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Resonant two-qubit gates for fermionic simulations with spin qubits

T0 review · 2 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A single exchange pulse superposing baseband and resonant drives implements the full fSim gate family in spin qubits; the authors validate it with an iSWAP at 93.8(5)% fidelity.

desk verdict Solid demonstration of a resonant fSim-type gate in germanium hole spins, with a genuinely useful calibration protocol; the 93.8% fidelity should be treated as provisional because the IRB reference group is not a two-qubit 2-design. read the letter →

arxiv 2507.13781 v1 pith:PYLZJFK4 submitted 2025-07-18 cond-mat.mes-hall quant-ph

Konstantinos Tsoukalas , Alexei Orekhov , Bence Hetényi , Uwe von Lüpke , Jeth Arunseangroj , Inga Seidler , Lisa Sommer , Eoin G. Kelly
show 10 more authors
Leonardo Massai Michele Aldeghi Marta Pita-Vidal Stephen W. Bedell Stephan Paredes Felix J. Schupp Matthias Mergenthaler Gian Salis Andreas Fuhrer Patrick Harvey-Collard
This is my paper
classification cond-mat.mes-hallquant-ph
keywords spinqubitsfSimgatesiSWAPresonantexchangegermaniumholespinsinterleavedrandomizedbenchmarkingquantumprocesstomographyfermionicsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the full fermionic-simulation gate family, fSim, can be implemented in gate-defined spin qubits with a single exchange pulse that superposes a baseband barrier excursion and a resonant drive, avoiding the large exchange energies and separate phase-calibration steps that made earlier resonant SWAP schemes impractical. The authors develop calibration routines, using off-resonant free-induction-decay measurements for the conditional phase and partial tomographies for single-qubit phase corrections, and use them to realize a resonant iSWAP gate between two hole spins in germanium, reporting 93.8(5)% fidelity by interleaved randomized benchmarking. Quantum process tomography identifies qubit decoherence as the dominant error source and confirms the phase calibration. If correct, the result gives spin processors a native, tunable two-qubit gate directly useful for linear-depth fermionic simulation, not just the CZ and SWAP endpoints previously demonstrated.

What carries the argument

The central object is the fSim gate $fSim(\gamma,\zeta) = iSWAP^{-2\gamma/\pi} CZ^{\zeta/\pi}$, built from a single voltage pulse on the inter-dot barrier: a smooth-edged Tukey-windowed baseband excursion with a superimposed ac drive at the swap resonance $f_{SWAP} = \sqrt{\Delta E_z^2 + J^2}/h$. The ac part drives coherent $|\uparrow\downarrow\rangle \leftrightarrow |\downarrow\uparrow\rangle$ oscillations that set $\gamma$, while the time-integrated exchange $\zeta = \int J_{dc}(t)\,dt/\hbar + \bar{J}_{ac}t_{ac}/\hbar$ accumulates the conditional phase. The load-bearing mechanism is the drive phase, which absorbs ramp-induced and residual phases so they can be corrected with virtual Z rotations; this is what removes the need for a separate CZ calibration pulse and keeps the gate short.

What would settle it

Repeat the interleaved benchmarking of the same calibrated diabatic iSWAP gate using a full two-qubit Clifford reference group instead of the single-qubit-Clifford set described in App. F.2; if the extracted fidelity moves outside 93.8(5)% by more than the stated uncertainty, the reported fidelity is not a rigorous estimate of the gate.

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Extended reading notes

Core claim

The central claim is that simultaneous resonant and baseband exchange pulses on a single barrier gate produce the fSim interaction in one pulse, with the swap parameter set by the resonant drive duration and amplitude ($\gamma = j_{12}t_{ac}/4\hbar$) and the conditional phase set by the time-integrated exchange from both dc and ac components. After virtual-Z corrections of the single-qubit phases and a drive-phase update, the realized unitary is $fSim(\gamma,\zeta) = iSWAP^{-2\gamma/\pi} CZ^{\zeta/\pi}$. On a germanium double quantum dot holding two hole spins, the authors calibrate the iSWAP point $fSim(-\pi/2,2\pi)$ and measure 93.8(5)% fidelity for the diabatic gate (5 ns ramp, 343 ns total) and 88.9(7)% for the adiabatic gate (100 ns ramp, 485 ns total) using interleaved randomized benchmarking. Quantum process tomography of the diabatic gate gives a gate fidelity of 86.3% after removing state-preparation-and-measurement errors, identifies qubit decoherence as the dominant error source, and places calibration errors at roughly the level of the ~3% single-qubit gate error floor.

Load-bearing premise

The 93.8(5)% fidelity rests on the assumption that a reference set of only single-qubit Clifford gates randomizes the iSWAP error channel well enough for the standard interleaved-benchmarking formula to give an unbiased fidelity estimate.

Editorial extensions

If this is right

  • Spin qubits gain a native, tunable fSim gate without pulsing the exchange far above the Zeeman difference, avoiding the charge-noise penalty of baseband SWAP approaches.
  • The iSWAP point is reached with a single calibrated pulse: 93.8(5)% fidelity with a fast 5 ns ramp and 88.9(7)% with a 100 ns ramp, the shorter gate performing better because dephasing is the dominant error.
  • The off-resonant Ramsey calibration route generalizes to arbitrary fSim($\gamma,\zeta$) parameters, so the same pulse scheme can be tuned to other points of the gate family rather than only iSWAP.
  • Because the drive phase can be updated when virtual Z gates are applied, the gate is compatible with virtual Z rotations and with pulse-shaping and synchronization methods for further error reduction.
  • Process tomography indicates that decoherence, not calibration, limits current performance; longer coherence times and larger Zeeman differences should directly improve fidelity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A benchmark using the full two-qubit Clifford group rather than the single-qubit-Clifford reference set of App. F.2 would test whether the 93.8(5)% number is unbiased; if the extracted fidelity shifts beyond the quoted uncertainty, the reported value is a conditional estimate, not a rigorous gate fidelity.
  • The same drive-phase freedom should make continuous Givens rotations available to spin qubits by sweeping $\gamma$ instead of stopping at the iSWAP point; the paper notes compatibility with this direction but does not demonstrate the rotations.
  • A quantitative dephasing model using the measured coherence times (1.8 and 2.6 $\mu$s) and gate durations (343 and 485 ns) would yield a predicted error floor; comparing it with the measured 93.8% would show how much headroom the pulse scheme still has.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper reports a method for realizing tunable fermionic simulation (fSim) two-qubit gates in semiconductor spin qubits by applying a single barrier pulse that combines a baseband exchange pulse with a resonant exchange drive. The authors derive the resulting unitary in the rotating-wave approximation, calibrate the swap angle γ and conditional phase ζ using Ramsey sequences and partial tomography, and demonstrate a resonant iSWAP gate between two hole spins in germanium. The headline result is a 93.8(5)% fidelity extracted from interleaved randomized benchmarking, with quantum process tomography used to attribute the remaining error mainly to decoherence. The manuscript also provides a detailed theoretical appendix covering the unitary evolution, single-qubit phase corrections, and tomographic analysis.

Significance. If the central claims hold, this is a useful contribution: it provides a way to implement the full fSim(γ,ζ) family natively in spin qubits with a single pulse, avoiding the large exchange values used in diabatic SWAP gates and remaining compatible with virtual Z rotations. The paper's strengths include the explicit analytic derivation of the gate unitary in Appendix C, the independent support from swap chevrons, conditional Ramsey measurements, and partial tomography, and the transparent discussion of SPAM handling in the QPT analysis. However, the headline fidelity claim is load-bearing and rests on a benchmarking protocol whose validity for two-qubit gates is not established.

major comments (2)
  1. [Sec. V and App. F.2] The interleaved randomized benchmarking fidelity of 93.8(5)% is not a rigorous estimate of the iSWAP gate fidelity. The reference group used in App. F.2 is the set of two-qubit Clifford gates composed only of single-qubit gates, i.e., the local Clifford group C1 × C1. This group is a 2-design on each qubit separately, but it is not a unitary 2-design on the two-qubit Hilbert space, and it does not twirl two-qubit-correlated error channels, including the error channel of the interleaved iSWAP gate, into a global depolarizing channel. The formula F = 1 − (d−1)/d (1 − α_interleaved/α_reference) cited from Ref. [40] is derived under the full-Clifford twirl assumption. Consequently, α_reference and α_interleaved need not be single depolarizing parameters, and their ratio is not guaranteed to equal the average gate fidelity. The authors should either benchmark with a full two-qubit Clifford reference group or clearly restrict the claim to a protocol-dependent estimate and temper the abstract accordingly.
  2. [Sec. V and Fig. 4] The SPAM-corrected quantum process tomography fidelity for the same diabatic iSWAP gate is 86.3%, about 7.5 percentage points below the interleaved RB value. The manuscript attributes this discrepancy to SPAM assumptions and neglected single-qubit errors, but that explanation is not quantitatively anchored: the quoted SPAM-corrected QPT number is stated without a detailed derivation in the main text, and the reader cannot see how the SPAM channel model converts the raw tomography into this value. This gap is consistent with an upward bias in the local-Clifford IRB estimate, so the discrepancy should be analyzed explicitly, for example by applying the same SPAM correction to a full-Clifford RB run or by reporting both numbers with a clear statement of which one is claimed to be the gate fidelity.
minor comments (3)
  1. [Sec. IV] The sentence 'calibration errors arising form the diabatic activation of J' should read 'arising from the diabatic activation of J'.
  2. [Sec. V and App. E, Table I] The SPAM-corrected QPT fidelity for the diabatic gate is quoted as 86.3% in the main text, but Table I reports values up to 89.5% (standard method, Λ−p) and 86.0% (ML method, Λ−m). The definition of the number quoted in the text should be reconciled with the table entries.
  3. [App. F.2] The description of the interleaved RB recovery gate is somewhat terse: it states that the recovery gate 'may include multiple iSWAP gates' after transpilation, but the number of interleaved iSWAP gates per sequence and its effect on the decay curve offset are not quantified. A sentence explaining how the alpha extraction accounts for this offset would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the fSim derivation is self-contained (App. C), the iSWAP fidelity is an experimental benchmark rather than a fitted input, and the IRB/QPT concerns are validity limitations, not circular reductions.

full rationale

The central derivation chain is not circular. Appendix C derives the fSim unitary from the time-dependent exchange Hamiltonian in the rotating-wave approximation, giving gamma = j12*tac/(4hbar) in Eq. (C22) and zeta = ∫Jdc(hbar^-1)dt + Jbar_ac*hbar^-1*tac in Eq. (C23). These relations are not assumed from the target iSWAP gate; they are parameterizations of the physical evolution. The subsequent calibration independently sets gamma via resonant swap chevrons and zeta via off-resonant Ramsey exchange extraction and partial tomography, and the fSim unitary is then checked with process tomography and randomized benchmarking. The headline 93.8(5)% iSWAP fidelity is a measured outcome of interleaved RB, not a quantity made equal to an input by construction. The skeptical concern that App. F.2 uses a two-qubit Clifford group composed only of single-qubit gates as the IRB reference group is a legitimate statistical-validity issue: the local Clifford group is not a unitary 2-design on the four-dimensional Hilbert space, so the depolarizing-noise formula cited from Ref. [40] may not rigorously apply. But this is not circularity; the fidelity estimate is not derived from the calibration parameters by definition. Similarly, the SPAM correction in App. E assumes a commuting SPAM channel structure that the authors explicitly acknowledge is not generally valid, and the QPT fidelity (86.3%) differs from the RB value; this is an acknowledged limitation of the tomographic model, not a self-referential reduction. No load-bearing argument rests on a self-citation: the cited prior work [32] is used for device details, and the theory of resonant exchange driving is standard or externally supported. Therefore no circular step is exhibited, and the paper's core claim stands as an experimental demonstration with independent calibration and characterization.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard exchange-spin Hamiltonian, the rotating-wave approximation, and the IRB/QPT noise models. No new physical entity is introduced. The main loads are calibration measurements such as J̄ac, j12, Δ1, and Δ2 that set the gate parameters, plus the unvalidated use of a local-Clifford reference group for interleaved randomized benchmarking.

free parameters (5)
  • J̄ac, average exchange induced by the ac drive = calibrated per gate, e.g. at vBac=5.3 mV
    Enters the conditional phase in Eq. (1) and Eq. (C23); measured off-resonantly at fac=30 MHz and assumed equal to the on-resonant average exchange.
  • j12, exchange Rabi coupling = set by vBac=4.3 mV (diabatic) or 5.3 mV (adiabatic)
    Defines γ through Eq. (C22) and is extracted from the swap oscillation FFT in Fig. 2(b).
  • Δ1, Δ2, qubit frequency shifts during the pulse = 6.23 MHz and -1.69 MHz (diabatic, Table III)
    Used to compute the single-qubit phase corrections θ1 and θ2; extracted from rf spectroscopy in Fig. 1(c).
  • tdc, tac, pulse durations = 333/290 ns (diabatic), 285/253 ns (adiabatic)
    Tuned to realize γ=π/2 and ζ=2π; these are the central control parameters of the demonstrated iSWAP gate.
  • θ1, θ2, single-qubit phase corrections = 0.90 rad and 2.68 rad mod 2π (adiabatic, Table III)
    Calibrated by conditional Ramsey and partial tomography; enter the post-pulse correction U'post.
assumptions (5)
  • domain assumption Time-dependent Hamiltonian H_I/H_II of Eq. (C3)/(C11): exchange term (J/4)Σ σi⊗σi plus independent qubit frequency shifts Δ1, Δ2.
    Standard isotropic Heisenberg exchange model for exchange-coupled spin qubits. If exchange anisotropy or state-dependent g-factor corrections are significant, the extracted fSim parameters would misdescribe the gate.
  • domain assumption Rotating-wave approximation in interval II, leading to Eq. (C12).
    Counter-rotating terms are neglected; the paper notes in Section VI that RWA breaking can become limiting at higher drive strengths.
  • domain assumption Adiabatic treatment of the ramps in intervals I and III, or neglect of diabatic calibration errors for tramp=5 ns.
    Eq. (C4) and Eqs. (C7)-(C9) assume either Jdc much smaller than the qubit frequency difference or adiabatic instantaneous eigenstates; Section IV states that calibration errors from diabatic activation are small and thus neglected.
  • domain assumption SPAM channel commutes with single-qubit Clifford gates and can be represented as a single CPTP channel, Eq. (E12).
    Required for the QPT SPAM correction; the paper itself states this is not generally valid and points to Ref [54] for a more general treatment.
  • domain assumption The reference RB sequence built only from single-qubit Clifford gates provides a valid depolarizing parameter for the IRB formula.
    App. F.2 uses a local-Clifford reference with the full-Clifford IRB formula of Ref [40]; no validation or citation supports this substitution, and it is the weakest premise behind the headline fidelity.

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Cite this review

Pith. "Pith review of Resonant two-qubit gates for fermionic simulations with spin qubits." pith.science (2026). https://pith.science/paper/PYLZJFK4

@misc{pith2026250713781,
  author       = {Pith},
  title        = {Pith review of: Resonant two-qubit gates for fermionic simulations with spin qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PYLZJFK4}},
  note         = {Machine review of arXiv:2507.13781}
}
read the original abstract

In gate-defined semiconductor spin qubits, the highly tunable Heisenberg exchange interaction is leveraged to implement fermionic two-qubit gates such as CZ and SWAP. However, the broader family of fermionic simulation (fSim) gates remains unexplored, and has the potential to enhance the performance of near-term quantum simulation algorithms. Here, we demonstrate a method to implement the fSim gate set in spin qubits using a single pulse combining baseband and resonant exchange drives. This approach minimizes gate duration and drive amplitude, mitigating decoherence and crosstalk. We validate its effectiveness by realizing a resonant iSWAP gate between two hole spins in germanium, achieving a fidelity of 93.8(5)% extracted with interleaved randomized benchmarking. Quantum process tomography confirms accurate gate calibration and identifies qubit decoherence as the dominant error source. Our results establish a practical route toward a versatile and efficient two-qubit gate set for spin-based quantum processors.

Figures

Figures reproduced from arXiv: 2507.13781 by the authors.

Figure 1
Figure 1. Single qubit gates and exchange calibration. (a) A false-colored scanning electron micrograph of a six-QD device nominally identical to the one used in the experiments. Below, a schematic of the device cross section along the dashed black line with the blue and red spins indicating the position of the two hole spin qubits. (b) Randomized benchmarking of the single-qubit Clifford gates for each qubit, along with thei… view at source ↗
Figure 2
Figure 2. Resonant Exchange Oscillations. (a) Swap oscillations induced by superposing an oscillating signal, of frequency fac and of amplitude vBac = 4 mV, with a baseband barrier pulse of amplitude vBdc with ramp time tramp = 100 ns. (b) Fast Fourier transform (FFT) reveals the speed of the swap, driven at fac = fSWAP, for different drive amplitudes vBac. (c) Rabi drive of Q1 followed by a resonant exchange drive. (d) Popul… view at source ↗
Figure 3
Figure 3. Resonant iSWAP phase calibration. (a) Schematic of the pulse shape applied to vB12 (upper trace) to realize a resonant fSim gate. An ac drive of frequency fac is superimposed with a Tukey-shaped baseband pulse. The baseband pulse results in an exchange of Jdc (lower trace), while the induced exchange modulation results in an additional exchange component Jac arising from the non-linear dependence on vB12. The condit… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (a) i) Circuit diagram for the reference Clifford-based RB sequence (left), and the iSWAP interleaved sequence (right). ii) IRB results of the diabatic iSWAP. iii) Interleaved RB results for the adiabatic iSWAP gate. The probability scales are normalized by fitting sho…
Figure 5
Figure 5. Figure 5: The free induction decay obtained from Ramsey experiments for Q1 (left) and Q2 (right) at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Exchange oscillations between two neighboring spins (a) (i) Oscillations induced in the population of the |↑↓⟩ state as a function of the amplitude vBdc of a baseband square pulse applied on the barrier. (ii) Fast Fourier transform of (i) revealing the oscillation spee…
Figure 7
Figure 7. Figure 7: Parameters of the time dependent Hamiltonian when the baseband pulse is applied. For the driven part of the exchange [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Pauli transfer matrices of the full (physical) channel obtained from standard process tomography; the channel where [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Simulated examples of partial tomographies used for iSWAP gate phase tuning. (a) Tomography used to double-check [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

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Forward citations

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    Tomography calibration After extracting the approximate gate parameterstac and tdc and single-qubit phasesθ1 and θ2 with the Ramsey sequences, these parameters are further fine-tuned using tailored tomographic sequences. Firstly,tdc is tuned by preparing the states{|−−⟩ , |−+⟩...

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    Single-shot measurement (Fig. 3d, 4b and 8). Here all shots are collected. A threshold is determined by taking the average for outcomes of|↓↓⟩ and |↑↓⟩. This form of readout is used for all of the partial tomographies and full quantum process tomographies

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.