Hole Spin Qubit

Figure

Description

Hole spin qubits encode quantum information in the spin of valence-band holes confined in semiconductor quantum dots, most commonly in Ge/SiGe heterostructures. Unlike electron spin qubits that require micromagnets or oscillating magnetic fields for spin manipulation, hole spins benefit from strong spin-orbit coupling that enables all-electrical control via electric dipole spin resonance (EDSR).

The underlying physics originates from the $j=3/2$ character of valence-band holes. In a Ge/SiGe quantum well under biaxial compressive strain, the heavy-hole ($m_j=\pm 3/2$) and light-hole ($m_j=\pm 1/2$) subbands split, with the ground state being predominantly heavy-hole. Mixing between heavy-hole and light-hole states (mediated by confinement asymmetry, electric fields, and strain) generates the spin-orbit coupling that enables electrical spin control. This mixing also makes the hole g-factor highly anisotropic — the g-tensor depends strongly on the magnetic field direction relative to the confinement plane.

Two-qubit coupling uses exchange interaction between holes in neighboring dots, compatible with existing semiconductor gate-defined quantum dot control architectures. Recent progress in Ge/SiGe platforms has been rapid, with multi-qubit devices demonstrated.

The tradeoff is that the same spin-orbit coupling enabling fast control also couples the spin to electrical noise, requiring careful sweet-spot design and materials engineering to balance speed against coherence.

Hamiltonian

Effective single-qubit model:

$H=\frac{1}{2}g{\mu }_B\mathbf{B}\cdot \mathbf{\sigma }+\mathbf{E}(t)\cdot {\mathbf{d}}_{SO}(\mathbf{\sigma })$

where the first term is the Zeeman interaction (with an anisotropic g-tensor in general) and the second term is the spin-orbit-mediated electric driving, with ${\mathbf{d}}_{SO}$ the spin-orbit-induced electric dipole operator. Two-qubit coupling is typically exchange:

$H_{2q}=J(t){\mathbf{S}}_1\cdot {\mathbf{S}}_2$

Motivation

• Spin-orbit coupling turns electric fields into effective spin-control channels, eliminating micromagnets and oscillating magnetic field infrastructure needed for electron-spin ESR.
• Supports dense integration and fast gate operations in CMOS-compatible semiconductor processes.
• Ge/SiGe is isotopically purifiable (${}^{72}$Ge, ${}^{74}$Ge are spin-0), enabling low nuclear spin noise environments.
• The Ge/SiGe platform has shown the fastest progress toward multi-qubit semiconductor processors.

Experimental Status

Four-qubit Ge processor — Hendrickx et al. (2021):

• Demonstrated a four-qubit germanium quantum processor in a 2×2 quantum dot array.
• Achieved universal quantum logic with all-electrical control via EDSR.
• Single-qubit gate fidelities of 99–99.9% and two-qubit exchange gate fidelities of 98–99.5%.

Ongoing rapid progress (2021–present):

• Multiple groups (Veldhorst, Katsaros, Scappucci) scaling Ge/SiGe hole-spin devices to larger arrays.
• Hot-qubit operation demonstrated at elevated temperatures (up to ~1 K).
• Sweet-spot engineering reducing charge-noise sensitivity while maintaining fast gate speeds.

18-qubit modular array — Dijkema et al. (2026):

• Demonstrated operation of an 18-qubit array in germanium based on an extendable 2×N modular architecture.
• Achieved simultaneous initialization, control, and readout across the entire array using parallel operation of modular unit cells.
• Average single-qubit gate fidelities of 99.8% and median of 99.9% across the array.
• Characterized nearest-neighbor exchange couplings throughout the device and implemented controlled-Z gates.
• Generated a three-qubit Greenberger–Horne–Zeilinger (GHZ) state.
• Establishes a modular, extendable architecture for planar semiconductor quantum processors.

Key Metrics

Metric	Value	Notes	Fidelity reference
1Q gate time	1–50 ns	Fast EDSR control	—
1Q fidelity	99.8–99.9%	18-qubit Ge array	Dijkema et al. 2026
2Q fidelity	98–99.5%	Exchange-based	Hendrickx et al. 2021
$T_2^{\ast }$	1–20 μs	Device/material dependent	—
Operating temperature	20 mK – 1 K	Some hot-qubit demonstrations	—
Largest array	18 qubits	Modular 2×N architecture	Dijkema et al. 2026

References

Key experimental demonstration

• N. W. Hendrickx et al., “A four-qubit germanium quantum processor,” Nature 591, 580 (2021)

Scaling milestone

• J. J. Dijkema et al., “Simultaneous operation of an 18-qubit modular array in germanium,” arXiv:2604.01063 (2026)

Review

• G. Scappucci et al., “The germanium quantum information route,” Nature Rev. Mater. 6, 926 (2021)

Linked Papers

• hendrickx-2021-ge-4qubit
• scappucci-2021-ge-review
• dijkema-2026-simultaneous-operation-of-an

Related Entries

• spin-qubit — broader spin qubit family; holes offer faster electrical control than electrons
• singlet-triplet-qubit — electron-spin two-dot encoding; related control physics
• kane-qubit — donor-based spin qubit in silicon