Always-on Exchange Only (AEON)

Figure

Description

The Always-on Exchange-Only (AEON) qubit is a three-spin encoded qubit in a linear triple quantum dot (TQD) array where the nearest-neighbor exchange couplings $J_L$ (dots 1–2) and $J_R$ (dots 2–3) are kept permanently on. There is no direct tunnel coupling between the outer dots ($t_{13}=0$). The qubit is encoded in the $S_{\text{tot}}=1/2$ subspace of three singly-occupied quantum dots in the (1,1,1) charge configuration.

The defining feature of the AEON qubit is its double sweet spot: the qubit frequency $E_{01}$ is first-order insensitive to charge noise in both independent detuning parameters $\epsilon$ (dot 1 vs. dot 3) and ${\epsilon }_M$ (dot 2 vs. average of dots 1 and 3) simultaneously. Crucially, the sweet spot position depends only on the Coulomb energies — not on the tunnel couplings $t_l$ and $t_r$ — so gates can be performed by tuning barrier gates while remaining at the sweet spot throughout.

All single-qubit operations use baseband (DC) exchange pulses — no microwave drive is required. Two-qubit entangling gates between adjacent AEON qubits can be implemented with a single exchange pulse, a dramatic simplification over the 18+ sequential pairwise pulses needed for the original 3-DFS exchange-only encoding.

At the sweet spot, the AEON qubit has no transition dipole moment ($g_{\perp }=0$), meaning it does not couple transversely to a superconducting resonator. Long-range coupling requires longitudinal (curvature) coupling to a cavity, or adiabatic conversion to the RX qubit regime where transverse coupling is available.

The qubit can be smoothly interconverted with other three-spin encodings: the RX qubit (for initialization, readout, and resonator coupling) and the 3-DFS exchange-only qubit (for a true off-state/memory with all exchange couplings turned off).

Hamiltonian

The AEON qubit is described by a Hubbard model for a linear TQD with only nearest-neighbor tunneling ($t_{13}=0$). In the qubit subspace ($S_{\text{tot}}=1/2$, $S_{\text{tot}}^z=1/2$), the effective Hamiltonian reduces to:

$H_{\text{eff}}=J_L{\mathbf{S}}_1\cdot {\mathbf{S}}_2+J_R{\mathbf{S}}_2\cdot {\mathbf{S}}_3$

where $J_L=2t_l^2({\tilde{U}}_1+{\tilde{U}}_2^{\prime })/f_l(\epsilon ,{\epsilon }_M)$ and $J_R=2t_r^2({\tilde{U}}_2+{\tilde{U}}_3)/f_r(\epsilon ,{\epsilon }_M)$, with ${\tilde{U}}_i$ the Coulomb energy changes for double occupancy of dot $i$. No $J_{13}$ term appears.

In the two-state qubit basis $\{|0_Q⟩,|1_Q⟩\}$:

$H_{\text{eff}}=-\frac{J}{2}{\sigma }_z-\frac{\sqrt{3}j}{2}{\sigma }_x$

where $J=(J_L+J_R)/2$ and $j=(J_L-J_R)/2$. The qubit energy gap is $E_{01}=\sqrt{J^2+3j^2}=\sqrt{J_L^2+J_R^2-J_L{J}_R}$.

Double sweet spot

The sweet spot conditions $\partial E_{01}/\partial \epsilon =0$ and $\partial E_{01}/\partial {\epsilon }_M=0$ yield:

${\epsilon }_{\text{ss}}=\frac{1}{4}(-{\tilde{U}}_1+{\tilde{U}}_2^{\prime }-{\tilde{U}}_2+{\tilde{U}}_3),{\epsilon }_{M,\text{ss}}=\frac{1}{4}({\tilde{U}}_1-{\tilde{U}}_2^{\prime }-{\tilde{U}}_2+{\tilde{U}}_3)$

These depend only on Coulomb energies, not on $t_l$ or $t_r$ — enabling full gate control while remaining at the sweet spot.

Single-Qubit Gates

All single-qubit rotations are performed via baseband (DC) voltage pulses on the tunnel barrier gates, modulating $J_L$ and $J_R$ simultaneously while remaining at the double sweet spot:

• $Z$ rotation: Symmetric exchange ($J_L=J_R$, i.e., $j=0$) → precession around $\hat{z}$
• General rotations: Asymmetric exchange ($J_L\ne J_R$) → rotation around an axis in the $xz$-plane. Combined with $Z$, this gives universal single-qubit control
• Pauli $X$: Can be decomposed as $X=R_{\hat{n}}(\pi )\cdot Z\cdot R_{\hat{n}}(\pi )$ with $\hat{n}=-(\hat{x}+\hat{z})/\sqrt{2}$, achieved with $t_l=(\sqrt{6}+\sqrt{2})t_r/2$

No microwave pulses are needed — this is purely baseband, all-electrical control.

Two-Qubit Gates

Two AEON qubits in a linear array (dots 1–2–3–4–5–6) are coupled via the inter-qubit exchange $J_c$ between neighboring dots (e.g., dots 3 and 4). With intra-qubit couplings always on, the effective inter-qubit Hamiltonian in the weak coupling regime ($J_c\ll J^{(A)},J^{(B)}$) is:

$H_c=\delta J_z({\sigma }_z^A+{\sigma }_z^B)/2+J_{zz}{\sigma }_z^A{\sigma }_z^B+J_{\perp }({\sigma }_x^A{\sigma }_x^B+{\sigma }_y^A{\sigma }_y^B)$

with all coefficients proportional to $J_c$. For the linear geometry, $\delta J_z/J_c=J_{zz}/J_c=1/36$ and $J_{\perp }/J_c=-1/24$ when $J^{(A)}\approx J^{(B)}$.

A CPHASE/CZ gate can be implemented with a single exchange pulse — requiring $\int J_{zz}(t)dt=\pi /4$. Estimated gate times range from ~20 ns (butterfly geometry with spin swaps) to a few hundred ns (linear geometry with conservative $J_c\sim 10$ MHz). This is a dramatic improvement over the 18+ sequential pairwise pulses required for the original 3-DFS encoding.

The inter-qubit sweet spot condition ($\partial J_c/\partial {\epsilon }_3=\partial J_c/\partial {\epsilon }_4=0$) can also be satisfied by tuning average dot energies, keeping both qubits and the coupler charge-noise-insensitive.

Resonator Coupling

At the double sweet spot, the AEON qubit has zero transition dipole moment ($g_{\perp }=0$) — it does not couple transversely to a superconducting resonator. This is both a feature (suppressed decoherence from charge noise) and a constraint (no direct cavity QED).

Two strategies for long-range coupling:

1. Longitudinal (curvature) coupling — The second derivative of the qubit frequency with respect to detuning gives a non-zero longitudinal coupling $g_{\parallel }$ to the cavity photon number. This enables dispersive readout and modulated longitudinal gates without leaving the sweet spot. (Theoretical — Ruskov & Tahan 2019, 2021)

2. Conversion to RX regime — Adiabatically sweeping ${\epsilon }_M$ converts the AEON qubit to an RX qubit, which has a large transverse dipole for cavity coupling. Readout and long-range entanglement proceed in the RX regime, then the qubit is swept back to the AEON sweet spot for computation. (The RX-cavity strong coupling regime has been demonstrated — Landig et al., Nature 2018)

Experimental Status

The AEON qubit was first experimentally demonstrated by Broz, Hoke, Acuna, and Petta (2025) in a Si/SiGe quantum dot device:

• Platform: Triangular QD array (note: the original proposal uses a linear TQD; the triangular geometry also supports AEON-like operation with simultaneous always-on exchange)
• Gate set: Full single-qubit Clifford set with simultaneous exchange pulses
• Fidelity: Average Clifford gate fidelity $F_{C1}=99.86\%$ via blind randomized benchmarking
• Key advance: First demonstration of simultaneous (non-commuting) exchange pulses for an exchange-only qubit, versus conventional sequential pairwise pulsing

Two-qubit entangling gates and resonator coupling have not yet been experimentally demonstrated in the AEON regime.

Comparison with Related Encodings

Property	3-DFS Exchange-Only	RX Qubit	AEON
QD energy levels	General	${\epsilon }_2\gg {\epsilon }_1\approx {\epsilon }_3$	${\epsilon }_1\approx {\epsilon }_2\approx {\epsilon }_3$
Sweet spot	None (DFS only)	Partial (1 of 2 detunings)	Full (both detunings)
Single-qubit gates	4 sequential exchange pulses	Microwave drive	3 simultaneous baseband pulses
Two-qubit gates	18+ sequential pulses	Dipole-dipole or single exchange pulse	Single exchange pulse
Resonator coupling	N/A	Transverse ($g_{\perp }$ large)	Longitudinal only ($g_{\perp }=0$)
Idle/memory	All exchange off	Always-on, $f_Q\sim$ 0.5–2 GHz	Exchange off (converts to 3-DFS) or always-on

(Table adapted from Shim & Tahan 2016, Table I)

References

Original proposal

• Y.-P. Shim and C. Tahan, “Charge-noise-insensitive gate operations for always-on, exchange-only qubits,” PRB 93, 121410(R) (2016) — arXiv:1602.00320

Two-qubit gates

• A. C. Doherty and M. P. Wardrop, “Two-qubit gates for resonant exchange qubits,” PRL 111, 050503 (2013) — showed that always-on exchange enables CZ gate in a single inter-qubit exchange pulse

Longitudinal resonator coupling (theoretical)

• R. Ruskov and C. Tahan, “Quantum-limited measurement of spin qubits via curvature couplings to a cavity,” PRB 99, 245306 (2019) — arXiv:1704.05876
• R. Ruskov and C. Tahan, “Modulated longitudinal gates on encoded spin qubits via curvature couplings to a superconducting cavity,” PRB 103, 035301 (2021) — arXiv:2010.01233
• R. Ruskov and C. Tahan, “Longitudinal (curvature) couplings of an N-level qudit to a superconducting resonator at the adiabatic limit and beyond,” PRB 109, 245303 (2024) — arXiv:2312.03118

RX qubit–resonator strong coupling (related experimental)

• A. J. Landig, J. V. Koski, P. Scarlino et al., “Coherent spin–photon coupling using a resonant exchange qubit,” Nature 560, 179 (2018) — demonstrated strong coupling of RX qubit to SC cavity (~31 MHz); AEON could convert to this regime

Experimental demonstration

• J. D. Broz, J. C. Hoke, E. Acuna, and J. R. Petta, “Demonstration of an always-on exchange-only spin qubit,” arXiv:2508.01033 (2025) — $F_{C1}=99.86\%$ average Clifford fidelity, Si/SiGe triangular QD array, single-qubit gates only

Background: exchange-only qubits

• D. P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, and K. B. Whaley, “Universal quantum computation with the exchange interaction,” Nature 408, 339 (2000) — original exchange-only qubit proposal
• 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 pulse sequences

Linked Papers

• shim-2016-aeon

Related Entries

• rx-qubit
• loss-divincenzo-qubit
• exchange-only-qubit

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	>1 s	Spin relaxation in Si	Shulman et al. 2012
Qubit coherence $T_2$	10–100 μs	Enhanced by double sweet-spot operation	Shim & Tahan 2016
Gate fidelity (1Q)	99.86%	Average Clifford fidelity, blind RB (experimental)	Broz et al. 2025
Gate fidelity (1Q, theory)	99–99.5%	Baseband exchange at sweet spot (theoretical)	Shim & Tahan 2016
Gate fidelity (2Q)	95–99%	Single exchange pulse CZ (theoretical estimate)	Doherty & Wardrop 2013
Gate time (1Q)	1–50 ns	DC barrier gate pulses	Shim & Tahan 2016
Gate time (2Q)	~20–200 ns	Single exchange pulse (geometry-dependent)	Shim & Tahan 2016
Operating temperature	20–100 mK	Si/SiGe or GaAs	—
Qubit footprint	~150–300 nm pitch	3 dots per logical qubit	—

Related Qubits

• exchange-only-qubit — parent architecture (sequential pulses, no sweet spot)
• singlet-triplet-qubit — two-spin cousin
• loss-divincenzo-qubit — single-spin ancestor
• rx-qubit — related always-on 3-spin qubit (partial sweet spot, microwave control, transverse cavity coupling)