Exchange-only qubit

Description

This is an encoded qubit defined in the two-dimensional subspace of a three- spin-half system. The two qubit states have the same total spin quantum numbers (Stot=1/2, Stotz=1/2), providing protection against some global magnetic field fluctuation. All the gate operations can be implemented by sequences of exchange interactions between neighboring spins. Single qubit gates require at most 3 or 4 exchange steps, while two-qubit gates require much longer exchange sequences (about 20 exchange steps).

Figure

Motivation

This qubit has inherent protection against fluctuation of global magnetic field. More importantly, it requires only fast electrical gate control (exchange pulses) for full set of single- and two-qubit gate operations, without using any microwave control.

References

• https://www.nature.com/articles/35042541
• https://journals.aps.org/pra/abstract/10.1103/PhysRevA.63.042307
• http://advances.sciencemag.org/content/1/4/e1500214

Linked Papers

• divincenzo-2000-exchange-only

Related Entries

• singlet-triplet-qubit
• rx-qubit
• hybrid-qubit
• aeon-qubit

Seed Metadata

• date_published: 2000-11-16

Physics

Logical qubit encoded in the $S=1/2$, $S_z=+1/2$ subspace of three electron spins in a triple quantum dot:

$|0_L⟩=|S_{12}⟩|\uparrow {⟩}_3,|1_L⟩=\sqrt{\frac{2}{3}}|T_{12}^{+}⟩|\downarrow {⟩}_3-\sqrt{\frac{1}{3}}|T_{12}^0⟩|\uparrow {⟩}_3$

Universal control uses only pairwise Heisenberg exchange $J_{ij}{\vec{S}}_i\cdot {\vec{S}}_j$ between any pair in the triple dot — no magnetic fields or gradients needed. The encoding forms a decoherence-free subspace against collective dephasing.

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	>1 s	Spin relaxation	DiVincenzo et al. 2000
Qubit coherence $T_2$	1–100 μs	DFS protects against uniform $B$ noise	Medford et al. 2013
Gate fidelity (1Q)	99–99.5%	All-exchange rotations	Medford et al. 2013
Gate fidelity (2Q)	95–99%	Between adjacent triples	Medford et al. 2013
Gate time (1Q)	1–50 ns	Exchange pulses	—
Gate time (2Q)	10–100 ns	Inter-triple exchange	—
Readout fidelity	95–99%	Spin-to-charge + charge sensor	Medford et al. 2013
Qubit footprint	~150–300 nm pitch	3 dots per logical qubit	—
Operating temperature	20–100 mK	GaAs or Si/SiGe	—
Connectivity	Nearest-neighbor	Between adjacent triple dots	—

Related Qubits

• loss-divincenzo-qubit — single-spin ancestor
• singlet-triplet-qubit — two-spin encoding (needs gradient)
• aeon-qubit — always-on variant