Single-Spin Quantum Dot (Loss-DiVincenzo) Qubit

Figure

Description

The Loss-DiVincenzo qubit encodes quantum information in the spin-1/2 of a single excess electron ($|\uparrow ⟩$, $|\downarrow ⟩$) trapped in a gate-defined quantum dot in a semiconductor heterostructure, typically Si/SiGe or Si-MOS. Proposed by Loss and DiVincenzo (1998), it is arguably the simplest physical realization of a qubit: a single electron spin in a magnetic field.

Since spin is a magnetic property, the qubit does not directly couple to the dominant electrical noise sources in the semiconductor environment, leading to inherently long coherence times — particularly in isotopically purified ${}^{28}\text{Si}$, where the nuclear spin bath is eliminated. $T_2$ coherence times exceeding 28 ms have been demonstrated.

Single-qubit gates are implemented via electric-dipole spin resonance (EDSR), which uses an AC electric field combined with a spin-orbit coupling gradient (or micromagnet) to drive spin rotations without requiring oscillating magnetic fields. Two-qubit entangling gates use the exchange interaction: by electrically tuning the tunnel barrier between adjacent quantum dots, the Heisenberg exchange coupling $J(t)$ is switched on, producing a $\sqrt{\text{SWAP}}$ gate that, combined with single-qubit rotations, forms a universal gate set.

The extremely small qubit footprint (~50–100 nm pitch) and compatibility with CMOS fabrication technology make spin qubits a leading candidate for large-scale quantum computing.

Hamiltonian

The single-spin Zeeman Hamiltonian in an external magnetic field $B_0$:

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

where $g\approx 2$ is the electron g-factor in silicon, ${\mu }_B$ is the Bohr magneton, and ${\omega }_Z=g{\mu }_B{B}_0/\hslash$ is the Zeeman splitting (typically $\sim 10-40\text{GHz}$ at $B_0\sim 0.5-1.5\text{T}$).

The two-qubit exchange Hamiltonian when the tunnel barrier between adjacent dots is lowered:

$H_{\text{ex}}(t)=J(t){\vec{S}}_1\cdot {\vec{S}}_2$

where $J(t)=4t_0^2(t)/U$ is the exchange coupling, $t_0$ is the interdot tunneling matrix element (electrically tunable via gate voltage), and $U$ is the on-site charging energy. Pulsing $\int Jdt=\pi \hslash /2$ produces a $\sqrt{\text{SWAP}}$ gate.

Motivation

Individual spin with $S=1/2$ is the simplest realization of a qubit. The electron spin qubit in a semiconductor quantum dot provides easy electrical control of exchange coupling, potentially excellent scalability via lithographic patterning, and compatibility with existing CMOS semiconductor fabrication technology. Isotopically purified ${}^{28}\text{Si}$ eliminates the nuclear spin bath, yielding coherence times orders of magnitude longer than in GaAs. The extremely small qubit footprint makes it a strong candidate for the high qubit densities needed for fault-tolerant quantum computing.

Experimental Status

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

• First single-shot readout of an individual electron spin in a quantum dot using spin-to-charge conversion.

High-fidelity single-qubit gates — Yoneda et al. (2018):

• Demonstrated 99.9% single-qubit gate fidelity in a Si/SiGe quantum dot with charge-noise-limited coherence.

Universal gate set in silicon — Noiri et al. (2022):

• Demonstrated fast universal two-qubit gates above the fault-tolerance threshold in silicon.
• Exchange-based $\sqrt{\text{SWAP}}$ gate fidelity of 99–99.8%.

Long coherence in ${}^{28}\text{Si}$ — Veldhorst et al. (2014):

• Demonstrated electrical control of a long-lived spin qubit in a Si/SiGe quantum dot.
• Hahn echo $T_2\sim 28\text{ms}$ in isotopically purified silicon.

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$	1–45 s	Electron spin in Si/SiGe	Elzerman et al. 2004
$T_2$ (echo)	0.5–28 ms	Hahn echo in ${}^{28}$Si	Veldhorst et al. 2014
1Q gate fidelity	99.6–99.95%	EDSR driven	Yoneda et al. 2018
2Q gate fidelity	99–99.8%	Exchange-based $\sqrt{\text{SWAP}}$	Noiri et al. 2022
Gate time (1Q)	1–100 μs	Depends on drive mechanism	—
Gate time (2Q)	1–100 ns	Exchange pulse	—
Readout fidelity	98–99.5%	Spin-to-charge conversion + SET	Noiri et al. 2022
Qubit footprint	~50–100 nm pitch	Very small; CMOS-compatible	—
Operating temperature	20 mK–1 K	Silicon: some operation at >1 K	—
Connectivity	Nearest-neighbor (1D/2D)	Exchange range ~100 nm	—

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)
• 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)

Coherence characterization

• E. Kawakami et al., “Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot,” Nat. Nanotechnol. 9, 666 (2014)

Linked Papers

• loss-divincenzo-1998-quantum-dots

Related Entries

• singlet-triplet-qubit — two-spin encoding, no local fields needed for universal control
• exchange-only-qubit — three-spin encoding, exchange-only control
• aeon-qubit — always-on exchange variant
• semiconductor-charge-qubit — charge-based encoding (shorter coherence)
• kane-qubit — donor spin in silicon, similar physics with different confinement
• silicon-spin-qubit — broader family of silicon-based spin qubits
• flip-flop-qubit — long-range dipole-coupled spin qubit overcoming exchange-distance limitation