Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate ${1/T}_{1}$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate ${1/T}_{1}$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.

arXiv:cond-mat/0203319Physical review. B, Condensed matterJul 16, 2002105 citations

Switchable spin–photon coupling with hole spins in single-quantum dots

C. Sagaseta, M. J. Calderón, J. C. Abadillo-Uriel

Abstract Spin qubits in semiconductor quantum dots offer a gate-tunable platform for quantum information processing. While two-qubit interactions are typically realized through exchange coupling between neighboring spins, coupling spin qubits to photons via hybrid spin-circuit QED (cQED) devices enables long-range interactions and integration with other cQED platforms. Here, we investigate hole spin–photon coupling in compact single quantum dot setups. By incorporating ubiquitous strain inhomogeneities to our theory, we identify three main spin–photon coupling channels: a vector-potential-spin–orbit geometric mechanism–dominant for vertical magnetic fields–, an inhomogeneous Rashba term generalizing previous spin–orbit field models, and strain-induced g -tensor terms–most relevant for in-plane fields. Comparing Si, unstrained (relaxed) Ge, and biaxially strained Ge wells, we find that Si and unstrained Ge provide optimal coupling strengths (tens of MHz) thanks to their reduced heavy-hole, light-hole splitting. We demonstrate efficient switching of the spin–photon coupling while preserving sweet spot conditions by operating with an in-plane magnetic field. Finally, we evaluate quantum state transfer and two-qubit gate protocols, achieving ≳ 99 % fidelity for state transfer and > 90 % for two-qubit gates with realistic coherence times, establishing single-dot hole spins as a viable platform for compact spin-cQED architectures and highlighting unstrained Ge as a promising candidate for spin–photon interactions.Abstract Spin qubits in semiconductor quantum dots offer a gate-tunable platform for quantum information processing. While two-qubit interactions are typically realized through exchange coupling between neighboring spins, coupling spin qubits to photons via hybrid spin-circuit QED (cQED) devices enables long-range interactions and integration with other cQED platforms. Here, we investigate hole spin–photon coupling in compact single quantum dot setups. By incorporating ubiquitous strain inhomogeneities to our theory, we identify three main spin–photon coupling channels: a vector-potential-spin–orbit geometric mechanism–dominant for vertical magnetic fields–, an inhomogeneous Rashba term generalizing previous spin–orbit field models, and strain-induced g -tensor terms–most relevant for in-plane fields. Comparing Si, unstrained (relaxed) Ge, and biaxially strained Ge wells, we find that Si and unstrained Ge provide optimal coupling strengths (tens of MHz) thanks to their reduced heavy-hole, light-hole splitting. We demonstrate efficient switching of the spin–photon coupling while preserving sweet spot conditions by operating with an in-plane magnetic field. Finally, we evaluate quantum state transfer and two-qubit gate protocols, achieving ≳ 99 % fidelity for state transfer and > 90 % for two-qubit gates with realistic coherence times, establishing single-dot hole spins as a viable platform for compact spin-cQED architectures and highlighting unstrained Ge as a promising candidate for spin–photon interactions.

arXiv:2510.05301Materials for Quantum TechnologyFeb 2, 20260 citations

SiGe/Si(111)/SiGe heterostructure for Si spin qubits with electrons confined in L valley of conduction band

Takafumi Tokunaga, Hiromichi Nakazato

In Si(111) crystals, a strong biaxial tensile strain applied within the (111) plane is considered to shift the lowest energy point of the conduction band from the $Δ$ valley to the L valley. Electrons confined in this L valley experience a splitting of their quadruply degenerate energy levels into an undegenerate single-level ground state (L1) and a triply degenerate excited state (L3). The energy of the single-level ground state is sufficiently low relative to the energies of the L3 valley and the $Δ$ valley, making it optimal as a two-level system for a qubit. Using deformation potential theory and incorporating quantum effects from electron confinement in the SiGe/Si(111)/SiGe structure, we determine the value of the biaxial tensile strain causing the shift of the conduction band energy minimum from the $Δ$ valley to the L valley, along with the corresponding Ge concentration. We also calculate the critical thickness for the plastic relaxation of the Si quantum well under this large biaxial tensile strain and examine the feasibility of realizing it as a SiGe/Si(111)/SiGe heterostructure.In Si(111) crystals, a strong biaxial tensile strain applied within the (111) plane is considered to shift the lowest energy point of the conduction band from the $Δ$ valley to the L valley. Electrons confined in this L valley experience a splitting of their quadruply degenerate energy levels into an undegenerate single-level ground state (L1) and a triply degenerate excited state (L3). The energy of the single-level ground state is sufficiently low relative to the energies of the L3 valley and the $Δ$ valley, making it optimal as a two-level system for a qubit. Using deformation potential theory and incorporating quantum effects from electron confinement in the SiGe/Si(111)/SiGe structure, we determine the value of the biaxial tensile strain causing the shift of the conduction band energy minimum from the $Δ$ valley to the L valley, along with the corresponding Ge concentration. We also calculate the critical thickness for the plastic relaxation of the Si quantum well under this large biaxial tensile strain and examine the feasibility of realizing it as a SiGe/Si(111)/SiGe heterostructure.

quant-pharXiv:2604.13435Apr 16, 2026

{1/T}_{1}

as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.

In Si(111) crystals, a strong biaxial tensile strain applied within the (111) plane is considered to shift the lowest energy point of the conduction band from the

Δ

valley to the L valley. Electrons confined in this L valley experience a splitting of their quadruply degenerate energy levels into an undegenerate single-level ground state (L1) and a triply degenerate excited state (L3). The energy of the single-level ground state is sufficiently low relative to the energies of the L3 valley and the

Δ

valley, making it optimal as a two-level system for a qubit. Using deformation potential theory and incorporating quantum effects from electron confinement in the SiGe/Si(111)/SiGe structure, we determine the value of the biaxial tensile strain causing the shift of the conduction band energy minimum from the

Δ

valley to the L valley, along with the corresponding Ge concentration. We also calculate the critical thickness for the plastic relaxation of the Si quantum well under this large biaxial tensile strain and examine the feasibility of realizing it as a SiGe/Si(111)/SiGe heterostructure.