Donor Spin Qubits in Silicon

• Donor spin qubits are quantum bits encoded using the spin states of donor electrons or nuclei in semiconductors, offering long coherence times and multiple control methods.
• They leverage precise donor placement via STM lithography or deterministic ion implantation to form various architectures such as single donors, donor molecules, and donor chains.
• Advanced platforms integrate optical, electrical, and resonator-based control to achieve high-fidelity operations and scalable coupling for quantum computing.

Searching arXiv for recent and foundational papers on donor spin qubits in silicon and related donor-based platforms. Donor spin qubits are qubits encoded in the spin degrees of freedom of donor impurities in semiconductors, most extensively group-V donors in silicon and, in related photonic proposals, singly-ionized chalcogen donors. In the canonical silicon realization, a neutral donor binds one electron whose spin is hyperfine-coupled to the donor nucleus, so the electron spin, the nuclear spin, or a composite electron–nuclear manifold can serve as the computational degree of freedom. The platform combines isotopically enriched $^{28}$Si, which suppresses nuclear-spin noise, with atomistic placement by scanning-tunnelling-microscope lithography or deterministic ion implantation, and it supports architectures based on single donors, donor molecules, exchange-coupled donor pairs, donor chains, flip-flop qubits, and photonic or resonator interfaces (Morello et al., 2020, Hile et al., 2018, Koh et al., 12 Feb 2026).

1. Physical basis and donor species

The fundamental object is a donor-bound electron in a semiconductor host. For a neutral group-V donor in silicon, the spin Hamiltonian in frequency units can be written as

$$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$

where $A$ is the isotropic hyperfine constant and $H_Q$ is the nuclear electric-quadrupole interaction for nuclei with $I>1/2$ (Morello et al., 2020). In the high-field regime, the eigenstates approximate the product basis $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$, and ESR transitions occur at $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$ (Morello et al., 2020).

Phosphorus remains the reference donor species. In isotopically enriched $^{28}$Si, $^{31}$P provides an electron bound state with Bohr radius $a_0\approx1.22$ nm and binding energy $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$0 meV, while its nuclear spin $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$1 couples strongly to the bound electron with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$2 MHz or, in the review tabulation, $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$3 MHz (Holmes et al., 2023, Morello et al., 2020). The same review lists $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$4As with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$5 and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$6 MHz, $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$7Sb with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$8 and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$9 MHz, $A$0Sb with $A$1 and $A$2 MHz, and $A$3Bi with $A$4 and $A$5 MHz (Morello et al., 2020). The heavy donors add quadrupole physics and nuclear electric resonance, while Bi combines a very large hyperfine interaction with strong Stark tunability (Usman et al., 2015).

The donor-qubit concept also extends beyond shallow group-V donors. In $A$6Si, singly-ionized chalcogen donors such as $A$7Se$A$8 bind one electron with binding energy $A$9 meV and hyperfine constant $H_Q$0 GHz, while parity-allowed $H_Q$1 optical transitions at $H_Q$2m create a cavity-QED-compatible donor-spin platform (Morse et al., 2016). This broader donor taxonomy matters because different donor species emphasize different control channels: shallow donors favor electrical and exchange-based control, whereas chalcogen donors emphasize optical initialization, readout, and photon-mediated coupling.

2. Qubit encodings and effective Hamiltonians

The simplest encoding uses the donor electron spin. In isotopically purified $H_Q$3Si, a single substitutional P atom supports an electron spin qubit, while the nuclear spin provides a long-lived memory; one summary gives nuclear $H_Q$4 and electron $H_Q$5 for a single P donor in a $H_Q$6Si host (Hile et al., 2018). A complementary encoding uses the donor nucleus itself. For a single $H_Q$7P donor near a Si/SiO$H_Q$8 interface, the combined orbital, electron-spin, and nuclear-spin Hamiltonian allows the qubit splitting

$H_Q$9

with $I>1/2$0 tuned electrically through donor–interface hybridization (Simon et al., 2020).

Composite encodings widen the design space. In zero magnetic field, the phosphorus donor Hamiltonian reduces to $I>1/2$1, so the eigenstates become the singlet $I>1/2$2 and triplet manifold $I>1/2$3, with the $I>1/2$4 transition forming a clock transition because $I>1/2$5 (Morse et al., 2018). In donor-based flip-flop qubits, the computational basis is encoded in electron–nuclear states such as $I>1/2$6 and $I>1/2$7 when the electron is partially displaced toward an interface or shared within a donor double dot (Morello et al., 2020, Koh et al., 12 Feb 2026). In the donor–donor flopping-mode proposal, a 2P–1P system yields an effective Hamiltonian

$I>1/2$8

with $I>1/2$9 providing the electrically driven flip-flop coupling and $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$0 acting as the unwanted longitudinal gradient (Krauth et al., 2021).

Multi-donor structures generate further encodings. Exchange-coupled donor pairs obey

$$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$1

and in the weak-exchange regime $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$2 they support frequency-selective conditional rotations (Mądzik et al., 2020). Odd-sized donor chains can behave as a spin-$$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$3 “extended qubit” with low-energy gap $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$4, providing a transport bus between distant source and target donors (Mohiyaddin et al., 2016). A further extension uses nearby $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$5Si nuclei as a register around the donor electron; this register exploits the donor-induced “frozen-core” environment rather than treating all residual $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$6Si spins only as a decoherence source (Wolfowicz et al., 2015).

3. Placement precision and device fabrication

Two fabrication paradigms dominate: STM-defined donors and deterministic implantation. Scanning-tunnelling-microscope hydrogen-resist lithography permits patterning of exposed silicon dimers with a resolution below the lattice constant. In the 1P–2P addressability experiment, PH$$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$7 dosing at room temperature followed by a $$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$8C anneal embeds exactly one P atom per three exposed dimers, while slightly larger lithographic patches incorporate pairs of P atoms into a single quantum-dot site. After incorporation, a 55 nm epitaxial silicon overgrowth encapsulates the donors, and delta-doped regions define reservoirs and gates; a nearby highly doped Si SET acts as both local charge sensor and reservoir (Hile et al., 2018).

Deterministic ion implantation trades atomic STM placement for CMOS compatibility and wafer-scale processing. In the PF$$\lvert \uparrow,m_I\rangle,\lvert \downarrow,m_I\rangle$$9 strategy, the molecule ion dissociates on impact so that one P and two F atoms are co-implanted at the same lateral coordinate, but the bystander F ions increase the ion-beam-induced-charge signal and therefore the single-ion detection confidence. The reported values are $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$0 for $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$1 keV P$\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$2 alone and $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$3 for PF$\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$4 at $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$5 keV, with placement uncertainty $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$6 nm for P in PF$\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$7 versus $\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$8 nm for P$\nu_e(m_I)=\gamma_e B_0 \pm (A/2)m_I$9 alone at the same detection confidence (Holmes et al., 2023). Secondary ion mass spectrometry and ESR further show that after donor activation anneal the F diffuses away from the active region and no $^{28}$0F hyperfine splitting remains in the donor spectrum (Holmes et al., 2023).

Counted heavy-donor implantation extends the same logic. Focused-ion-beam implantation of Sb$^{28}$1 at 120 keV, combined with a planar p–n diode detector adjacent to the quantum dot construction zone, produces $^{28}$2 electron–hole pairs per ion and a detector signal of $^{28}$3 mV above baseline noise. The reported single-ion detection efficiency is $^{28}$4, and self-alignment to $^{28}$5 nm wide polysilicon gates reduces the lateral uncertainty to $^{28}$6 nm at 95% confidence (Singh et al., 2015). A related hybrid donor–quantum-dot architecture proposed aligned single-ion implantation through a dynamic shadow mask with real-time single-ion detection, targeting $^{28}$7 nm lateral precision relative to predefined quantum dots (Schenkel et al., 2011).

4. Initialization, control, and readout

The mature control stack is based on ESR, NMR, and spin-dependent tunnelling. In the implanted-donor review, electron spins are initialized by spin-selective tunnelling to a cold SET reservoir at $^{28}$8 mK, with electron spin-to-charge conversion yielding fidelities $^{28}$9. Nuclear spins are initialized and read out by hyperfine-selective mapping to the electron, giving repetitive near-QND readout with fidelities $^{31}$0; coherent control uses ESR at $^{31}$1–40 GHz with $^{31}$2-pulses as short as 150 ns, neutral-donor NMR at $^{31}$3–200 MHz with $^{31}$4-pulses $^{31}$5–30 $^{31}$6s, and, for high-spin nuclei, nuclear electric resonance at $^{31}$7–10 MHz (Morello et al., 2020).

Built-in frequency addressability has been demonstrated by hyperfine engineering. A 1P donor next to a 2P molecule at $^{31}$8 nm separation shows two hyperfine peaks separated by $^{31}$9 MHz for the single donor and three peaks with average splitting $a_0\approx1.22$0 MHz for the donor molecule. Because the two qubits differ in ESR frequency by $a_0\approx1.22$1 MHz, the device achieves individual addressability without strong magnetic or electric field gradients or micromagnets; the same experiment used single-shot, energy-selective spin readout at $a_0\approx1.22$2 mK and $a_0\approx1.22$3 T with a $a_0\approx1.22$4 MHz chirp over 150 $a_0\approx1.22$5s, and reported readout fidelity $a_0\approx1.22$6 (Hile et al., 2018).

Electrical control can replace oscillating magnetic fields. Wang et al. proposed all-electrical control in a 2P–1P donor double dot, where the difference in total hyperfine coupling across the $a_0\approx1.22$7 transition induces an electric dipole and electrically driven spin resonance. Near charge degeneracy, the single-photon Rabi frequency is

$a_0\approx1.22$8

and the specific design example with $a_0\approx1.22$9 MHz/(kV/m) and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$00 kV/m gives $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$01 MHz, corresponding to $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$02-pulses in $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$03 ns (Wang et al., 2017). A related donor–donor flopping-mode proposal uses multi-donor occupation with antiparallel nuclear spins to suppress the longitudinal magnetic-field gradient and reports $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$04-$$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$05 gate error rates of $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$06 under realistic noise models (Krauth et al., 2021).

Optical approaches provide a distinct control layer. Zero-field optical magnetic resonance on phosphorus donors in enriched silicon exploits donor-bound-exciton transitions to hyperpolarize the donor and access the $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$07 clock transition, with initialization, manipulation, and readout fidelities $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$08 and Hahn echo coherence around $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$09 s (Morse et al., 2018). For group-V donors more generally, far-IR and near-IR spin-selective transitions have been analyzed for P, As, Sb, and Bi, including optical pumping via $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$10 and two-photon $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$11 schemes through donor-bound excitons (Gullans et al., 2015). In the chalcogen-donor platform, optical pumping yields near-unit hyperpolarization in $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$12 ms at 4.2 K and cavity-QED readout is projected to exceed $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$13 fidelity without exciting the donor (Morse et al., 2016).

5. Coherence, relaxation, and measurement backaction

Coherence metrics depend strongly on isotopic purity, donor environment, and encoding. For single P donors in natural Si, one summary gives $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$14 ns with linewidth $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$15 MHz, extended to $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$16s in $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$17Si, while electron $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$18 s at low temperature (Hile et al., 2018). In a PF$$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$19-implanted $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$20Si qubit device, the measured electron coherence values are $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$21s and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$22s, comparable to previous P-implanted devices and with no detected nearby $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$23F nuclear spins (Holmes et al., 2023). Ionized donors in bulk $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$24Si reach much longer nuclear times, with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$25 ms and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$26 seconds under clock-transition conditions (Holmes et al., 2023).

Donor molecules and donor–interface coupling introduce new relaxation channels. In natural Si, the 2P donor molecule exhibits linewidth $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$27 MHz and apparent dephasing $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$28 ns because the larger envelope overlaps more $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$29Si nuclei, although isotopic purification is expected to restore ms-scale coherence as in single donors (Hile et al., 2018). Near the Si/SiO$$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$30 interface, donor states hybridized with interface orbitals show phonon-assisted spin relaxation with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$31 when the applied field is weak compared to the orbital spacing, together with spin-relaxation hot-spots where orbital states with opposite spin strongly hybridize and cool-spots where different relaxation channels interfere destructively (Huang et al., 2017).

Long-lived nuclear subspaces can be built around the donor rather than against it. Wolfowicz et al. showed that nearby $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$32Si nuclei in the donor “frozen core” reach coherence times in the second timescale: the donor nucleus has $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$33 s, a nearby $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$34Si with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$35 MHz has $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$36 s, and CPMG with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$37 extends $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$38 to $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$39 s (Wolfowicz et al., 2015). Chalcogen donors provide another clock-transition route, with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$40 min, $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$41 ms, and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$42 s at low field (Morse et al., 2016).

Measurement itself can limit nuclear lifetimes. In multi-donor qubits occupied by a single electron, electron tunnelling during readout turns the hyperfine interaction on and off non-adiabatically, giving single-spin flip probabilities $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$43 and an additional nuclear spin flip-flop mechanism specific to multi-donor dots. Monir et al. show that increasing the hyperfine difference $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$44 suppresses the flip-flop probability as $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$45, and that the engineered-Stark 2P lifetimes exceed those of 1P once $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$46 MHz (Monir et al., 2023). This corrects the common assumption that adding donors necessarily worsens nuclear backaction.

6. Coupling, transport, and scalable silicon architectures

Two-qubit logic in donor systems is not limited to the strong-exchange regime. In a MOS-compatible silicon device with two exchange-coupled implanted $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$47P donors, the measured coupling is $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$48 MHz, while the individual hyperfine couplings are $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$49 MHz and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$50 MHz. Because $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$51, the target ESR line depends on the control-spin state, and a native controlled-rotation gate is obtained by a simple ESR pulse; the reported $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$52-pulse durations are $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$53–250 ns, with the gate remaining functional for any $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$54 in the interval $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$55 (Mądzik et al., 2020). This weak-exchange operating mode is explicitly designed to reduce sensitivity to donor-placement variation.

Hyperfine engineering provides an orthogonal route to addressability. The 1P–2P device cited above achieves $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$56 MHz built-in ESR detuning at only $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$57 nm spacing, and the same work argues that donor molecule size and geometry can provide a library of distinct resonance frequencies; one stated example is that four distinct 2P configurations plus a single donor could yield five qubits addressable within a $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$58 GHz ESR bandwidth (Hile et al., 2018). A plausible implication is that exchange-based connectivity and frequency-based addressability need not be engineered by the same physical knob.

Donor chains address on-chip transport. Mohiyaddin et al. modeled odd-sized chains with nearest-neighbor Heisenberg exchange and showed that operating in interface mode greatly relaxes donor placement tolerances because the exchange dependence becomes less steep. For $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$59 nm, interface mode permits a 7-donor chain $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$60 nm long at 90% yield, whereas bulk-like mode permits only $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$61 nm. Their adiabatic transport protocol uses $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$62–10 GHz and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$63–100 ns, and following the stated guidelines yields spin-state transport over $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$64 nm with fidelity $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$65 under realistic noise and fabrication constraints (Mohiyaddin et al., 2016).

Long-range couplers increasingly rely on electric dipoles and resonators rather than direct exchange. For donor nuclear qubits, electrically induced donor–interface dipoles enable dipole–dipole cZ gates in $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$66 ns at $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$67m, while single-qubit $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$68 gates take $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$69 ns and composite $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$70 gates reach fidelity $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$71 at $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$72 V/m (Simon et al., 2020). For donor-based flip-flop qubits coupled to superconducting resonators, the central trade-off is between spin–charge admixture and decoherence: with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$73 GHz and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$74 GHz, the simultaneous regime $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$75 and $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$76 for $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$77 is narrowly realized for $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$78–16 GHz with sufficient $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$79 and low $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$80, and squeezed input fields can mitigate charge-photon-coupling and photon-loss constraints (Koh et al., 12 Feb 2026).

7. Extensions beyond the standard phosphorus-in-silicon setting

The donor-spin category includes broader material and control proposals that illuminate the general design space. Atomistic tight-binding studies of P, As, Sb, and Bi donors under strain and electric field show that a hybrid control scheme based on (001) compressive strain and in-plane (100 or 010) fields results in higher gate fidelities and/or faster gate operations for all four donor species, while only Bi is predicted to benefit similarly from both in-plane and out-of-plane fields (Usman et al., 2015). These calculations also show donor-dependent Stark curvatures and saturation behaviors of the hyperfine interaction, emphasizing that “donor spin qubit” is not a single fixed Hamiltonian but a family of donor-specific operating points.

Photonic donor platforms relax the requirement of atomically precise inter-donor spacing. In $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$81Si, singly-ionized chalcogen donors offer mid-IR electric-dipole transitions, optical initialization, $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$82 min, $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$83 s, cavity-QED single-shot readout projected above $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$84, and coupling variations below 10% for donor-placement uncertainty plus annealing $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$85 nm; the same proposal notes that no atomically precise donor spacing is required because the optical interface tolerates $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$86 nm placement error (Morse et al., 2016). This stands in deliberate contrast to exchange-only schemes.

Non-silicon donor-spin proposals test how much of the silicon donor toolkit is host-independent. In germanium, shallow donor spins in quasi-2D phononic crystals have been proposed as qubits whose Zeeman splitting lies inside a phonon bandgap, suppressing one-phonon relaxation so that $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$87 s and enabling virtual-phonon-mediated couplings with $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$88 in structures with unit-cell sizes of 100–150 nm (Smelyanskiy et al., 2014). In ZnO, indium ion implantation followed by annealing produces neutral donors with donor-bound-exciton linewidth less than 10 GHz, hyperfine coupling $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$89 MHz, and longitudinal relaxation times reaching $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$90 s at $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$91 T, while two-laser CPT resolves the $$H = (\gamma_e S_z - \gamma_n I_z)\,B_0 + A\,S\cdot I + H_Q + (\gamma_e S_x - \gamma_n I_x)\,B_1\cos(2\pi f t),$$92 In nuclear manifold (Wang et al., 2022). These systems remain less developed than the silicon platform, but they underscore that donor-spin qubits are a materials class rather than a single-device format.

Across these implementations, a recurring misconception is that donor-spin scalability is synonymous with atomically tuned exchange between nearest neighbors. The literature instead supports several non-exclusive strategies: weak-exchange conditional ESR, hyperfine-engineered donor molecules, interface-mode donor chains, donor–interface dipoles, optical chalcogen nodes, and superconducting-resonator coupling (Mądzik et al., 2020, Hile et al., 2018, Morse et al., 2016). This suggests that the central problem in donor-spin quantum engineering is not merely donor placement, but the joint optimization of hyperfine structure, orbital admixture, readout backaction, and the coupling mechanism chosen for scale-up.