Exchange-only qubit

Description

The exchange-only (EO) qubit, also called the 3-spin decoherence-free subsystem (3-DFS) qubit, encodes a logical qubit in the two-dimensional $S_{\text{tot}}=1/2$, $S_{\text{tot}}^z=1/2$ subspace of three electron spins in a linear triple quantum dot. Both logical states share the same total spin quantum numbers, providing inherent protection against uniform magnetic field fluctuations (decoherence-free subspace).

The key advantage: all gate operations use only pairwise exchange interactions — fast, baseband (DC) electrical pulses on gate electrodes. No microwave drive, no magnetic field gradients, no spin-orbit coupling required. This makes the EO qubit the simplest fully electrically controlled spin qubit.

Single-qubit gates require 3–4 sequential exchange pulses (or 3 simultaneous pulses in the always-on variant). Two-qubit gates between adjacent encoded qubits require ~18–20 sequential exchange pulses in the original serial protocol, though this is dramatically reduced to a single exchange pulse in the always-on (AEON) variant.

Figure

Hamiltonian

The three-spin system is controlled by pairwise Heisenberg exchange:

$H=J_{12}(t){\mathbf{S}}_1\cdot {\mathbf{S}}_2+J_{23}(t){\mathbf{S}}_2\cdot {\mathbf{S}}_3$

where $J_{ij}(t)=4t_{ij}^2/U_{ij}$ is the exchange coupling controlled by gate voltage tuning of the tunnel barrier between dots $i$ and $j$. In the original proposal, exchange couplings are pulsed on and off sequentially. In the always-on (AEON) variant, both $J_{12}$ and $J_{23}$ remain on and gates are performed by modulating their ratio.

Logical encoding

$|0_L⟩=|S{⟩}_{12}|\uparrow {⟩}_3=\frac{1}{\sqrt{2}}(|\uparrow \downarrow \uparrow ⟩-|\downarrow \uparrow \uparrow ⟩)$

$|1_L⟩=\sqrt{\frac{2}{3}}|T_{+}{⟩}_{12}|\downarrow {⟩}_3-\sqrt{\frac{1}{3}}|T_0{⟩}_{12}|\uparrow {⟩}_3=-\frac{1}{\sqrt{6}}(|\uparrow \downarrow \uparrow ⟩+|\downarrow \uparrow \uparrow ⟩-2|\uparrow \uparrow \downarrow ⟩)$

Both states have $S=1/2$, $S_z=+1/2$. The quadruplet state $|Q⟩=|\uparrow \uparrow \uparrow ⟩$ with $S=3/2$ is separated by the exchange gap and does not interact with the qubit subspace.

Gate operations

• $J_{12}$ alone generates rotation about one axis (e.g., $\hat{z}$) in the logical Bloch sphere
• $J_{23}$ alone generates rotation about a non-collinear axis (at 120° to the first)
• Combining these in sequence gives universal single-qubit control
• An arbitrary single-qubit rotation requires 3 exchange pulses (Fong & Wandzura 2011); specific Cliffords can take fewer
• Two-qubit gates via inter-triple exchange: 19 pulses (Fong & Wandzura optimized sequence) for CNOT

Motivation

• Inherent DFS protection against uniform magnetic field fluctuations
• All-electrical control — only fast DC voltage pulses on gate electrodes
• No microwave drive, no magnetic field gradients required
• Small qubit footprint (3 dots, ~150–300 nm pitch)
• Natural path to scaled architectures in Si/SiGe or GaAs
• Foundation for the RX qubit (always-on + microwave) and AEON qubit (always-on + baseband + double sweet spot)

Experimental Status

First demonstrated by Medford et al. (2013) in a GaAs/AlGaAs triple quantum dot:

• Coherent exchange oscillations and single-qubit rotations
• $T_2^{\ast }\sim 2\mu \text{s}$ (limited by nuclear spin bath in GaAs)

Demonstrated in Si/SiGe by Eng et al. (2015):

• Higher-fidelity operation with reduced nuclear noise
• Three-dot device with individually controllable exchange couplings

The always-on variant (AEON) demonstrated by Broz et al. (2025):

• Average Clifford fidelity $F_{C1}=99.86\%$ (blind randomized benchmarking)
• Simultaneous exchange pulses, Si/SiGe triangular QD array

References

Original proposal

• D. P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, and K. B. Whaley, “Universal quantum computation with the exchange interaction,” Nature 408, 339 (2000)

Optimized pulse sequences

• D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley, “Universal fault-tolerant quantum computation on decoherence-free subspaces,” PRA 63, 042307 (2001)
• B. H. Fong and S. M. Wandzura, “Universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem code,” QIC 11, 1003 (2011) — optimized to 19-pulse CNOT

Two-qubit gates (always-on variant)

• A. C. Doherty and M. P. Wardrop, “Two-qubit gates for resonant exchange qubits,” PRL 111, 050503 (2013) — single exchange pulse CZ when intra-qubit couplings are always on

Experimental demonstrations

• J. Medford et al., “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotech. 8, 654 (2013) — first demonstration, GaAs
• K. Eng et al., “Isotopically enhanced triple-quantum-dot qubit,” Sci. Adv. 1, e1500214 (2015) — Si/SiGe demonstration
• J. D. Broz et al., “Demonstration of an always-on exchange-only spin qubit,” arXiv:2508.01033 (2025) — AEON variant, $F_{C1}=99.86\%$

Linked Papers

• divincenzo-2000-exchange-only

Related Entries

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

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	>1 s	Spin relaxation in Si/SiGe	Simmons et al. 2011
Qubit coherence $T_2^{\ast }$	2–20 μs	GaAs (nuclear-limited) to Si/SiGe	Medford et al. 2013
Qubit coherence $T_2^{\text{echo}}$	10–100 μs	Hahn echo, material-dependent	Eng et al. 2015
Gate fidelity (1Q)	99.86%	AEON variant, blind RB (experimental)	Broz et al. 2025
Gate fidelity (1Q, sequential)	96–99%	Standard sequential exchange	Eng et al. 2015
Gate fidelity (2Q)	95–99%	Theoretical estimate (sequential)	Fong & Wandzura 2011
Gate time (1Q)	1–50 ns	3–4 exchange pulses	—
Gate time (2Q)	50–500 ns	~19 sequential pulses or 1 pulse (AEON)	—
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	—