Hybrid Qubit (Semiconductor Double Dot)

Figure

Description

The quantum-dot hybrid qubit encodes quantum information in three electrons confined to a double quantum dot. Its relevant charge sectors are $(2,1)$ and $(1,2)$, where the ordered pair gives the left- and right-dot occupations. The encoding combines charge mobility with a fixed total-spin manifold: both logical states have $S=1/2$ and a common $S_z$, while their singlet-versus-triplet character in the doubly occupied dot distinguishes them.

For a left-doubly-occupied convention, the asymptotic spin basis is

$$|L,S⟩=|S⟩|\downarrow ⟩,|L,T⟩=\sqrt{\frac{1}{3}}|T_0⟩|\downarrow ⟩-\sqrt{\frac{2}{3}}|T_{-}⟩|\uparrow ⟩,$$

with analogous states $|R,S⟩$ and $|R,T⟩$ when the right dot is doubly occupied. The logical $|0⟩$ and $|1⟩$ are the two lowest eigenstates after interdot tunneling hybridizes these four charge-spin basis states; they are not bare charge configurations.

Electrical modulation of detuning or tunnel coupling drives the qubit because its eigenstates contain charge admixture. At favorable operating points, the two logical energies have nearly parallel dependence on detuning, suppressing first-order charge-noise dephasing while retaining a usable electric dipole. The central design tension remains speed versus noise: moving toward an anticrossing increases electrical controllability but also increases charge sensitivity.

Hamiltonian

A representative four-state Hamiltonian in the ordered basis $\{|L,S⟩,|L,T⟩,|R,S⟩,|R,T⟩\}$ is

$$H_q=\left(\begin{array}{cccc}\epsilon /2& 0& {\Delta }_1& -{\Delta }_2\\ 0& \epsilon /2+E_L& -{\Delta }_3& {\Delta }_4\\ {\Delta }_1& -{\Delta }_3& -\epsilon /2& 0\\ -{\Delta }_2& {\Delta }_4& 0& -\epsilon /2+E_R\end{array}\right),$$

where $\epsilon$ is the double-dot detuning, $E_L$ and $E_R$ are the singlet-triplet splittings of the left and right dots, and ${\Delta }_{1\dots 4}$ are spin-conserving interdot tunnel matrix elements. The logical states are the two lowest eigenstates of $H_q$; the next levels are leakage states.

After projection into the logical subspace, a small detuning drive can be written

$$H_{\mathrm{eff}}=\frac{\hslash {\omega }_q}{2}{\sigma }_z+\frac{\delta \epsilon (t)}{2}\left(d_z{\sigma }_z+d_x{\sigma }_x\right),$$

where $d_z$ and $d_x$ are matrix elements of the detuning operator in the qubit eigenbasis. Transverse response drives rotations, longitudinal response shifts the qubit frequency, and a detuning sweet spot satisfies $\partial {\omega }_q/\partial \epsilon =0$.

Motivation

• Combine the fast electrical control of charge-like states with the spin structure and common-mode magnetic-noise rejection of an $S=1/2$ encoding.
• Implement universal single-qubit control without a micromagnet or nuclear-state preparation.
• Use sweet-spot operation, resonant driving, and engineered tunnel couplings to reduce the charge-noise cost of electrical control.
• Provide a compact double-dot alternative to three-dot exchange-only encodings, albeit with a less favorable demonstrated coherence and fidelity record than leading modern silicon spin qubits.

Experimental Status

Original proposal and pulse protocol — Shi et al. and Koh et al. (2012):

• Shi et al. proposed the three-electron, silicon double-dot encoding and its electrically controlled singlet-triplet/tunnel-coupling Hamiltonian.
• Koh et al. developed nonadiabatic pulse-gated one- and two-qubit sequences that traverse charge-like anticrossings.

First experimental demonstration — Kim et al. (2014):

• Demonstrated universal control and process tomography in a Si/SiGe double dot.
• Achieved sub-100-ps rotations, with measured process fidelities of 85-89% for the reported $X$ rotations and 94-96% for the reported $Z$ rotations.
• Measured $T_2^{\ast }\approx 2$ ns in the charge-like $X$-rotation regime and $T_2^{\ast }\approx 10$ ns for the more spin-like $Z$ evolution.

Resonant control — Kim et al. (2015):

• Used microwave detuning modulation at a charge-noise-protected operating point.
• Reported $X$-axis $\pi$ rotations in under 5 ns with fidelity above 93%, $Z$ rotations with fidelity above 96%, and dynamical-decoupling coherence beyond 150 ns.

Readout advances — Harpt et al. and Park et al. (2025):

• Harpt et al. demonstrated parametric longitudinal resonator readout in an ultra-dispersive regime with qubit-resonator detuning of roughly 10 GHz.
• Park et al. demonstrated single-shot latched readout using barrier-gate control with one reservoir, obtaining readout SNR 10.2 and 98% reset/initialization probability after 2 ms, versus 80% without reset pulses.
• These results improve readout integration and reset, but they do not establish a newer single-qubit gate-fidelity record for the encoding.

Key Metrics

Metric	Value	Notes	Fidelity reference
DC-pulsed rotation time	$<100$ ps	Demonstrated about two Bloch-sphere axes	Kim et al. 2014
DC-pulsed process fidelity	85-89% ($X$); 94-96% ($Z$)	Process-tomography values depend on rotation angle	Kim et al. 2014
Resonant $\pi$-gate performance	$<5$ ns and $>93\%$ ($X$); 50 ps and $>96\%$ ($Z$)	Microwave detuning drive at a protected operating point	Kim et al. 2015
Dynamically decoupled coherence	$>150$ ns	Hahn echo and Carr-Purcell sequences	Kim et al. 2015
Ultra-dispersive readout detuning	$\sim 10$ GHz	Parametric longitudinal resonator coupling	Harpt et al. 2025
Latched-readout SNR / reset probability	10.2 / 98% after 2 ms	Barrier-gate pulsing; 15-fold reset speedup	Park et al. 2025

References

Original proposals

• Z. Shi et al., “Fast Hybrid Silicon Double-Quantum-Dot Qubit,” Phys. Rev. Lett. 108, 140503 (2012); arXiv:1110.6622
• T. S. Koh et al., “Pulse-Gated Quantum-Dot Hybrid Qubit,” Phys. Rev. Lett. 109, 250503 (2012); arXiv:1207.5581

Experimental milestones

• D. Kim et al., “Quantum control and process tomography of a semiconductor quantum dot hybrid qubit,” Nature 511, 70-74 (2014); arXiv:1401.4416
• D. Kim et al., “High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit,” npj Quantum Information 1, 15004 (2015); arXiv:1502.03156
• B. Harpt et al., “Ultra-dispersive resonator readout of a quantum-dot qubit using longitudinal coupling,” npj Quantum Information 11, 5 (2025); arXiv:2407.08869
• S. Park et al., “Single-shot latched readout of a quantum dot qubit using barrier gate pulsing,” npj Quantum Information 11, 148 (2025); arXiv:2408.15380

Linked Papers

• shi-2012-fast-hybrid-double-dot
• koh-2012-pulse-gated-dot
• kim-2014-control-process-tomography
• kim-2015-resonant-hybrid-qubit
• harpt-2025-ultra-dispersive-hybrid-readout
• park-2025-latched-hybrid-readout

Evergreen context

• charge-noise-sweet-spot — the hybrid qubit is a clean semiconductor example of why speed from charge admixture only becomes useful when the operating point is flattened against detuning noise.
• exchange-interaction-in-quantum-dots — tunnel coupling and detuning set the exchange-mediated hybridization in the double dot.
• heisenberg-exchange-in-quantum-dots — useful after projecting the charge sector into the logical $S=1/2$ subspace.
• divincenzo-criteria — hybrid qubits make an explicit control-speed-versus-coherence trade rather than maximizing either quantity alone.

Related Entries

• exchange-only-qubit — three-electron, three-dot encoding with purely exchange control
• spin-qubit — broader semiconductor spin-qubit family
• semiconductor-charge-qubit — the charge-like limit of electrically driven double-dot control
• hole-spin-qubit — fast electrical spin control through spin-orbit coupling rather than deliberate charge hybridization
• qubit-readout — spin-to-charge, latched, and resonator-based measurement methods
• circuit-qed — framework for the 2025 longitudinal-resonator readout experiment