Demonstration of an always-on exchange-only spin qubit

Domain: physics
Published: 2026-04-03
Editorial outcome: minor_revision

Abstract
In conventional exchange-only (EO) spin qubit demonstrations, quantum gates have been implemented using sequences of individually pulsed pairwise exchange interactions with only one exchange coupling active at a time. Alternatively, multiple non-commuting exchange interactions can be pulsed simultaneously, reducing circuit depths and providing protection against leakage. We demonstrate high-fidelity quantum control of an always-on exchange-only (AEON) qubit, operated using simultaneous exchange pulses in a triangular quantum dot (QD) array. We use blind randomized benchmarking to characterize the performance of the full AEON single-qubit Clifford gate set, achieving an average Clifford gate fidelity F C1 = 99.86%. Extensions of this work may enable more efficient EO two-qubit entangling gates as well as the implementation of native i-Toffoli gates in Loss-DiVincenzo single-spin qubits.

Introduction
Gate-defined semiconductor QDs are an attractive platform for scalable quantum computing owing to their small size, compatibility with existing semiconductor fabrication techniques, and potential for operation at temperatures above 1 K [1–7]. In QDs, quantum information is typically stored in the spins of confined electrons or holes, which benefit from long coherence times [8, 9] and the availability of a fast, electrically controlled exchange interaction for coupling nearest neighbor spins [10, 11]. However, single-spin qubit control is difficult, requiring either precise engineering of local magnetic fields or the use of materials with strong spin-orbit coupling, both of which add to design complexity [12–14].

The EO qubit was developed to circumvent the need for single-spin control by encoding a single qubit in a subspace of three physical spins, which support universal quantum control through the exchange interaction alone [15]. The encoded gates are typically implemented using sequences of pulsed pairwise exchange interactions, where no more than two spins interact at any given time [16–19]. This serial mode of operation is chosen for its practical simplicity, as qubit control is characterized by a single parameter — a time-integrated exchange energy J (t) coupling spins i and j — which is easy to tune and calibrate [18]. However, this simplicity comes at the cost of large gate depths, with recently demonstrated single-qubit gates requiring up to four exchange pulses and two-qubit gates as many as twenty-eight [18, 19]. EO gates can be designed to further mitigate leakage error sources, but at the cost of even longer sequence lengths, such as the 16-pulse single-qubit gates designed to dynamically decouple magnetic and charge noise [20], or the 44-pulse leakage-controlled two-qubit gates which suppress spreading of leakage errors [19].

The AEON qubit is a variant of the EO qubit that uses simultaneously pulsed pairs of exchange couplings to construct quantum gates [21]. A key advantage of the AEON qubit is significantly shorter gate depths, with single-qubit gates requiring no more than two simultaneous exchange pulses [22] and two-qubit gates as little as one [23, 24]. Moreover, these gates are naturally protected from leakage due to an induced energy gap between the qubit and leakage subspaces [23–25].

Here we report full control of an AEON qubit in a Si/SiGe triangular QD array [26]. Sensitivity to charge noise is mitigated by operating exchange at a double sweet spot (DSS), which is first-order insensitive to fluctuations of the chemical potentials of all three confined electrons [21, 27]. We implement a calibration procedure for AEON qubit gates that simultaneously calibrates both the axis and angle of rotation. With this procedure, we realize a complete set of gates and extract a single-qubit Clifford gate fidelity F C1 = 99.86% via blind randomized benchmarking (BRB). Our results show that AEON qubit performance is on par with state-of-the-art EO qubits operated using sequential exchange pulses [18].

Results
Measurements are performed on a triangular triple QD device consisting of a single layer of etch-defined gate electrodes fabricated on top of an isotopically enriched 28Si/SiGe heterostructure (800 ppm 29Si) [3, 26]. A scanning electron microscope image of a nominally identical device is shown in Fig. 1(a). Voltages applied to plunger gates (P i ) form QDs in the underlying 28Si quantum well, each tuned to confine a single electron. Voltages applied to exchange gates (X i,j ) control the exchange coupling between neighboring QDs. In practice, devices are tuned using virtual gates, linear combinations of physical gate voltages that selectively control key dot parameters while compensating for device cross-capacitances [28–30]. Specifically, the virtual plunger gate voltage V˜ Pi controls the chemical potential ✏ i of dot i and the virtual exchange gate voltage V˜ Xi,j controls the tunnel coupling t i,j between dots i and j (see Methods for more details). The remaining gate electrodes are used to load electrons into the dots from charge reservoirs (B, T ) and to form a dot charge sensor (M, Z ) [31].

The Hamiltonian for the three singly-occupied exchange-coupled QDs is given by:

Hˆ(t)=J 1,2 (t)Sˆ 1 · Sˆ 2 +J 2,3 (t)Sˆ 2 · Sˆ 3 +J 1,3 (t)Sˆ 1 · Sˆ 3 , (1)

where Sˆ i are the dot spin operators and we set ¯h=1 such that J i,j can be interpreted as either an energy or angular frequency. We introduce the notation k-J to describe the number k of nonzero J i,j contained in Hˆ . EO or AEON qubit control is then distinguished by the restriction of Hˆ to 1-J or 2-J exchange, respectively. That is, an AEON qubit is distinguished from an EO qubit by its mode of operation. EO qubit control is consists of serial pulsing of exchange where only a single exchange interaction is active at a time, while AEON control consists of simultaneous exchange where at least two exchange interactions are active at a time (2-J exchange).

Both the EO and AEON qubit are encoded identically in the collective three-electron spin state of the array, which occupies an eight-dimensional Hilbert space [15]. In terms of the total (three-electron) spin S and its projection m S , this Hilbert space decomposes into a S=3/2 quadruplet (m S = ±1/2, ±3/2) and two S=1/2 doublets (m S = ±1/2). The exchange interaction, which conserves both S and m S , only couples states within the two doublets. The qubit is encoded by defining | 0 i = | S=1/2, S 13 =0, m S = ±1/2 i and | 1 i = | S=1/2, S 13 =1, m S = ±1/2 i, where S 13 is the combined spin of dots 1 and 3 and m S = ±1/2 acts as an extra gauge degree of freedom [1]. The state | 0 i corresponds to a singlet between dots 1 and 3, with the uncoupled spin of dot 2 determining the qubit’s gauge. We use standard Pauli spin blockade techniques [11] to initialize the qubit into the singlet state | 0 i and to map the occupation of | 0 i onto the charge configuration, which can then be measured using the dot charge sensor [31]. The specific value of m S is randomly assigned during initialization and is left unresolved by measurement.

Expressed in the qubit basis, Eq. 1 takes the form:

Hˆ(t)= 1/2 [p3J - (t) ˆ x +(J 1,3 (t) J + (t)) ˆ z ], (2)

where ˆ i are the standard Pauli operators, and we define J + = (J 1,2 +J 2,3 )/2 and J - = (J 1,2 J 2,3 )/2. A detailed derivation of Eq. 2 from Eq. 1 is provided in the supplemental material of Ref. [18]. In the Bloch sphere picture, time-evolution under Hˆ corresponds to a rotation with angle ✓ about an axis rˆ=(cos('),0,sin(')) in the xz-plane, as described by the unitary operator

Rˆ ' (✓)= T exp[ i Z0 ⌧ Hˆ(t)dt] (3)

⇡ cos(✓/2) 1 i sin(✓/2)[r x ˆ x +r z ˆ z ], (4)

where T is the time-ordering operator, ✓ = ⌦(t)dt, ⌦= p3J - 2 +(J 1,3 J + )2, r x = cos(') = p3J - /⌦, and r z = sin(')=(J 1,3 J + )/⌦. The approximation in Eq. 4 is exact only when [Hˆ(t),Hˆ(t 0 )]=0 for all times t and t 0 , which requires that the ratios of nonzero J i,j remain constant over the duration of the exchange pulses. This condition is trivially met for 1-J exchange, which drives rotations about one of three non-orthogonal axes separated by 120 ◦ in the xz-plane [see Fig. 1(b)]. We label these as zˆ= (0,0,1), nˆ = (p3,0,1)/2, and mˆ = (p3,0, 1)/2.

By interleaving rotations about any two of these axes, an arbitrary single-qubit gate can be constructed using at most four 1-J exchange pulses [18]. In contrast, 2-J exchange allows for rotations about an arbitrary axis in the xz-plane [see Fig. 1(c)]. Using 2-J exchange, any single-qubit gate can be implemented using no more than two pulses [22]. Because the two constituent interactions are non-commuting, 2-J qubit operation generally requires full temporal control of the voltage waveforms. However, we verify through experiment that even without implementing this level of control Eq. 4 still provides an accurate description of 2-J operation.

Due to its encoding in a Zeeman doublet, the qubit’s dynamics are invariant to global magnetic fields [15, 32–34]. However, fluctuating magnetic field gradients generated by nearby spinful nuclei can induce decoherence and leakage out of the qubit subspace [35, 36]. We mitigate leakage by applying a small global magnetic field B 3 mT to suppress transitions that do not conserve m S , leaving a single (gauge-dependent) leakage state, | S=3/2, m S = ±1/2 i, spin-degenerate with the qubit subspace. 1-J exchange partially breaks this remaining degeneracy by introducing an energy gap between states with S 13 = 0 and S 13 = 1. On the other hand, 2-J exchange energetically separates the S = 1/2 qubit and the S = 3/2 subspaces, highly suppressing leakage [see Fig. 1(d)].

To characterize the 2-J exchange landscape, we sweep the amplitudes of two virtual exchange gate voltages applied simultaneously during a 10 ns pulse, producing the fingerpinch plots shown in Fig. 2 [37]. The data reveal oscillations of the probability P | 0 i of measuring the encoded | 0 i state as a function of exchange gate voltages, as expected from Eq. 4. The insets in Fig. 2 show simulations of the corresponding ideal two-level system evolution, assuming an uncoupled exponential dependence of exchange energy J i,j on the virtual exchange gate voltage V˜ Xi,j . While the measured data qualitatively resembles the simulations, nonlinear and, in some cases, non-monotonic deviations are evident due to a complicated cross-dependence of the 2-J exchange interaction on gate voltages [38].

In principle, the strength of a 2-J exchange interaction depends on both the interdot tunnel couplings and the dot chemical potentials. In a triple-dot system, the chemical potentials are typically parameterized using a common mode and two differential modes [39]. Exchange is insensitive to the common mode, defined as ✏¯= ✏ 1 +✏ 2 +✏ 3 , but sensitive to the differential modes: the tilt detuning, ✏ t =(✏ 2 ✏ 1 )/2, and the dimple detuning, ✏ d = ✏ 3 (✏ 1 +✏ 2 )/2. However, it is possible to operate 2-J exchange at a DSS where the sensitivity to the two differential modes vanishes to first order, as demonstrated in Fig. 3(a), thereby reducing decoherence due to charge noise [21, 27, 39–41]. Although exchange energies retain a second-order dependence on chemical potentials at the DSS [21], these contributions are expected to be negligible compared to the dominant first-order dependence on the interdot tunnel couplings, as is the case for 1-J exchange operated at the analogous symmetric operating point [41].

Operating at the DSS, we characterize coherence by measuring the qubit’s time-evolution during 2-J exchange pulses, as plotted in Fig. 3(b). We quantify coherence by the number of exchange oscillations N osc that occur before the amplitude decays to 1/e of its initial value. For comparison, we also plot the measured time-evolution for 1-J exchange operated at symmetric operating points in Fig. 3(c) (see Supplementary Information for 1-J fingerprint plots and associated operating points). We find that the N osc for 2-J exchange is generally greater than for 1-J exchange, despite both regimes operating at sweet spots with vanishing first-order sensitivity to chemical potential fluctuations. More detailed device modeling may be helpful for understanding the coherence enhancement during 2-J operation.

To calibrate a 2-J exchange rotation Rˆ ' (✓), both the rotation axis ' and angle ✓ must be tuned. We directly optimize the fidelity of a composite pulse sequence designed to be simultaneously sensitive to both 2-J rotation parameters. The composite sequence is defined as Uˆ(N)=UˆN ax UˆN ang and reduces to the identity 1 ˆ when the 2-J rotation is perfectly calibrated. This occurs when Rˆ ' (✓) = Rˆ '⇤ (✓ ⇤ ) for the target rotation angles ' ⇤ and ✓ ⇤. The two components of Uˆ differ in their sensitivity: Uˆ ang is primarily sensitive to errors in ' and Uˆ ax to errors in ✓. Explicitly, we define Uˆ ang = Rˆ ' 2q(✓) and Uˆ ax =[Rˆ ⌘ ( )Rˆ ' (✓)]2, where q is a positive integer chosen such that q✓ = s⇡ for some odd integer s, and Rˆ ⌘ ( ) is a pre-calibrated rotation with = ⇡ and ⌘ = ' ⇤ ⇡/2. Similar sequences are used in the context of robust phase estimation and gate set tomography to amplify deviations from target gate parameters [42, 43]. Finally, to map the fidelity F(Uˆ,1 ˆ) of Uˆ relative to the identity onto the measured probability P | 0 i , we twirl Uˆ over the set of 1-J single-qubit Clifford gates [44].

A specific rotation Rˆ ' (✓) is calibrated by sweeping the amplitudes of the exchange gate pulses to produce a two-dimensional map of F. An example sweep for a 2-J ⇡-rotation about the zˆ-axis is shown in Fig. 4, where a pre-calibrated 2-J ⇡-rotation about the xˆ-axis is used as Rˆ ⌘ ( ) in the construction of Uˆ ax . As the exchange voltages are varied, F oscillates periodically, producing a series of interference peaks whose frequency—and therefore sensitivity — increases with the sequence length N. Only the central peak corresponds to the optimal calibration condition ' = ' ⇤ and ✓ = ✓ ⇤, which we track by performing successive sweeps with increasing values of N =1,2,4,..., continuing until reductions in the signal-to-noise ratio prevents scaling beyond N =24. This calibration procedure is effectively a two-dimensional extension of the robust phase estimation protocol of Kimmel et al. [42] and similarly benefits from a Heisenberg scaling of the gate error with sequence length N. In practice, we perform low-resolution sweeps for intermediate values of N and use a generic peak-finding algorithm to locate the central maximum, reserving a high-resolution sweep and analytic fit (see supplementary information) for the final N =24 iteration. Using this procedure, a full calibration of a single 2-J rotation takes approximately five minutes.

Using this calibration procedure, we tune nine distinct 2-J exchange pulses corresponding to rotations of ⇡/2, ⇡, and 3⇡/2 about each of the axes: zˆ, xˆ, and xˆ. The locations of these pulses in bias space are indicated by the colored markers in Fig. 2. To evaluate the performance of each pulse, we perform interleaved BRB, which involves interleaving a calibrated 2-J rotation into BRB sequences constructed from 1-J exchange pulses [18]. Details on the calibration procedure and interleaved BRB measurements are given in the Supplementary Information.

To quantitatively assess the AEON qubit performance, we execute BRB on 2-J single-qubit Clifford gates constructed from the best performing 2-J pulses [18]. In Fig. 5 we compare 2-J gate fidelities to the BRB performance of standard 1-J EO single-qubit gates in the same device. Our measurements yield a 2-J single qubit Clifford gate fidelity F C1 = 99.86%, slightly surpassing the best 1-J BRB fidelity of 99.84% obtained from rotations about the nˆ and zˆ axes. Additionally, the 2-J leakage error per Clifford, 0.015%, is approximately half that of the average 1-J leakage error per Clifford, 0.029%, with the 1-J leakage error being comparable to the value measured in similar devices [3, 19, 26]. This reduction is consistent with the leakage-protected nature of the 2-J gates, as each Clifford gate spends roughly half of its duration at idle where exchange is negligible.

Although 2-J BRB outperforms 1-J BRB, this advantage primarily arises from its shorter gate depths: a 2-J single-qubit Clifford gate requires an average of 1.9 exchange pulses, compared to 2.7 pulses for a 1-J Clifford gate. When this difference is taken into account, the total 2-J error per exchange pulse (" pp 0.076%) is in fact higher than that of the best-performing 1-J gates (" pp 0.060%). This outcome is somewhat unexpected given the larger N osc and lower leakage rates observed for 2-J exchange, which imply a reduced sensitivity to charge and hyperfine noise — the dominant noise sources in EO qubits [18, 19]. This discrepancy suggests an increased contribution from coherent errors during 2-J pulsing, possibly due to imperfect calibration or enhanced sensitivity to pulse overlap [18], but we suspect the dominant contribution stems from the non-commutativity of 2-J exchange—i.e. breakdowns in the approximation of Eq. 4 — due to differences in the transient exchange response to the two simultaneous voltage pulses. Nonetheless, the residual error can likely be mitigated through pulse-shaping techniques and the reduced gate depths afforded by simultaneous exchange already confer a measurable advantage — one that is expected to become even more significant for two-qubit operations [37].

Methods
A. Virtual gates

Virtual gate voltages V˜ are related to physical gate voltages V through a compensation matrix C, such that V˜ =CV [28–30]. Ideally, the chemical potential ✏ i is only affected by a voltage V applied to the the plunger gate P i . In reality, voltages applied to neighboring gates will also affect ✏ i . The virtual gates, as defined by C, are designed to compensate for this cross-coupling to first order. Explicitly, in this work we used:

[V˜ P1 V˜ P2 V˜ P3 ]T = [1 0.169 0.129; 0.112 1 0.118; 0.139 0.176 1] [V P1 V P2 V P3 ]T

[V˜ X1,2 V˜ X1,3 V˜ X2,3 ]T = [1 0 0; 0 1 0; 0 0 1] [V X1,2 V X1,3 V X2,3 ]T

Here, the matrix elements are defined as C i,j = (@✏ i /@V Pj )/(@✏ i /@V Pi ) with analogous definitions for exchange gates. We determine the values of the C i,j by tracking shifts of electron loading lines for each dot as a function of gate voltage.

In the Fig. 2 data, we also compensated for first-order cross-coupling between exchange gates using:

[V˜ X1,2 V˜ X1,3 V˜ X2,3 ]T = [1 0.08 0.08; 0.24 1 0.18; 0.15 0.19 1] [V X1,2 V X1,3 V X2,3 ]T

where d ij,kl = (@J ij /@V˜ Xkl )/(@J ij /@V˜ Xij ). Here, the d ij,kl were determined by tracking the first exchange fringe in the fingerpinch plots as a function of neighboring exchange gate voltage near the center of the sweep. To simplify notation, we drop the superscripts in the labels of the virtual exchange gates in Fig. 2. We emphasize that exchange gate compensation was not used in any of the other data presented in this work (in particular, it was not applied for the calibration sweeps shown in Fig. 4).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work experimentally demonstrates the always-on exchange-only (AEON) qubit, a variation of the exchange-only (EO)\nqubit encoded in a three-spin system. The AEON qubit exhibits two key features: (i) a double sweet spot (DSS) where the\nqubit is insensitive to detuning fluctuations up to first order, and (ii) the ability to tune multiple exchange interactions by\ncontrolling the barrier potential while remaining on the DSS, enabling the implementation of all gate operations within this\nregime.\nIn this work, the AEON qubit is realized in a triangular triple quantum dot system in isotopically enriched silicon.\nA significant challenge in implementing the AEON qubit lies in the simultaneous calibration of multiple gate voltages to both\nlocate the DSS and apply gate operations effectively. The authors address this by employing virtual gates and calibration\nschemes to identify the optimal gate voltages. The experimental results show that the AEON qubit performs slightly better\nwhen utilizing two simultaneous exchange interactions, as compared to operating with a single exchange interaction at a\ntime.\nWhile the performance improvement over conventional EO qubits is modest, this work demonstrates the calibration of multi-\nexchange operations, which could be highly beneficial in larger systems containing multiple AEON qubits.\nThis is an important experimental contribution, showcasing the AEON qubit for the first time, and providing a viable\nalternative to traditional EO qubits. I recommend its acceptance for publication in Nature Communications.\nHowever, I would like the authors to address the following points:\nThe observed performance gain is modest. What do you identify as the main limiting factors? Would pulse-shape\nengineering, which ensures the Hamiltonian commutes at different times, potentially help to improve performance?\nOne of the key technical advancements in this work is the calibration scheme for controlling two exchange interactions (2-J),\nwhich appears to be more complex than the 1-J calibration. Could you comment on whether this complexity might present\nchallenges in scaling up to larger systems with more quantum dots?", "reviewer_2": "The manuscript “Demonstration of an always-on exchange-only spin qubit” by Joseph D.\nBroz et.al demonstrates high-fidelity control of an always-on exchange-only (AEON) qubit.\nThe control is implemented via simultaneous exchange pulses in a triangular quantum dot\n(QD) array, and the achieved averaged fidelity is 99.86%. Although they claimed the\nadvantage for the AEON qubit, this fidelity is comparable to the work in Ref [18], and is still\nlower than 99.9%. This means the AEON scheme did not work that well. Meanwhile, two-\nqubit control is also lack in their manuscript. More importantly, the recent reported single-\nqubit control for spin qubits in silicon has reached fidelity surpassing 99.99%\n(arXiv:2507.11918, 2025). Therefore, I think the AEON scheme is technically sound,\nhowever, I do not believe it to be of sufficiently high significance to warrant publication in\nNature communications.\nAlso, I have some minor suggestions:\n1. The authors are encouraged to introduce how to implement EO qubit and AEON in\ndetail. Particularly, they should compare how difference between the two qubits. Also,\nthe definition of the so-called 1-J and 2-J exchange controls in the manuscript is not so\nclear.\n2. It is not so clear to the reader that how to derive Eq.2 from Eq.1. Can the authors add\nsome derivation in detail in the appendix?", "reviewer_3": "The authors of the manuscript show the formation of an AEON qubit in a series of three quantum dots and demonstrate the\noperation of the qubit at the DSS point. They examine two different modes of driving exchange oscillations between the\ndifferent dots in the qubit, with the key difference between the modes being the difference in the axes around which the qubit\nis being driven. Finally, the authors perform interleaved BRB of the exchange oscillations and demonstrate that high fidelity\nexchange oscillations are performed. In general, the manuscript is well-written, and the work is highly interesting. However, I\nwould strongly suggest that the comments below are addressed before the manuscript is published, particularly surrounding\nthe apparent contradiction between Fig.3 and the text.\nTo what extent have the authors characterised the position of the DSS? I assumed that the authors chose the DSS point to\nbe where the differential detunings are zero, but do the authors expect any 2nd order terms to dominate there and based on\nthe charge noise level, do the authors expect the DSS to shift slightly depending on the exact charge configuration?\nI am confused by what appears to be a contradiction between Fig.3 and the text in the last paragraph of the quantum control\nsection. In Fig.3, b) and c) are respectively 1-J and 2-J oscillations, clearly indicating that 2-J oscillations are worse than 1-J.\nBut the text claims Nosc for 2-J is greater than 1-J, which is the opposite of what is shown in Fig.3. Then, the authors claim\nthat operating at the DSS should yield similar Nosc for both regimes. Could the authors explain in greater detail why they\nbelieve this is the case? My naïve intuition is that the 2-J oscillations would be susceptible to noise against more axes and\ntherefore, it makes sense that 2-J oscillations are performing worse. The higher values of Nosc for 2-J exchange is\nreferenced again in the later section – and it is unclear if then Fig.3 is labelled wrong. I am concerned with the\ninconsistencies in the explanations given the inconsistency in the way the results are described.\nOn that note, do the authors find that interleaved BRB suffer from the same problems that interleaved RB has, which is that\nthere can be decoupling effects introduced in the reference sequences, which in principle would overestimate the fidelities of\nthe gates being interleaved and could potentially give fidelities of > 100% if decoupling is particularly good. Have the\nauthors considered other forms of benchmarks and explore how they compared relative to interleaved BRB?\nWhat are the steps needed to go from these intra-dot exchange oscillations to performing a single qubit gate? I am assuming\nthat 1-J exchange oscillations are sufficient and that going to 2-J and 3-J exchange is a matter of improving the protection\nagainst noise.\nAlso, can the authors comment more on the leakage observed in this system, i.e., how significant it is and whether the\nleakage observed was due to readout or during operation? This question stems from just the basic understanding that\nleakage is a non-negligible source of noise and I am interested in how impactful it is here, beyond just the number being\nquoted."}, "author_response": "We thank all the reviewers for their time, careful evaluations, and insightful feedback, which we\nhave incorporated into an improved manuscript. Below, we address each of the reviewer’s\ncomments point by point and summarize the resulting changes made to the manuscript.\nReviewer 1\nComment 1:\nThe observed performance gain is modest. What do you identify as the main limiting factors?\nWould pulse-shape engineering, which ensures the Hamiltonian commutes at different times,\npotentially help to improve performance?\nResponse:\nThe modest performance gain of 2-J over 1-J Clifford gates is primarily attributed to reduced\ngate depths. On average, a 2-J Clifford requires 1.9 exchange pulses, compared to 2.7 exchange\npulses for a 1-J Clifford. More broadly, for arbitrary single-qubit unitaries we expect roughly a\ntwofold reduction in gate depth when using 2-J exchange rather than 1-J exchange (Ref. 22).\nHowever, blind randomized benchmarking (BRB) measurements show that the average error per\n2-J exchange pulse (0.076%) is actually higher than the best average error per 1-J pulse\n(0.060%). Some care is warranted in interpreting this comparison: a complete 1-J Clifford set\ncan be compiled using only two exchange axes, whereas implementing arbitrary 2-J rotations\nnecessarily involves all three. The elevated 2-J error could therefore partially reflect poorer\nperformance along the third axis.\nTo understand the discrepancy more systematically, it is useful to distinguish between noise-\ndriven errors and coherent control errors. Our measurements indicate that 2-J exchange is less\nsensitive than 1-J exchange to the two dominant noise mechanisms: charge noise, as quantified\nby and hyperfine-induced fluctuations, as inferred from the leakage rate extracted from\nBRB. This suggests that the reduced per-pulse fidelity of 2-J exchange is not noise-limited but\ninst𝑁𝑁ea os d c arises from coherent errors. While we cannot rule out contributions from imperfect\ncalibration or increased 2-J susceptibility to overlap of sequentially applied exchange pulses (see\nRefs. 18 and 19), we suspect that the dominant effect is transient pulse distortion: during the\nrising and falling edges of the pulse, the ratio of the two simultaneous exchange couplings\ndeviates from its intended value, violating the idealized rotation model (Eq. 4 of the main text).\nIn future work, we plan to investigate these transient effects more directly using advanced\ncharacterization tools such as gate-set tomography, and to explore pulse-shape engineering—\nguided by optimal-control methods—as a path toward mitigating these coherent errors.\nChanges made in response to comment:\nWe modified paragraph 2, first column, fifth page to include a discussion of this point:\nAlthough 2-J BRB outperforms 1-J BRB, this advantage primarily arises from its shorter\ngate depths: a 2-J single-qubit Clifford gate requires an average of 1.9 exchange pulses,\ncompared to 2.7 pulses for a 1-J Clifford gate. When this difference is taken into account,\nthe total 2-J error per exchange pulse ( ) is in fact higher than that of the\nbest-performing 1-J gates ( ). This outcome is somewhat unexpected given\n𝜖𝜖pp ≈ 0.076%\nthe larger and lower leakage rates observed for 2-J exchange, which imply a reduced\n𝜖𝜖pp ≈ 0.060%\nsensitivity to charge and hyperfine noise --- the dominant noise sources in EO qubits [18,\n𝑁𝑁osc\n19]. This discrepancy suggests an increased contribution from coherent errors during 2-J\npulsing, possibly due to imperfect calibration or enhanced sensitivity to pulse overlap\n[18], but we suspect the dominant contribution stems from the non-commutativity of 2-J\nexchange --- i.e. breakdowns in the approximation of Eq. 4 --- due to differences in the\ntransient exchange response to the two simultaneous voltage pulses. Nonetheless, the\nresidual error can likely be mitigated through pulse-shaping techniques and the reduced\ngate depths afforded by simultaneous exchange already confer a measurable advantage ---\none that is expected to become even more significant for two-qubit operations [37].\nComment 2:\nOne of the key technical advancements in this work is the calibration scheme for controlling two\nexchange interactions (2-J), which appears to be more complex than the 1-J calibration. Could\nyou comment on whether this complexity might present challenges in scaling up to larger systems\nwith more quantum dots?\nResponse:\nWe expect that the extent to which the calibration scheme poses challenges for scaling to multi-\nqubit systems will depend strongly on the specific device geometry (e.g. linear, square 2D array,\n2D hex array). In a close-packed geometry, cross-coupling between neighboring gate electrodes\nmay be substantial, potentially necessitating modifications to the calibration protocol. In\ncontrast, in a more conservative architecture -- where adjacent qubits interact only through a\nsingle exchange gate electrode -- we anticipate that the present protocol should generalize\nwithout significant changes.\nMore broadly, as in the one-dimensional analogue (Ref. 42), our calibration procedure exhibits\nHeisenberg scaling with respect to the sequence length , making it both efficient and well-\nsuited for multi-qubit extensions. In principle, calibration of different qubits could also be carried\nout in parallel, with the possible exception of immediate𝑁𝑁ly adjacent qubits where cross-talk\neffects are strongest.\nChanges made in response to comment:\nWe modified paragraph 2, second column, fourth page to include a discussion of this point:\nA specific rotation is calibrated by sweeping the amplitudes of the exchange gate\npulses to produce a two-dimensional map of F. An example sweep for a 2-J -rotation\n𝑅𝑅𝜑𝜑(𝜃𝜃)\nabout the -axis is shown in Fig. 4, where a pre-calibrated 2-J -rotation about the -axis\n𝜋𝜋\n𝑧𝑧̂ 𝜋𝜋 𝑥𝑥\nis used as in the construction of . As the exchange voltages are varied, F\noscillates periodically, producing a series of interference peaks whose frequency --- and\n𝑅𝑅𝜂𝜂(𝜒𝜒) 𝑈𝑈ax\ntherefore sensitivity --- increases with the sequence length N. Only the central peak\ncorresponds to the optimal calibration condition and , which we track by\nperforming successive sweeps with increasing values of∗ N=1,2,4,…∗, continuing until\n𝜑𝜑 = 𝜑𝜑 𝜃𝜃 = 𝜃𝜃\nreductions in the signal-to-noise ratio prevents scaling beyond N = 24. This calibration\nprocedure is effectively a two-dimensional extension of the robust phase estimation\nprotocol of Kimmel et al. [41] and similarly benefits from a Heisenberg scaling with\nrespect to sequence length N, making it well suited for larger multi-qubit systems. In\npractice, we perform low-resolution sweeps for intermediate values of N and use a\ngeneric peak-finding algorithm to locate the central maximum, reserving a high-\nresolution sweep and analytic fit (see supplementary information) for the final N=24\niteration. Using this procedure, a full calibration of a single 2-J rotation takes\napproximately five minutes.\nReviewer 2:\nComment 1:\nAlthough they claimed the advantage for the AEON qubit, this fidelity is comparable to the work\nin Ref [18], and is still lower than 99.9%. This means the AEON scheme did not work that well.\nMeanwhile, two-qubit control is also lack in their manuscript. More importantly, the recent\nreported single-qubit control for spin qubits in silicon has reached fidelity surpassing 99.99%\n(arXiv:2507.11918, 2025).\nResponse:\nWe agree that the improvement of the AEON qubit over the EO qubit measured in the same\ndevice (and similar devices) is modest. However, we believe that this modest improvement is\nalready quite interesting given the large gains (over an order of magnitude shorter gate\noperations) expected when applied to large multi-qubit systems. Meanwhile, our work answers\nthree outstanding questions regarding simultaneous exchange control needed for AEON qubit\nimplementation:\n1. Will charge noise be too costly for effectively implementing AEON qubits?\nAnswer: By operating at a DSS, we are able to realize simultaneous exchange\noscillations with quality factors that actually exceed those of non-simultaneous\nexchange operated at an analogous symmetric operating point.\n2. Can quantum gates be effectively calibrated given the complicated cross-coupling of the\nexchange interaction?\nAnswer: We have demonstrated a calibration protocol that is robust to cross-\ncoupling between exchange interactions and that is quite efficient, achieving\nHeisenberg scaling with respect to the number of applications of the target gate.\nMore generally, this protocol represents a two-dimensional extension of an\nexisting protocol based on robust phase estimation that is useful for cases where\ngate parameters must be calibrated simultaneously.\n3. Will the error due to imperfect and slightly different pulsing between the different\nexchange interactions be a fundamental limitation?\nAnswer: While this may be a dominant error source for the AEON qubit, our\nresults provide an upper-bound on the size of this error and we find that it is still\nlow enough that the AEON qubit provides a net-benefit relative to the\nconventional EO qubit.\nLastly, we would like to emphasize that the 99.99% single qubit gate fidelities reported by the\nreviewer are associated with Loss-DiVincenzo (LD) single spin qubits, not exchange only spin\nqubits. LD spin qubits generally require the incorporation of a micromagnet for the efficient\ndriving of electric dipole spin resonance. It is unlikely that micromagnets can be incorporated\ninto industrially fabricated spin qubit devices with multiple back-end-of-line (BEOL) layers that\nincrease the distance between the micromagnet and spins, thereby reducing Rabi frequencies.\nThe investigation of other spin qubit modalities, for example exchange only spin qubits and\nsinglet triplet spin qubits, is therefore warranted. Exchange only spin qubits, in particular,\nbenefit from short gate times that are enabled by large exchange couplings. In contrast, slow 1 –\nsingular focus on one performance metric, in this case the LD single qubit gate fidelity, is\nmisguided, as would be a comparison with much different physical systems (e.g. trapped ions,\nwhere the fidelities are orders of magnitude higher than any solid state qubit).\nComment 2:\nThe authors are encouraged to introduce how to implement EO qubit and AEON in detail.\nParticularly, they should compare how difference between the two qubits. Also, the definition of\nthe so-called 1-J and 2-J exchange controls in the manuscript is not so clear.\nResponse:\nWe define the technical difference between the EO/AEON qubits in the second paragraph, first\ncolumn, second page: EO or AEON qubit control is then distinguished by the restriction of to\n1-J or 2-J exchange, respectively. But agree that it should be further clarified given its central\n𝐻𝐻\nimportance to our results.\nChanges made in response to comment:\nWe have added several sentences to the second paragraph, first column of the second page to\nmake the distinction between an EO qubit and AEON qubit clearer:\nEO or AEON qubit control is then distinguished by the restriction of to 1-J or 2-J\nexchange, respectively. That is, an AEON qubit is distinguished from an EO qubit by its\n𝐻𝐻\nmode of operation. EO qubit control is consists of serial pulsing of exchange where only\na single exchange interaction is active at a time, while AEON control consists of\nsimultaneous exchange where at least two exchange interactions are active at a time (2-J\nexchange).\nBoth the EO and AEON qubit are encoded identically in the collective three-electron spin\nstate of the array, which occupies an eight-dimensional Hilbert space [15]…\nComment 3:\nIt is not so clear to the reader that how to derive Eq.2 from Eq.1. Can the authors add some\nderivation in detail in the appendix?\nResponse:\nA detailed derivation of Eq. 2 from Eq. 1 is provided in section 1 of the supplemental material of\nRef. 18.\nChanges made in response to comment:\nWe have added a sentence immediately following the introduction of Eq. 2 pointing to the\nderivation in Ref. 18:\nA detailed derivation of Eq. 2 from Eq. 1 is provided in the supplemental material of Ref.\n[18].\nReviewer 3:\nComment 1:\nTo what extent have the authors characterised the position of the DSS? I assumed that the\nauthors chose the DSS point to be where the differential detunings are zero, but do the authors\nexpect any 2nd order terms to dominate there and based on the charge noise level, do the authors\nexpect the DSS to shift slightly depending on the exact charge configuration?\nResponse:\nWe have not characterized the location of the DSS beyond performing sweeps of the type shown\nin Fig. 3a of the main text, from which we estimate the DSS position by eye. For each 2-J\nrotation axis, we select a single DSS point corresponding to a -rotation (for a 10 ns pulse) and\nuse this same point for all other rotation angles. Because we employ virtual gates that\ncompensate the linear cross-capacitance of the exchange gates𝜋𝜋 onto the plunger gates, we find\nthat the shift in the DSS position across different rotation angles is negligible. Long term drifts\nof the charge configuration and thus DSS due to charge noise are also possible, but these could\nbe handled with intermittent recalibration sequences. A more detailed investigation -- such as\nmapping the insensitivity region as a function of plunger-gate voltages, in analogy with Ref. 41 -\n- would likely yield valuable insights, and we plan to pursue this in future work.\nRegarding higher-order terms at the DSS, Ref. 21 provides a detailed theoretical analysis within\nthe context of the Fermi–Hubbard model. While this work shows that exchange does acquire a\nsecond-order dependence on differential detunings, it also demonstrates a first-order dependence\non tunnel couplings. We expect this latter channel to dominate the impact of charge noise on\nexchange coherence, analogous to the behavior seen in the non-simultaneous exchange case\ndiscussed in Ref. 41.\nChanges made in response to comment:\nWe have added the following sentence at the end of paragraph 2, second column, page 3:\nAlthough exchange energies retain a second-order dependence on chemical potentials at\nthe DSS [21], these contributions are expected to be negligible compared to the dominant\nfirst-order dependence on the interdot tunnel couplings, as is the case for 1-J exchange\noperated at the analogous symmetric operating point [41].\nComment 2:\nI am confused by what appears to be a contradiction between Fig.3 and the text in the last\nparagraph of the quantum control section. In Fig.3, b) and c) are respectively 1-J and 2-J\noscillations, clearly indicating that 2-J oscillations are worse than 1-J. But the text claims Nosc\nfor 2-J is greater than 1-J, which is the opposite of what is shown in Fig.3.\nResponse:\nThe confusion likely arises because Fig. 3b displays 2-J exchange oscillations while Fig. 3c\ndisplays 1-J exchange oscillations, which is inconsistent with the ordering used in the original\ncaption text.\nChanges made in response to comment:\nWe have updated the wording in the Fig. 3 caption to read “Measured 2- and 1-J exchange\noscillations…” so that it matches the ordering of the sub-figures. We have also added labels to\npanels (b) and (c) to clearly indicate which data correspond to 1-J exchange oscillations and\nwhich correspond to 2-J exchange oscillations (see below).\nComment 3:\nThen, the authors claim that operating at the DSS should yield similar Nosc for both regimes.\nCould the authors explain in greater detail why they believe this is the case?\nResponse:\nWe operate both 1- and 2-J exchange at “sweet spots” that are first-order insensitive to the\nchemical potentials. For 2-J exchange this is the DSS, for 1-J exchange it is typically referred to\nas the symmetric operating point (SOP) (Ref. 41). At both types of sweet spots, the dominant\nchannel through which charge noise couples into the system is modulation of the interdot tunnel\ncouplings. Granted there is only a single interdot tunnel coupling involved in 1-J exchange and\ntwo interdot tunnel couplings involved in 2-J exchange, but a significant portion of their energies\ninteracts destructively. This can be seen quantitatively by computing the derivatives of Eq. 2\n𝑑𝑑Ω\nof the main text for all gate electrode voltages . Here, is as defined on page 2 of the main\n𝑑𝑑𝑉𝑉𝑖𝑖\ntext and describes the frequency of exchange oscillations, so that these derivatives describe the\n𝑉𝑉𝑖𝑖 Ω\nsensitivity of this frequency to gate-referred voltage fluctuations.\nChanges made in response to comment:\nThat being said, these derivatives depend on a model of exchange energy as a function of gate\nvoltage, which may vary significantly between the 1- and 2-J regimes. We have therefore\nrewritten the ending of the first paragraph, first column of page 4 to reduce the strength of our\nclaim:\nOperating at the DSS, we characterize coherence by measuring the qubit's time-evolution\nduring 2-J exchange pulses, as plotted in Fig. 3(b). We quantify coherence by the number\nof exchange oscillations that occur before the amplitude decays to 1/e of its initial\nvalue. For comparison, we also plot the measured time-evolution for 1-J exchange\n𝑁𝑁osc\noperated at symmetric operating points in Fig. 3(c) (see Supplementary Information for\n1-J fingerprint plots and associated operating points). We find that the for 2-J\nexchange is generally greater than for 1-J exchange, despite both regimes operating at\n𝑁𝑁osc\nsweet spots with vanishing first-order sensitivity to chemical potential fluctuations. More\ndetailed device modeling may be helpful for understanding the coherence enhancement\nduring 2-J operation.\nComment 4:\nDo the authors find that interleaved BRB suffer from the same problems that interleaved RB has,\nwhich is that there can be decoupling effects introduced in the reference sequences, which in\nprinciple would overestimate the fidelities of the gates being interleaved and could potentially\ngive fidelities of > 100% if decoupling is particularly good. Have the authors considered other\nforms of benchmarks and explore how they compared relative to interleaved BRB?\nResponse:\nWe indeed find that the leakage rates extracted from 2-J interleaved BRB are typically negative,\nwhich we attribute to a dynamical decoupling effect (see Table 1 in the Supplementary\nInformation). For this reason, we choose to emphasize standard BRB in the main text,\ncomparing sequences composed solely of 2-J exchange pulses with those composed solely of 1-J\npulses. In future work, we plan to perform a more detailed error analysis of 2-J exchange using\ngate-set tomography, although this protocol will require modifications to properly account for\nleakage states in the EO qubit encoding.\nComment 4:\nWhat are the steps needed to go from these intra-dot exchange oscillations to performing a\nsingle qubit gate? I am assuming that 1-J exchange oscillations are sufficient and that going to\n2-J and 3-J exchange is a matter of improving the protection against noise.\nResponse:\nThe key steps required to transition from intra-dot exchange oscillations to fully calibrated\nsingle-qubit gates are outlined at the beginning of the Gate Calibration and Benchmarking\nsection in the main text. In particular, we introduce an efficient calibration procedure based on\nthe robust phase-estimation protocol of Kimmel et al. (Ref. 42), which enables the simultaneous\ncalibration of both the rotation angle and rotation axis of a 2-J rotation. This is essential because\nthese quantities are intrinsically coupled at the Hamiltonian level (Eq. 4) and are further coupled\ndue to exchange cross-coupling. In this way, calibrating 2- and 3-J exchange is fundamentally\ndifferent than calibrating 1-J exchange, which can be achieved directly using 1-J exchange\noscillations.\nComment 5:\nAlso, can the authors comment more on the leakage observed in this system, i.e., how significant\nit is and whether the leakage observed was due to readout or during operation?\nResponse:\nThe measured leakage error of 0.029% for the 1-J EO qubit implementation is comparable to the\nvalue measured in similar SLEDGE devices (see Refs. 3, 19, 26). For the 2-J AEON qubit\nimplementation, the measured leakage error of 0.015% is about half of this value, which is\nconsistent with the interleaved BRB results and the leakage-protected nature of 2-J exchange\n(effectively, the AEON qubit is only exposed to significant leakage during idle periods between\nexchange pulses, which make up about half of the quantum circuit).\nThe leakage error measured using BRB corresponds only to the leakage during gate operations.\nThe leakage error during readout is subsumed into the SPAM fidelity (essentially given by the\ncontrast of the two curves in Fig. 5 extrapolated to 0 Clifford operations) and is comparable\nbetween AEON and EO qubit implementations (as we should expect, since readout is performed\nidentically in both cases).\nChanges made in response to comment:\nWe have added a statement in the third paragraph, first column, of the fifth page to give context\nto the leakage error:\nAdditionally, the 2-J leakage error per Clifford, 0.015%, is approximately half that of the average\n1-J leakage error per Clifford, 0.029%, with the 1-J leakage error being comparable to the value\nmeasured in similar devices [3, 19, 26].\nAdditional Changes:\n• There was a typo in the text of Fig. 1(d). We changed MHz to\nMHz.\n𝐽𝐽𝑘𝑘,𝑙𝑙 = 100 𝐽𝐽𝑘𝑘,𝑙𝑙 = 2𝜋𝜋×\n• There was a typo in Fig. 1(a). The charge configurations were mislabeled. We changed\n100\n(clockwise from upper left) 102, 210, 012, 120 to 120, 012, 210, 102.\n• We added a short statement in the conclusion to emphasize the expected improvement of\nentangling operations for the AEON versus EO qubit:\nFirst, 2-J exchange offers substantial reductions in gate depths for entangling\noperations, reducing the number of exchange pulses by well over an order of\nmagnitude as compared to typical EO qubit entangling gates [23, 24]."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors addressed all referees' comments satisfactorily, and I recommend its acceptance for publication.", "reviewer_2": "The revised manuscript has clarified the distinction between AEON and LD qubits,\nemphasizing that their present fidelities cannot be compared in a simplistic manner and\nthat additional factors such as controllability and scalability must also be taken into account.\nI agree with this perspective, which addresses the point I was most concerned about and\ndirectly defines the significance of the AEON qubit. However, a key issue that is central to\nthe interpretation of the work is still not fully resolved, namely, the physical origin of the\nperformance advantage. The current version continues to emphasize the higher Clifford\nfidelity of AEON gates. However, the data show that the per-pulse error of 2-J operations\n(0.076%) is larger than that of 1-J operations (0.060%). This indicates that the fidelity\nimprovement arises primarily from reduced pulse depth rather than intrinsically improved\nnoise resilience. The manuscript should more clearly state this distinction and avoid\nimplying a fundamental superiority of AEON control unless supported by additional\nevidence. A brief comparison at fixed total gate time, or a concise filter-function or noise-\nspectral discussion, would be sufficient to clarify this point.", "reviewer_3": "I think the authors have sufficiently addressed my comments and I support publication of the manuscript."}, "author_response": "Resubmission of Broz et al., “Demonstration of an always-on exchange-only spin qubit,” NCOMMS-25-\n68445-T\nDear Editors,\nThank you for sending our manuscript out for a second round of review. Reviewers 1 and 3 now\ncompletely support publication in Nature Communications. We are pleased that Reviewer 2 carefully\nconsidered our response and appreciates our perspective, stating “I agree with this perspective, which\naddresses the point I was most concerned about and directly defines the significance of the AEON\nqubit.” Reviewer 2 posed a final technical question which we address in the response below.\nBest regards,\nJason Petta\nReviewer comments are in blue and our responses are in black.\nReviewer 2:\nThe revised manuscript has clarified the distinction between AEON and LD qubits, emphasizing that their\npresent fidelities cannot be compared in a simplistic manner and that additional factors such as\ncontrollability and scalability must also be taken into account. I agree with this perspective, which\naddresses the point I was most concerned about and directly defines the significance of the AEON\nqubit. However, a key issue that is central to the interpretation of the work is still not fully resolved, namely,\nthe physical origin of the performance advantage. The current version continues to emphasize the\nhigher Clifford fidelity of AEON gates. However, the data show that the per-pulse error of 2-J operations\n(0.076%) is larger than that of 1-J operations (0.060%). This indicates that the fidelity improvement\narises primarily from reduced pulse depth rather than intrinsically improved noise resilience. The\nmanuscript should more clearly state this distinction and avoid implying a fundamental superiority of\nAEON control unless supported by additional evidence. A brief comparison at fixed total gate time, or a\nconcise filter-function or noise-spectral discussion, would be sufficient to clarify this point.\nResponse:\nWe appreciate the Reviewer’s consideration of our stance that it is not practical to compare the\nperformance of different quantum computing platforms using a single metric such as gate fidelity.\nOther factors, such as scalability, gate speed, and connectivity are just as important in the overall\nperformance of a quantum processor. We are pleased that the Reviewer’s most serious concern has\nbeen addressed satisfactorily.\nThe Reviewer has also commented on the general interpretation of our work. The main contribution of\nthe manuscript is the first demonstration of an AEON qubit. Figure 2 shows that we can control two\nexchange couplings simultaneously. Figure 3(a) further shows that fine tuning to a double sweet spot is\npossible. One important unanticipated result relates to the data sets presented in Figs. 3(a,b). We\nexpected N to be smaller for 2-J control as compared with 1-J control simply because 2-J control\nosc\nwould be susceptible to charge noise on two exchange couplings. Instead, we find that N for 2-J\nosc\ncontrol is significantly larger than for 1-J. This result has been reproduced across several triangle devices\nand is believed to be general. We objectively state in the manuscript that “More detailed device\nmodeling may be helpful for understanding the coherence enhancement during 2-J operation.” In terms\nof the interpretation of blind randomized benchmarking (BRB) performance, we reproduce directly from\nthe main text “Although 2-J BRB outperforms 1-J BRB, this advantage primarily arises from its shorter\ngate depths: a 2-J single-qubit Clifford gate requires an average of 1.9 exchange pulses, compared to 2.7\npulses for a 1-J Clifford gate.” We believe this statement is clear as is. We anticipate that our\nexperimental results will spur on the development of sophisticated noise models. We also believe that\nsuch work is best performed by theoretical device modeling groups."}]

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