Single-Spin Quantum Dot (Loss-DiVincenzo) Qubit

Figure

Description

The Loss-DiVincenzo qubit is the canonical gate-defined semiconductor spin qubit: quantum information is encoded in the spin-1/2 of a single excess electron, typically $|\downarrow ⟩$ and $|\uparrow ⟩$, confined in an electrostatically defined quantum dot. Proposed by Loss and DiVincenzo in 1998, it turned the simple idea of an electron spin in a tunable quantum dot into a concrete quantum-computing architecture with single-qubit control, exchange-based entangling gates, and spin-selective readout.

In modern realizations, the platform is usually implemented in Si/SiGe or Si-MOS heterostructures. The spin degree of freedom couples only weakly to electric noise, which helps enable long coherence times, while nanoscale gates still allow electrical tuning of confinement, tunnel couplings, and exchange. In isotopically enriched ${}^{28}\mathrm{Si}$, where the nuclear-spin bath is strongly suppressed, Hahn-echo coherence times have reached $\sim 28\mathrm{ms}$.

Single-qubit control is typically performed by electric-dipole spin resonance (EDSR), using an oscillating gate electric field together with a micromagnet gradient or effective spin-orbit coupling. Two-qubit entangling gates use the electrically tunable Heisenberg exchange interaction between neighboring dots. The architecture has progressed from Elzerman single-shot spin readout in 2004, to $>99.9\%$ single-qubit control in 2018, to above-threshold two-qubit gates in 2022, six-qubit universal control in 2022, and industry-compatible 300 mm foundry-fabricated unit cells with $>99\%$ fidelity in all operations in 2025.

Its appeal is a combination of compact footprint, CMOS compatibility, and direct electrical tunability. The hard part is not the basic qubit definition but the materials and control stack: valley splitting, charge noise, wiring density, and calibration overhead all become central as the architecture scales.

Hamiltonian

For a single confined electron in a static magnetic field $B_0$, the qubit is set by the Zeeman term

$H_Z=\frac{1}{2}g{\mu }_B{B}_0{\sigma }_z=\frac{\hslash {\omega }_Z}{2}{\sigma }_z,$

where $g\approx 2$ in silicon and ${\omega }_Z=g{\mu }_B{B}_0/\hslash$. In an EDSR drive picture, the control term can be written as

$H_{\mathrm{drive}}(t)=\frac{\hslash {\Omega }_R(t)}{2}\cos (\omega t+\varphi ){\sigma }_x,$

where ${\Omega }_R$ is the electrically induced Rabi frequency generated by a magnetic-field gradient or effective spin-orbit coupling.

For two neighboring dots, the entangling interaction is the exchange Hamiltonian

$H_{\mathrm{ex}}(t)=J(t){\mathbf{S}}_1\cdot {\mathbf{S}}_2,$

where $J(t)$ is tuned electrically through the interdot barrier and detuning. In the Hubbard-model limit, $J\sim 4t_c^2/U$ for tunnel coupling $t_c$ and charging energy $U$. Appropriate exchange pulses generate $\sqrt{\mathrm{SWAP}}$ gates, and with a Zeeman-energy difference between qubits the same interaction can be used to realize CZ-like entangling operations.

Motivation

The Loss-DiVincenzo architecture is attractive because it uses the simplest possible microscopic qubit in a semiconductor: one electron spin in one dot. That gives it several enduring strengths:

• Long coherence in purified silicon: suppressing ${}^{29}$Si removes most hyperfine dephasing.
• All-electrical tunability: confinement, loading, exchange, and much of the control stack are gate-controlled.
• Tiny footprint: quantum-dot pitch is typically tens of nanometres, enabling dense arrays.
• CMOS pathway: the device concept is unusually compatible with mature semiconductor fabrication.
• Clear architectural lineage: singlet-triplet, exchange-only, and several other semiconductor-spin encodings grow naturally out of the same gate-defined quantum-dot toolbox.

Experimental Status

Single-shot spin readout, Elzerman et al. (2004):

• First single-shot readout of an individual electron spin in a quantum dot via spin-to-charge conversion.
• Established reservoir-assisted initialization and energy-selective tunnelling readout as core ingredients of the architecture.

Long-lived electrically controlled single spin, Kawakami et al. (2014):

• Demonstrated electrical control of a long-lived Si/SiGe single-spin qubit.
• Reported Hahn-echo coherence up to $\sim 28\mathrm{ms}$ in isotopically enriched silicon.

High-fidelity single-qubit control, Yoneda et al. (2018):

• Demonstrated a single-spin quantum-dot qubit with coherence limited by charge noise and single-qubit fidelity above $99.9\%$.

Above-threshold universal two-qubit gates, Noiri et al. (2022):

• Demonstrated single-qubit fidelity of $99.8\%$ and two-qubit fidelity of $99.5\%$ in a ${}^{28}\mathrm{Si}$/SiGe double quantum dot.
• Established fast exchange-based entangling control above the surface-code threshold.

Six-qubit universal processor, Philips et al. (2022):

• Demonstrated universal control, initialization, and measurement on a six-qubit silicon quantum-dot processor.
• Marked an important shift from isolated high-fidelity pairs to small programmable arrays.

300 mm foundry-compatible unit cell, Steinacker, Stuyck et al. (2025):

• Demonstrated a silicon spin-qubit unit cell fabricated in an industrial 300 mm process with $>99\%$ fidelity in all operations and SPAM fidelity $>99.9\%$.
• Showed that high-fidelity operation survives the transition from tailored academic devices to foundry-compatible fabrication.

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_2$ (Hahn echo)	$\sim 28\mathrm{ms}$	Single electron in enriched Si/SiGe	Kawakami et al. 2014
1Q gate fidelity	$>99.9\%$	Single-spin EDSR control	Yoneda et al. 2018
2Q gate fidelity	$99.5\%$	Exchange-based CZ in ${}^{28}$Si/SiGe	Noiri et al. 2022
1Q gate time	$\sim 100\mathrm{ns}$	Fast EDSR control in double-dot device	Noiri et al. 2022
2Q gate time	$\sim 50\mathrm{ns}$	Exchange-based entangling gate	Noiri et al. 2022
$T_1$	$6.3\mathrm{s}$	300 mm foundry Si-MOS unit cell	Steinacker, Stuyck et al. 2025
SPAM fidelity	$>99.9\%$	300 mm foundry Si-MOS unit cell	Steinacker, Stuyck et al. 2025
Operating temperature	$1.1\mathrm{K}$ demonstrated	Universal silicon-dot logic above 1 K	Petit et al. 2020
Largest demonstrated programmable array	6 qubits	Universal control in silicon quantum dots	Philips et al. 2022

References

Original proposal

• D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120 (1998) — arXiv:cond-mat/9701055

Experimental demonstrations

• J. M. Elzerman et al., “Single-shot read-out of an individual electron spin in a quantum dot,” Nature 430, 431 (2004)
• E. Kawakami et al., “Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot,” Nat. Nanotechnol. 9, 666 (2014)
• J. Yoneda et al., “A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%,” Nat. Nanotechnol. 13, 102 (2018)
• A. Noiri et al., “Fast universal quantum gate above the fault-tolerance threshold in silicon,” Nature 601, 338 (2022) — arXiv:2108.02626
• S. G. J. Philips et al., “Universal control of a six-qubit quantum processor in silicon,” Nature 609, 919 (2022) — arXiv:2202.09252
• P. Steinacker, N. D. Stuyck et al., “Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity,” Nature 646, 81 (2025) — arXiv:2410.15590

Linked Papers

• loss-divincenzo-1998-quantum-dots
• elzerman-2004-single-shot-read
• kawakami-2014-electrical-control-long
• yoneda-2018-dot-spin-qubit
• noiri-2022-silicon-1q-fidelity
• philips-2022-universal-control-six
• steinacker-2025-300mm-foundry-silicon

Evergreen context

• exchange-interaction-in-quantum-dots — the original entangling primitive of the Loss-DiVincenzo architecture
• heisenberg-exchange-in-quantum-dots — the minimal two-spin Hamiltonian behind exchange gates
• sqrt-swap-as-universal-gate — the native entangling gate family of the architecture

Related Entries

• spin-qubit — umbrella concept for spin-based encodings
• silicon-spin-qubit — broader silicon implementation family
• singlet-triplet-qubit — two-spin encoding variant
• exchange-only-qubit — three-spin encoding with exchange-only control
• aeon-qubit — always-on exchange variant
• kane-qubit — donor-spin alternative in silicon
• qubit-readout — spin-to-charge conversion and charge-sensing context
• semiconductor-charge-qubit — charge-based sibling architecture