, V; yellow, S; gray, C; red, O; Ph4P groups are omitted for clarity); (e) Rabi oscillations for 2−5 that verify quantum control in each member of the series.Data were recorded in 1:1 DMF/Tol at 20 K, and 14 dB attenuation of B1.The spin-flip operation time of 52 ns is highlighted (adapted with permission from [42]).

Figure 2 .
Figure 2. Molecular structures of 2-5 (a-d) (Green, V; yellow, S; gray, C; red, O; Ph 4 P groups are omitted for clarity); (e) Rabi oscillations for 2−5 that verify quantum control in each member of the series.Data were recorded in 1:1 DMF/Tol at 20 K, and 14 dB attenuation of B 1 .The spin-flip operation time of 52 ns is highlighted (adapted with permission from [42]).

Figure 3 .
Figure 3. (a-c) Molecular structures of 6−8 (Green, V; gray, C; red, O; hydrogen atoms are omitted for clarity); (d) Frequency dependence of the imaginary component of the AC susceptibility of bulk 6 in Bdc = 0.2 T multiplied by temperature to be readable in the whole 2-80 K temperature range; (e) Pulsed EPR Hahn echo decay traces for a frozen 1 mM CH2Cl2-toluene solution of 6 at indicated temperatures recorded at 343 mT.In the inset the employed pulse sequence; (f) Rabi oscillations for a frozen 1 mM CH2Cl2-toluene solution of 6 recorded at 4.3 K at 10 dB microwave attenuation (adapted with permission from [45]).

Figure 3 .
Figure 3. (a-c) Molecular structures of 6−8 (Green, V; gray, C; red, O; hydrogen atoms are omitted for clarity); (d) Frequency dependence of the imaginary component of the AC susceptibility of bulk 6 in B dc = 0.2 T multiplied by temperature to be readable in the whole 2-80 K temperature range; (e) Pulsed EPR Hahn echo decay traces for a frozen 1 mM CH 2 Cl 2 -toluene solution of 6 at indicated temperatures recorded at 343 mT.In the Inset the employed pulse sequence; (f) Rabi oscillations for a frozen 1 mM CH 2 Cl 2 -toluene solution of 6 recorded at 4.3 K at 10 dB microwave attenuation (adapted with permission from [45]).

Figure 4 .
Figure 4. (a) Molecular structures of 9 (Green, V; gray, C; red, O; blue, N; hydrogen atoms are omitted for clarity); (b) Echo decay traces for 9 at indicated temperatures performed at 345 mT.Solid lines are the best fits; (c) Rabi oscillations recorded for 9 at 300 K for different microwave attenuations performed at 345 mT (adapted with permission from [48]).

Figure 5 .
Figure 5. (a) Molecular structure of 10 (Green, V; yellow, S; gray, C; Ph4P groups are omitted for clarity); (b) Echo decay traces for diluted 10 at indicated temperatures performed at X-band; (c) Echo decay traces for diluted 4 at indicated temperatures performed at X-band.Solid lines are the best fits (adapted with permission from [47]).

Figure 4 .
Figure 4. (a) Molecular structures of 9 (Green, V; gray, C; red, O; blue, N; hydrogen atoms are omitted for clarity); (b) Echo decay traces for 9 at indicated temperatures performed at 345 mT.Solid lines are the best fits; (c) Rabi oscillations recorded for 9 at 300 K for different microwave attenuations performed at 345 mT (adapted with permission from [48]).

For 4 , 19 Figure 4 .
Figure 4. (a) Molecular structures of 9 (Green, V; gray, C; red, O; blue, N; hydrogen atoms are omitted for clarity); (b) Echo decay traces for 9 at indicated temperatures performed at 345 mT.Solid lines are the best fits; (c) Rabi oscillations recorded for 9 at 300 K for different microwave attenuations performed at 345 mT (adapted with permission from [48]).

Figure 5 .
Figure 5. (a) Molecular structure of 10 (Green, V; yellow, S; gray, C; Ph4P groups are omitted for clarity); (b) Echo decay traces for diluted 10 at indicated temperatures performed at X-band; (c) Echo decay traces for diluted 4 at indicated temperatures performed at X-band.Solid lines are the best fits (adapted with permission from [47]).

Figure 5 .
Figure 5. (a) Molecular structure of 10 (Green, V; yellow, S; gray, C; Ph 4 P groups are omitted for clarity); (b) Echo decay traces for diluted 10 at indicated temperatures performed at X-band; (c) Echo decay traces for diluted 4 at indicated temperatures performed at X-band.Solid lines are the best fits (adapted with permission from [47]).

Figure 6 .
Figure 6.(a) Structures of complexes 11-13; (b) Inversion recovery experiment (up) and Hahn echo experiment (down) for relaxation data of 11 in H 2 SO 4 (red triangles) and D 2 SO 4 (blue circles) at Q-band and 7 K (adapted with permission from [31]); (c) Rabi oscillations of a 0.1% CuPc:H 2 Pc film recorded at 5 K and 330.5 mT for different microwave powers (adapted with permission from [49]).

Figure 9 .
Figure 9. (a) Molecular structure of [Cr(C2O4)3] 3− in 16 (Light blue, Cr; red, O; gray, C; cations are omitted for clarity); (b) Calculated splitting of the MS energy levels with Hdc = 1000 G aligned along the z-axis of the molecule.Blue arrows indicate the six potential qubits; (c) T2 decay curves for 16 at indicated temperatures.Lines are best fits (adapted with permission from [33]).

Figure 9 .
Figure 9. (a) Molecular structure of [Cr(C2O4)3] 3− in 16 (Light blue, Cr; red, O; gray, C; cations are omitted for clarity); (b) Calculated splitting of the MS energy levels with Hdc = 1000 G aligned along the z-axis of the molecule.Blue arrows indicate the six potential qubits; (c) T2 decay curves for 16 at indicated temperatures.Lines are best fits (adapted with permission from [33]).

Figure 9 .
Figure 9. (a) Molecular structure of [Cr(C 2 O 4 ) 3 ] 3− in 16 (Light blue, Cr; red, O; gray, C; cations are omitted for clarity); (b) Calculated splitting of the M S energy levels with H dc = 1000 G aligned along the z-axis of the molecule.Blue arrows indicate the six potential qubits; (c) T 2 decay curves for 16 at indicated temperatures.Lines are best fits (adapted with permission from [33]).

Figure 10 .
Figure 10.(a) Depictions of the molecular structures of 16, 17 and 19 (left) and 18, 20 and 21 (right) (cations are omitted for clarity); (b) Rabi oscillations and pulse sequence for a solution of 19 at 5 K (adapted with permission from [33]).

Figure 10 .
Figure 10.(a) Depictions of the molecular structures of 16, 17 and 19 (left) and 18, 20 and 21 (right) (cations are omitted for clarity); (b) Rabi oscillations and pulse sequence for a solution of 19 at 5 K (adapted with permission from [33]).

Figure 11 .
Figure 11.(a) Molecular structure of [Fe(C5O5)3] 3− in 22 (Brown, Fe; red, O; gray, C; the Ph4P groups are omitted for clarity); (b) Magnetic field dependence of the MS levels of the s = 5/2 state in 22 for a magnetic field aligned perpendicular to the molecular z-axis (adapted with permission from [60]); (c) Rabi oscillations at Hdc = 1608 G with indicated B1 for 22a at 10 K(adapted with permission from [59]; (d) Rabi oscillations at Hdc = 1608 G with indicated B1 for 22b at 10 K (adapted with permission from [60].

Figure 11 .
Figure 11.(a) Molecular structure of [Fe(C 5 O 5 ) 3 ] 3− in 22 (Brown, Fe; red, O; gray, C; the Ph 4 P groups are omitted for clarity); (b) Magnetic field dependence of the M S levels of the s = 5/2 state in 22 for a magnetic field aligned perpendicular to the molecular z-axis (adapted with permission from [60]); (c) Rabi oscillations at H dc = 1608 G with indicated B 1 for 22a at 10 K(adapted with permission from [59]; (d) Rabi oscillations at H dc = 1608 G with indicated B 1 for 22b at 10 K (adapted with permission from [60].

Figure 12 .
Figure 12.(a) Molecular structures of GdW10 and 25; energy levels of GdW10 and 25 for Hdc = 10 mT; (b) Ac magnetic susceptibility measured at indicated temperatures and the relaxation times for GdW10 and 25 (adapted with permission from [70]); (c).Rabi oscillations for 25 at indicated microwave (adapted with permission from [71].

Figure 12 .
Figure 12.(a) Molecular structures of GdW 10 and 25; energy levels of GdW 10 and 25 for H dc = 10 mT; (b) Ac magnetic susceptibility measured at indicated temperatures and the relaxation times for GdW 10 and 25 (adapted with permission from [70]); (c) Rabi oscillations for 25 at indicated microwave (adapted with permission from [71].

Figure 12 .
Figure 12.(a) Molecular structures of GdW10 and 25; energy levels of GdW10 and 25 for Hdc = 10 mT; (b) Ac magnetic susceptibility measured at indicated temperatures and the relaxation times for GdW10 and 25 (adapted with permission from [70]); (c).Rabi oscillations for 25 at indicated microwave (adapted with permission from [71].

Figure 14 .
Figure 14.(a) Artist's view of a nuclear spin qubit transistor based on a single 27 molecule.The four anisotropic nuclear spin states of the Tb 3+ (colored circles) can be manipulated by an electric field pulse (adapted with permission from [40]); (b) The two ground states are each split into four different sub-states owing to the hyperfine coupling with the nuclear spin (I = 3/2).Colored lines denote the Iz components: purple, −3/2; blue, −1/2; green, 1/2; and red, 3/2.Two processes are responsible for the magnetization reversal (adapted with permission from[39]); (c) Ramsey interference fringes obtained by repeating time-dependent external magnetic field and pulse sequence for 100 times at 40 mK (adapted with permission from[40]); (d) Rabi oscillations obtained by repeating the above sequence in (c) for 100 times at 40 mK (adapted with permission from[40]).

Figure 14 .
Figure 14.(a) Artist's view of a nuclear spin qubit transistor based on a single 27 molecule.The four anisotropic nuclear spin states of the Tb 3+ (colored circles) can be manipulated by an electric field pulse (adapted with permission from [40]); (b) The two ground states are each split into four different sub-states owing to the hyperfine coupling with the nuclear spin (I = 3/2).Colored lines denote the I z components: purple, −3/2; blue, −1/2; green, 1/2; and red, 3/2.Two processes are responsible for the magnetization reversal (adapted with permission from[39]); (c) Ramsey interference fringes obtained by repeating time-dependent external magnetic field and pulse sequence for 100 times at 40 mK (adapted with permission from[40]); (d) Rabi oscillations obtained by repeating the above sequence in (c) for 100 times at 40 mK (adapted with permission from[40]).

Figure 15 .
Figure 15.(a) Molecular structure of Yb(trensal) in 28 (Pink, Yb; red, O; blue, N; gray, C, hydrogen atoms are omitted for clarity); (b) Zeeman diagram of the I = 5/2 isotope; (c) Temperature dependence of T1 and T2 determined by pulsed EPR for 7% 28 in Lu(trensal); (d) Echo intensity, proportional to the expectation value Sz , as a function of the length of the nutation pulse (tp) at selected field positions at T = 5 K (microwave attenuation = 3 dB) and its corresponding Fourier transforms (adapted with permission from [76]).

Figure 15 .
Figure 15.(a) Molecular structure of Yb(trensal) in 28 (Pink, Yb; red, O; blue, N; gray, C, hydrogen atoms are omitted for clarity); (b) Zeeman diagram of the I = 5/2 isotope; (c) Temperature dependence of T 1 and T 2 determined by pulsed EPR for 7% 28 in Lu(trensal); (d) Echo intensity, proportional to the expectation value S z , as a function of the length of the nutation pulse (t p ) at selected field positions at T = 5 K (microwave attenuation = 3 dB) and its corresponding Fourier transforms (adapted with permission from [76]).
a Reported T 2 values at the highest temperatures; b Best T 2 values; c Reported temperatures for Rabi oscillations.

µs T 2 /µs a T 2 /µs b T R /K c Ref.
a Reported T 2 values at the highest temperatures; b Best T 2 values; c Reported temperatures for Rabi oscillations.

Table 3 .
Other transition metals based single-ion spin qubits.

Table 3 .
Other transition metals based single-ion spin qubits.

Table 4 .
4f based single-ion spin qubits.Reported T 2 values at the highest temperatures; b Best T 2 values; c Reported temperatures for Rabi oscillations. a